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definitions.units
#
# This file is the units database for use with GNU units, a units conversion
# program by Adrian Mariano adrianm@gnu.org
#
# June 2016 Version 2.14
#
# Copyright (C) 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2004, 2005, 2006
# 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016
# Free Software Foundation, Inc
#
# This program is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 51 Franklin Street, Fifth Floor,
# Boston, MA 02110-1301 USA
#
############################################################################
#
# Improvements and corrections are welcome.
#
# Fundamental constants in this file are the 2014 CODATA recommended values.
#
# Most units data was drawn from
# 1. NIST Special Publication 811, Guide for the
# Use of the International System of Units (SI).
# Barry N. Taylor. 1995
# 2. CRC Handbook of Chemistry and Physics 70th edition
# 3. Oxford English Dictionary
# 4. Websters New Universal Unabridged Dictionary
# 5. Units of Measure by Stephen Dresner
# 6. A Dictionary of English Weights and Measures by Ronald Zupko
# 7. British Weights and Measures by Ronald Zupko
# 8. Realm of Measure by Isaac Asimov
# 9. United States standards of weights and measures, their
# creation and creators by Arthur H. Frazier.
# 10. French weights and measures before the Revolution: a
# dictionary of provincial and local units by Ronald Zupko
# 11. Weights and Measures: their ancient origins and their
# development in Great Britain up to AD 1855 by FG Skinner
# 12. The World of Measurements by H. Arthur Klein
# 13. For Good Measure by William Johnstone
# 14. NTC's Encyclopedia of International Weights and Measures
# by William Johnstone
# 15. Sizes by John Lord
# 16. Sizesaurus by Stephen Strauss
# 17. CODATA Recommended Values of Physical Constants available at
# http://physics.nist.gov/cuu/Constants/index.html
# 18. How Many? A Dictionary of Units of Measurement. Available at
# http://www.unc.edu/~rowlett/units/index.html
# 19. Numericana. http://www.numericana.com
# 20. UK history of measurement
# http://www.ukmetrication.com/history.htm
# 21. NIST Handbook 44, Specifications, Tolerances, and
# Other Technical Requirements for Weighing and Measuring
# Devices. 2011
# 22. NIST Special Publication 447, Weights and Measures Standards
# of the the United States: a brief history. Lewis V. Judson.
# 1963; rev. 1976
# 23 CRC Handbook of Chemistry and Physics, 96th edition
#
# Thanks to Jeff Conrad for assistance in ferreting out unit definitions.
#
###########################################################################
#
# If units you use are missing or defined incorrectly, please contact me.
# If your country's local units are missing and you are willing to supply
# them, please send me a list.
#
# I added shoe size information but I'm not convinced that it's correct.
# If you know anything about shoe sizes please contact me.
#
###########################################################################
###########################################################################
#
# Brief Philosophy of this file
#
# Most unit definitions are made in terms of integers or simple fractions of
# other definitions. The typical exceptions are when converting between two
# different unit systems, or the values of measured physical constants. In
# this file definitions are given in the most natural and revealing way in
# terms of integer factors.
#
# If you make changes be sure to run 'units --check' to check your work.
#
# The file is USA-centric, but there is some modest effort to support other
# countries. This file is now coded in UTF-8. To support environments where
# UTF-8 is not available, definitions that require this character set are
# wrapped in !utf8 directives.
#
# When a unit name is used in different countries with the different meanings
# the system should be as follows:
#
# Suppose countries ABC and XYZ both use the "foo". Then globally define
#
# ABCfoo <some value>
# XYZfoo <different value>
#
# Then, using the !locale directive, define the "foo" appropriately for each of
# the two countries with a definition like
#
# !locale ABC
# foo ABCfoo
# !endlocale
#
###########################################################################
!locale en_US
! set UNITS_ENGLISH US
!endlocale
!locale en_GB
! set UNITS_ENGLISH GB
!endlocale
!set UNITS_ENGLISH US # Default setting for English units
###########################################################################
# #
# Primitive units. Any unit defined to contain a '!' character is a #
# primitive unit which will not be reduced any further. All units should #
# reduce to primitive units. #
# #
###########################################################################
#
# SI units
#
kg ! # Mass of the international prototype
kilogram kg
s ! # Duration of 9192631770 periods of the radiation
second s # corresponding to the transition between the two hyperfine
# levels of the ground state of the cesium-133 atom
m ! # Length of the path traveled by light in a vacuum
meter m # during 1|299792458 seconds. Originally meant to be
# 1e-7 of the length along a meridian from the equator
# to a pole.
A ! # The current which produces a force of 2e-7 N/m between two
ampere A # infinitely long wires that are 1 meter apart
amp ampere
cd ! # Luminous intensity in a given direction of a source which
candela cd # emits monochromatic radiation at 540e12 Hz with radiant
# intensity 1|683 W/steradian. (This differs from radiant
# intensity (W/sr) in that it is adjusted for human
# perceptual dependence on wavelength. The frequency of
# 540e12 Hz (yellow) is where human perception is most
# efficient.)
mol ! # The amount of substance of a system which contains as many
mole mol # elementary entities as there are atoms in 0.012 kg of
# carbon 12. The elementary entities must be specified and
# may be atoms, molecules, ions, electrons, or other
# particles or groups of particles. It is understood that
# unbound atoms of carbon 12, at rest and in the ground
# state, are referred to.
K ! # 1|273.16 of the thermodynamic temperature of the triple
kelvin K # point of water
#
# The radian and steradian are defined as dimensionless primitive units.
# The radian is equal to m/m and the steradian to m^2/m^2 so these units are
# dimensionless. Retaining them as named units is useful because it allows
# clarity in expressions and makes the meaning of unit definitions more clear.
# These units will reduce to 1 in conversions but not for sums of units or for
# arguments to functions.
#
radian !dimensionless # The angle subtended at the center of a circle by
# an arc equal in length to the radius of the
# circle
sr !dimensionless # Solid angle which cuts off an area of the surface
steradian sr # of the sphere equal to that of a square with
# sides of length equal to the radius of the
# sphere
#
# Some primitive non-SI units
#
US$ ! # The US dollar is chosen arbitrarily to be the primitive
# unit of money.
bit ! # Basic unit of information (entropy). The entropy in bits
# of a random variable over a finite alphabet is defined
# to be the sum of -p(i)*log2(p(i)) over the alphabet where
# p(i) is the probability that the random variable takes
# on the value i.
###########################################################################
# #
# Prefixes (longer names must come first) #
# #
###########################################################################
yotta- 1e24 # Greek or Latin octo, "eight"
zetta- 1e21 # Latin septem, "seven"
exa- 1e18 # Greek hex, "six"
peta- 1e15 # Greek pente, "five"
tera- 1e12 # Greek teras, "monster"
giga- 1e9 # Greek gigas, "giant"
mega- 1e6 # Greek megas, "large"
myria- 1e4 # Not an official SI prefix
kilo- 1e3 # Greek chilioi, "thousand"
hecto- 1e2 # Greek hekaton, "hundred"
deca- 1e1 # Greek deka, "ten"
deka- deca
deci- 1e-1 # Latin decimus, "tenth"
centi- 1e-2 # Latin centum, "hundred"
milli- 1e-3 # Latin mille, "thousand"
micro- 1e-6 # Latin micro or Greek mikros, "small"
nano- 1e-9 # Latin nanus or Greek nanos, "dwarf"
pico- 1e-12 # Spanish pico, "a bit"
femto- 1e-15 # Danish-Norwegian femten, "fifteen"
atto- 1e-18 # Danish-Norwegian atten, "eighteen"
zepto- 1e-21 # Latin septem, "seven"
yocto- 1e-24 # Greek or Latin octo, "eight"
quarter- 1|4
semi- 0.5
demi- 0.5
hemi- 0.5
half- 0.5
double- 2
triple- 3
treble- 3
kibi- 2^10 # In response to the convention of illegally
mebi- 2^20 # and confusingly using metric prefixes for
gibi- 2^30 # powers of two, the International
tebi- 2^40 # Electrotechnical Commission aproved these
pebi- 2^50 # binary prefixes for use in 1998. If you
exbi- 2^60 # want to refer to "megabytes" using the
Ki- kibi # binary definition, use these prefixes.
Mi- mebi
Gi- gibi
Ti- tebi
Pi- pebi
Ei- exbi
Y- yotta
Z- zetta
E- exa
P- peta
T- tera
G- giga
M- mega
k- kilo
h- hecto
da- deka
d- deci
c- centi
m- milli
u- micro # it should be a mu but u is easy to type
n- nano
p- pico
f- femto
a- atto
z- zepto
y- yocto
#
# Names of some numbers
#
one 1
two 2
double 2
couple 2
three 3
triple 3
four 4
quadruple 4
five 5
quintuple 5
six 6
seven 7
eight 8
nine 9
ten 10
eleven 11
twelve 12
thirteen 13
fourteen 14
fifteen 15
sixteen 16
seventeen 17
eighteen 18
nineteen 19
twenty 20
thirty 30
forty 40
fifty 50
sixty 60
seventy 70
eighty 80
ninety 90
hundred 100
thousand 1000
million 1e6
# These number terms were described by N. Chuquet and De la Roche in the 16th
# century as being successive powers of a million. These definitions are still
# used in most European countries. The current US definitions for these
# numbers arose in the 17th century and don't make nearly as much sense. These
# numbers are listed in the CRC Concise Encyclopedia of Mathematics by Eric
# W. Weisstein.
shortbillion 1e9
shorttrillion 1e12
shortquadrillion 1e15
shortquintillion 1e18
shortsextillion 1e21
shortseptillion 1e24
shortoctillion 1e27
shortnonillion 1e30
shortnoventillion shortnonillion
shortdecillion 1e33
shortundecillion 1e36
shortduodecillion 1e39
shorttredecillion 1e42
shortquattuordecillion 1e45
shortquindecillion 1e48
shortsexdecillion 1e51
shortseptendecillion 1e54
shortoctodecillion 1e57
shortnovemdecillion 1e60
shortvigintillion 1e63
centillion 1e303
googol 1e100
longbillion million^2
longtrillion million^3
longquadrillion million^4
longquintillion million^5
longsextillion million^6
longseptillion million^7
longoctillion million^8
longnonillion million^9
longnoventillion longnonillion
longdecillion million^10
longundecillion million^11
longduodecillion million^12
longtredecillion million^13
longquattuordecillion million^14
longquindecillion million^15
longsexdecillion million^16
longseptdecillion million^17
longoctodecillion million^18
longnovemdecillion million^19
longvigintillion million^20
# These numbers fill the gaps left by the long system above.
milliard 1000 million
billiard 1000 million^2
trilliard 1000 million^3
quadrilliard 1000 million^4
quintilliard 1000 million^5
sextilliard 1000 million^6
septilliard 1000 million^7
octilliard 1000 million^8
nonilliard 1000 million^9
noventilliard nonilliard
decilliard 1000 million^10
# For consistency
longmilliard milliard
longbilliard billiard
longtrilliard trilliard
longquadrilliard quadrilliard
longquintilliard quintilliard
longsextilliard sextilliard
longseptilliard septilliard
longoctilliard octilliard
longnonilliard nonilliard
longnoventilliard noventilliard
longdecilliard decilliard
# The long centillion would be 1e600. The googolplex is another
# familiar large number equal to 10^googol. These numbers give overflows.
#
# The short system prevails in English speaking countries
#
billion shortbillion
trillion shorttrillion
quadrillion shortquadrillion
quintillion shortquintillion
sextillion shortsextillion
septillion shortseptillion
octillion shortoctillion
nonillion shortnonillion
noventillion shortnoventillion
decillion shortdecillion
undecillion shortundecillion
duodecillion shortduodecillion
tredecillion shorttredecillion
quattuordecillion shortquattuordecillion
quindecillion shortquindecillion
sexdecillion shortsexdecillion
septendecillion shortseptendecillion
octodecillion shortoctodecillion
novemdecillion shortnovemdecillion
vigintillion shortvigintillion
#
# Numbers used in India
#
lakh 1e5
crore 1e7
arab 1e9
kharab 1e11
neel 1e13
padm 1e15
shankh 1e17
#############################################################################
# #
# Derived units which can be reduced to the primitive units #
# #
#############################################################################
#
# Named SI derived units (officially accepted)
#
newton kg m / s^2 # force
N newton
pascal N/m^2 # pressure or stress
Pa pascal
joule N m # energy
J joule
watt J/s # power
W watt
coulomb A s # charge
C coulomb
volt W/A # potential difference
V volt
ohm V/A # electrical resistance
siemens A/V # electrical conductance
S siemens
farad C/V # capacitance
F farad
weber V s # magnetic flux
Wb weber
henry Wb/A # inductance
H henry
tesla Wb/m^2 # magnetic flux density
T tesla
hertz /s # frequency
Hz hertz
#
# Dimensions. These are here to help with dimensional analysis and
# because they will appear in the list produced by hitting '?' at the
# "You want:" prompt to tell the user the dimension of the unit.
#
LENGTH meter
AREA LENGTH^2
VOLUME LENGTH^3
MASS kilogram
CURRENT ampere
AMOUNT mole
ANGLE radian
SOLID_ANGLE steradian
MONEY US$
FORCE newton
PRESSURE FORCE / AREA
STRESS FORCE / AREA
CHARGE coulomb
CAPACITANCE farad
RESISTANCE ohm
CONDUCTANCE siemens
INDUCTANCE henry
FREQUENCY hertz
VELOCITY LENGTH / TIME
ACCELERATION VELOCITY / TIME
DENSITY MASS / VOLUME
LINEAR_DENSITY MASS / LENGTH
VISCOSITY FORCE TIME / AREA
KINEMATIC_VISCOSITY VISCOSITY / DENSITY
#
# units derived easily from SI units
#
gram millikg
gm gram
g gram
tonne 1000 kg
t tonne
metricton tonne
sthene tonne m / s^2
funal sthene
pieze sthene / m^2
quintal 100 kg
bar 1e5 Pa # About 1 atm
b bar
vac millibar
micron micrometer # One millionth of a meter
bicron picometer # One brbillionth of a meter
cc cm^3
are 100 m^2
a are
liter 1000 cc # The liter was defined in 1901 as the
oldliter 1.000028 dm^3 # space occupied by 1 kg of pure water at
L liter # the temperature of its maximum density
l liter # under a pressure of 1 atm. This was
# supposed to be 1000 cubic cm, but it
# was discovered that the original
# measurement was off. In 1964, the
# liter was redefined to be exactly 1000
# cubic centimeters.
mho siemens # Inverse of ohm, hence ohm spelled backward
galvat ampere # Named after Luigi Galvani
angstrom 1e-10 m # Convenient for describing molecular sizes
xunit xunit_cu # Used for measuring x-ray wavelengths.
siegbahn xunit # Originally defined to be 1|3029.45 of
xunit_cu 1.00207697e-13 m # the spacing of calcite planes at 18
xunit_mo 1.00209952e-13 m # degC. It was intended to be exactly
# 1e-13 m, but was later found to be
# slightly off. Current usage is with
# reference to common x-ray lines, either
# the K-alpha 1 line of copper or the
# same line of molybdenum.
angstromstar 1.00001495 angstrom # Defined by JA Bearden in 1965
fermi 1e-15 m # Convenient for describing nuclear sizes
# Nuclear radius is from 1 to 10 fermis
barn 1e-28 m^2 # Used to measure cross section for
# particle physics collision, said to
# have originated in the phrase "big as
# a barn".
shed 1e-24 barn # Defined to be a smaller companion to the
# barn, but it's too small to be of
# much use.
brewster micron^2/N # measures stress-optical coef
diopter /m # measures reciprocal of lens focal length
fresnel 1e12 Hz # occasionally used in spectroscopy
shake 1e-8 sec
svedberg 1e-13 s # Used for measuring the sedimentation
# coefficient for centrifuging.
gamma microgram # Also used for 1e-9 tesla
lambda microliter
spat 1e12 m # Rarely used for astronomical measurements
preece 1e13 ohm m # resistivity
planck J s # action of one joule over one second
sturgeon /henry # magnetic reluctance
daraf 1/farad # elastance (farad spelled backwards)
leo 10 m/s^2
poiseuille N s / m^2 # viscosity
mayer J/g K # specific heat
mired / microK # reciprocal color temperature. The name
# abbreviates micro reciprocal degree.
crocodile megavolt # used informally in UK physics labs
metricounce 25 g
mounce metricounce
finsenunit 1e5 W/m^2 # Measures intensity of ultraviolet light
# with wavelength 296.7 nm.
fluxunit 1e-26 W/m^2 Hz # Used in radio astronomy to measure
# the energy incident on the receiving
# body across a specified frequency
# bandwidth. [12]
jansky fluxunit # K. G. Jansky identified radio waves coming
Jy jansky # from outer space in 1931.
flick W / cm^2 sr micrometer # Spectral radiance or irradiance
pfu / cm^2 sr s # particle flux unit -- Used to measure
# rate at which particles are received by
# a spacecraft as particles per solid
# angle per detector area per second. [18]
pyron cal_IT / cm^2 min # Measures heat flow from solar radiation,
# from Greek work "pyr" for fire.
katal mol/sec # Measure of the amount of a catalyst. One
kat katal # katal of catalyst enables the reaction
# to consume or produce on mol/sec.
solarluminosity 384.6e24 W # A common yardstick for comparing the
# output of different stars.
# http://nssdc.gsfc.nasa.gov/planetary/factsheet/sunfact.html
#
# time
#
sec s
minute 60 s
min minute
hour 60 min
hr hour
day 24 hr
d day
da day
week 7 day
wk week
sennight 7 day
fortnight 14 day
blink 1e-5 day # Actual human blink takes 1|3 second
ce 1e-2 day
cron 1e6 years
watch 4 hours # time a sentry stands watch or a ship's
# crew is on duty.
bell 1|8 watch # Bell would be sounded every 30 minutes.
# French Revolutionary Time or Decimal Time. It was Proposed during
# the French Revolution. A few clocks were made, but it never caught
# on. In 1998 Swatch defined a time measurement called ".beat" and
# sold some watches that displayed time in this unit.
decimalhour 1|10 day
decimalminute 1|100 decimalhour
decimalsecond 1|100 decimalminute
beat decimalminute # Swatch Internet Time
#
# angular measure
#
circle 2 pi radian
degree 1|360 circle
deg degree
arcdeg degree
arcmin 1|60 degree
arcminute arcmin
' arcmin
arcsec 1|60 arcmin
arcsecond arcsec
" arcsec
'' "
rightangle 90 degrees
quadrant 1|4 circle
quintant 1|5 circle
sextant 1|6 circle
sign 1|12 circle # Angular extent of one sign of the zodiac
turn circle
revolution turn
rev turn
pulsatance radian / sec
gon 1|100 rightangle # measure of grade
grade gon
centesimalminute 1|100 grade
centesimalsecond 1|100 centesimalminute
milangle 1|6400 circle # Official NIST definition.
# Another choice is 1e-3 radian.
pointangle 1|32 circle # Used for reporting compass readings
centrad 0.01 radian # Used for angular deviation of light
# through a prism.
mas milli arcsec # Used by astronomers
seclongitude circle (seconds/day) # Astronomers measure longitude
# (which they call right ascension) in
# time units by dividing the equator into
# 24 hours instead of 360 degrees.
#
# Some geometric formulas
#
circlearea(r) units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi)
spherevolume(r) units=[m;m^3] range=[0,) 4|3 pi r^3 ; \
cuberoot(spherevolume/4|3 pi)
spherevol() spherevolume
square(x) range=[0,) x^2 ; sqrt(square)
#
# Solid angle measure
#
sphere 4 pi sr
squaredegree 1|180^2 pi^2 sr
squareminute 1|60^2 squaredegree
squaresecond 1|60^2 squareminute
squarearcmin squareminute
squarearcsec squaresecond
sphericalrightangle 0.5 pi sr
octant 0.5 pi sr
#
# Concentration measures
#
percent 0.01
% percent
mill 0.001 # Originally established by Congress in 1791
# as a unit of money equal to 0.001 dollars,
# it has come to refer to 0.001 in general.
# Used by some towns to set their property
# tax rate, and written with a symbol similar
# to the % symbol but with two 0's in the
# denominator. [18]
proof 1|200 # Alcohol content measured by volume at
# 60 degrees Fahrenheit. This is a USA
# measure. In Europe proof=percent.
ppm 1e-6
partspermillion ppm
ppb 1e-9
partsperbillion ppb # USA billion
ppt 1e-12
partspertrillion ppt # USA trillion
karat 1|24 # measure of gold purity
caratgold karat
gammil mg/l
basispoint 0.01 % # Used in finance
fine 1|1000 # Measure of gold purity
# The pH scale is used to measure the concentration of hydronium (H3O+) ions in
# a solution. A neutral solution has a pH of 7 as a result of dissociated
# water molecules.
pH(x) units=[1;mol/liter] range=(0,) 10^(-x) mol/liter ; (-log(pH liters/mol))
#
# Temperature
#
# Two types of units are defined: units for converting temperature differences
# and functions for converting absolute temperatures. Conversions for
# differences start with "deg" and conversions for absolute temperature start
# with "temp".
#
TEMPERATURE kelvin
TEMPERATURE_DIFFERENCE kelvin
# In 1741 Anders Celsius introduced a temperature scale with water boiling at
# 0 degrees and freezing at 100 degrees at standard pressure. After his death
# the fixed points were reversed and the scale was called the centigrade
# scale. Due to the difficulty of accurately measuring the temperature of
# melting ice at standard pressure, the centigrade scale was replaced in 1954
# by the Celsius scale which is defined by subtracting 273.15 from the
# temperature in Kelvins. This definition differed slightly from the old
# centigrade definition, but the Kelvin scale depends on the triple point of
# water rather than a melting point, so it can be measured accurately.
tempC(x) units=[1;K] domain=[-273.15,) range=[0,) \
x K + stdtemp ; (tempC +(-stdtemp))/K
tempcelsius() tempC
degcelsius K
degC K
# Fahrenheit defined his temperature scale by setting 0 to the coldest
# temperature he could produce in his lab with a salt water solution and by
# setting 96 degrees to body heat. In Fahrenheit's words:
#
# Placing the thermometer in a mixture of sal ammoniac or sea
# salt, ice, and water a point on the scale will be found which
# is denoted as zero. A second point is obtained if the same
# mixture is used without salt. Denote this position as 30. A
# third point, designated as 96, is obtained if the thermometer
# is placed in the mouth so as to acquire the heat of a healthy
# man." (D. G. Fahrenheit, Phil. Trans. (London) 33, 78, 1724)
tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \
(x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32
tempfahrenheit() tempF
degfahrenheit 5|9 degC
degF 5|9 degC
degreesrankine degF # The Rankine scale has the
degrankine degreesrankine # Fahrenheit degree, but its zero
degreerankine degF # is at absolute zero.
degR degrankine
tempR degrankine
temprankine degrankine
tempreaumur(x) units=[1;K] domain=[-218.52,) range=[0,) \
x degreaumur+stdtemp ; (tempreaumur+(-stdtemp))/degreaumur
degreaumur 10|8 degC # The Reaumur scale was used in Europe and
# particularly in France. It is defined
# to be 0 at the freezing point of water
# and 80 at the boiling point. Reaumur
# apparently selected 80 because it is
# divisible by many numbers.
degK K # "Degrees Kelvin" is forbidden usage.
tempK K # For consistency
# Gas mark is implemented below but in a terribly ugly way. There is
# a simple formula, but it requires a conditional which is not
# presently supported.
#
# The formula to convert to degrees Fahrenheit is:
#
# 25 log2(gasmark) + k_f gasmark<=1
# 25 (gasmark-1) + k_f gasmark>=1
#
# k_f = 275
#
gasmark[degR] \
.0625 634.67 \
.125 659.67 \
.25 684.67 \
.5 709.67 \
1 734.67 \
2 759.67 \
3 784.67 \
4 809.67 \
5 834.67 \
6 859.67 \
7 884.67 \
8 909.67 \
9 934.67 \
10 959.67
# Units cannot handle wind chill or heat index because they are two variable
# functions, but they are included here for your edification. Clearly these
# equations are the result of a model fitting operation.
#
# wind chill index (WCI) a measurement of the combined cooling effect of low
# air temperature and wind on the human body. The index was first defined
# by the American Antarctic explorer Paul Siple in 1939. As currently used
# by U.S. meteorologists, the wind chill index is computed from the
# temperature T (in °F) and wind speed V (in mi/hr) using the formula:
# WCI = 0.0817(3.71 sqrt(V) + 5.81 - 0.25V)(T - 91.4) + 91.4.
# For very low wind speeds, below 4 mi/hr, the WCI is actually higher than
# the air temperature, but for higher wind speeds it is lower than the air
# temperature.
#
# heat index (HI or HX) a measure of the combined effect of heat and
# humidity on the human body. U.S. meteorologists compute the index
# from the temperature T (in °F) and the relative humidity H (as a
# value from 0 to 1).
# HI = -42.379 + 2.04901523 T + 1014.333127 H - 22.475541 TH
# - .00683783 T^2 - 548.1717 H^2 + 0.122874 T^2 H + 8.5282 T H^2
# - 0.0199 T^2 H^2.
#
# Physical constants
#
# Basic constants
pi 3.14159265358979323846
c 2.99792458e8 m/s # speed of light in vacuum (exact)
light c
mu0 4 pi 1e-7 H/m # permeability of vacuum (exact)
epsilon0 1/mu0 c^2 # permittivity of vacuum (exact)
energy c^2 # convert mass to energy
e 1.6021766208e-19 C # electron charge
h 4.135667662e-15 eV s # Planck constant
hbar h / 2 pi
spin hbar
G 6.67408e-11 N m^2 / kg^2 # Newtonian gravitational constant
# This is the NIST 2006 value.
# The relative uncertainty on this
# is 1e-4.
coulombconst 1/4 pi epsilon0 # listed as "k" sometimes
# Physico-chemical constants
atomicmassunit 1.660539040e-27 kg # atomic mass unit (defined to be
u atomicmassunit # 1|12 of the mass of carbon 12)
amu atomicmassunit
amu_chem 1.66026e-27 kg # 1|16 of the weighted average mass of
# the 3 naturally occuring neutral
# isotopes of oxygen
amu_phys 1.65981e-27 kg # 1|16 of the mass of a neutral
# oxygen 16 atom
dalton u # Maybe this should be amu_chem?
avogadro grams/amu mol # size of a mole
N_A avogadro
gasconstant k N_A # molar gas constant
R gasconstant
boltzmann 1.38064852e-23 J/K # Boltzmann constant
k boltzmann
kboltzmann boltzmann
molarvolume mol R stdtemp / atm # Volume occupied by one mole of an
# ideal gas at STP.
loschmidt avogadro mol / molarvolume # Molecules per cubic meter of an
# ideal gas at STP. Loschmidt did
# work similar to Avogadro.
stefanboltzmann pi^2 k^4 / 60 hbar^3 c^2 # The power per area radiated by a
sigma stefanboltzmann # blackbody at temperature T is
# given by sigma T^4.
wiendisplacement 2.8977729e-3 m K # Wien's Displacement Law gives the
# frequency at which the the Planck
# spectrum has maximum intensity.
# The relation is lambda T = b where
# lambda is wavelength, T is
# temperature and b is the Wien
# displacement. This relation is
# used to determine the temperature
# of stars.
K_J90 483597.9 GHz/V # Direct measurement of the volt is difficult. Until
K_J 483597.8525 GHz/V # recently, laboratories kept Weston cadmium cells as
# a reference, but they could drift. In 1987 the
# CGPM officially recommended the use of the
# Josephson effect as a laboratory representation of
# the volt. The Josephson effect occurs when two
# superconductors are separated by a thin insulating
# layer. A "supercurrent" flows across the insulator
# with a frequency that depends on the potential
# applied across the superconductors. This frequency
# can be very accurately measured. The Josephson
# constant K_J, which is equal to 2e/h, relates the
# measured frequency to the potential. Two values
# given, the conventional (exact) value from 1990 and
# the current CODATA measured value.
R_K90 25812.807 ohm # Measurement of the ohm also presents difficulties.
R_K 25812.8074555 ohm # The old approach involved maintaining resistances
# that were subject to drift. The new standard is
# based on the Hall effect. When a current carrying
# ribbon is placed in a magnetic field, a potential
# difference develops across the ribbon. The ratio
# of the potential difference to the current is
# called the Hall resistance. Klaus von Klitzing
# discovered in 1980 that the Hall resistance varies
# in discrete jumps when the magnetic field is very
# large and the temperature very low. This enables
# accurate realization of the resistance h/e^2 in the
# lab. Two values given, the conventional (exact)
# value from 1990 and the current CODATA measured
# value.
# Various conventional values
gravity 9.80665 m/s^2 # std acceleration of gravity (exact)
force gravity # use to turn masses into forces
atm 101325 Pa # Standard atmospheric pressure
atmosphere atm
Hg 13.5951 gram force / cm^3 # Standard weight of mercury (exact)
water gram force/cm^3 # Standard weight of water (exact)
waterdensity gram / cm^3 # Density of water
H2O water
wc water # water column
mach 331.46 m/s # speed of sound in dry air at STP
standardtemp 273.15 K # standard temperature
stdtemp standardtemp
normaltemp tempF(70) # for gas density, from NIST
normtemp normaltemp # Handbook 44
# Weight of mercury and water at different temperatures using the standard
# force of gravity.
Hg10C 13.5708 force gram / cm^3 # These units, when used to form
Hg20C 13.5462 force gram / cm^3 # pressure measures, are not accurate
Hg23C 13.5386 force gram / cm^3 # because of considerations of the
Hg30C 13.5217 force gram / cm^3 # revised practical temperature scale.
Hg40C 13.4973 force gram / cm^3
Hg60F 13.5574 force gram / cm^3
H2O0C 0.99987 force gram / cm^3
H2O5C 0.99999 force gram / cm^3
H2O10C 0.99973 force gram / cm^3
H2O15C 0.99913 force gram / cm^3
H2O18C 0.99862 force gram / cm^3
H2O20C 0.99823 force gram / cm^3
H2O25C 0.99707 force gram / cm^3
H2O50C 0.98807 force gram / cm^3
H2O100C 0.95838 force gram / cm^3
# Atomic constants
Rinfinity 10973731.568539 /m # The wavelengths of a spectral series
R_H 10967760 /m # can be expressed as
# 1/lambda = R (1/m^2 - 1/n^2).
# where R is a number that various
# slightly from element to element.
# For hydrogen, R_H is the value,
# and for heavy elements, the value
# approaches Rinfinity, which can be
# computed from
# m_e c alpha^2 / 2 h
# with a loss of 4 digits
# of precision.
alpha 7.2973525664e-3 # The fine structure constant was
# introduced to explain fine
# structure visible in spectral
# lines. It can be computed from
# mu0 c e^2 / 2 h
# with a loss of 3 digits precision
# and loss of precision in derived
# values which use alpha.
bohrradius alpha / 4 pi Rinfinity
prout 185.5 keV # nuclear binding energy equal to 1|12
# binding energy of the deuteron
# Planck constants
planckmass 2.17651e-8 kg # sqrt(hbar c / G)
m_P planckmass
plancktime hbar / planckmass c^2
t_P plancktime
plancklength plancktime c
l_P plancklength
# Particle radius
electronradius (1/4 pi epsilon0) e^2 / electronmass c^2 # Classical
deuteronchargeradius 2.1413e-15 m
protonchargeradius 0.8751e-15 m
# Masses of elementary particles
electronmass 5.48579909070e-4 u
m_e electronmass
protonmass 1.007276466879 u
m_p protonmass
neutronmass 1.00866491588 u
m_n neutronmass
muonmass 0.1134289257 u
m_mu muonmass
deuteronmass 2.013553212745 u
m_d deuteronmass
alphaparticlemass 4.001506179127 u
m_alpha alphaparticlemass
taumass 1.90749 u
m_tau taumass
tritonmass 3.01550071632 u
m_t tritonmass
helionmass 3.01493224673 u
m_h helionmass
# particle wavelengths: the compton wavelength of a particle is
# defined as h / m c where m is the mass of the particle.
electronwavelength h / m_e c
lambda_C electronwavelength
protonwavelength h / m_p c
lambda_C,p protonwavelength
neutronwavelength h / m_n c
lambda_C,n neutronwavelength
# Magnetic moments
bohrmagneton e hbar / 2 electronmass
mu_B bohrmagneton
nuclearmagneton e hbar / 2 protonmass
mu_N nuclearmagneton
mu_mu -4.49044826e-26 J/T # Muon magnetic moment
mu_p 1.4106067873e-26 J/T # Proton magnetic moment
mu_e -928.4764620e-26 J/T # Electron magnetic moment
mu_n -0.96623650e-26 J/T # Neutron magnetic moment
mu_d 0.4330735040e-26 J/T # Deuteron magnetic moment
mu_t 1.504609503e-26 J/T # Triton magnetic moment
mu_h -1.074617522e-26 J/T # Helion magnetic moment
#
# Units derived from physical constants
#
kgf kg force
technicalatmosphere kgf / cm^2
at technicalatmosphere
hyl kgf s^2 / m # Also gram-force s^2/m according to [15]
mmHg mm Hg
torr atm / 760 # These units, both named after Evangelista
tor Pa # Torricelli, should not be confused. The
inHg inch Hg # torr is very close to the mm Hg.
inH2O inch water
mmH2O mm water
eV e V # Energy acquired by a particle with charge e
electronvolt eV # when it is accelerated through 1 V
lightyear c julianyear # The 365.25 day year is specified in
ly lightyear # NIST publication 811
lightsecond c s
lightminute c min
parsec au / tan(arcsec) # Unit of length equal to distance
pc parsec # from the sun to a point having
# heliocentric parallax of 1
# arcsec (derived from parallax
# second). A distant object with
# paralax theta will be about
# (arcsec/theta) parsecs from the
# sun (using the approximation
# that tan(theta) = theta).
rydberg h c Rinfinity # Rydberg energy
crith 0.089885 gram # The crith is the mass of one
# liter of hydrogen at standard
# temperature and pressure.
amagatvolume molarvolume
amagat mol/amagatvolume # Used to measure gas densities
lorentz bohrmagneton / h c # Used to measure the extent
# that the frequency of light
# is shifted by a magnetic field.
cminv h c / cm # Unit of energy used in infrared
invcm cminv # spectroscopy.
wavenumber cminv
kcal_mol kcal_th / mol N_A # kcal/mol is used as a unit of
# energy by physical chemists.
#
# CGS system based on centimeter, gram and second
#
dyne cm gram / s^2 # force
dyn dyne
erg cm dyne # energy
poise gram / cm s # viscosity, honors Jean Poiseuille
P poise
rhe /poise # reciprocal viscosity
stokes cm^2 / s # kinematic viscosity
St stokes
stoke stokes
lentor stokes # old name
Gal cm / s^2 # acceleration, used in geophysics
galileo Gal # for earth's gravitational field
# (note that "gal" is for gallon
# but "Gal" is the standard symbol
# for the gal which is evidently a
# shortened form of "galileo".)
barye dyne/cm^2 # pressure
barad barye # old name
kayser 1/cm # Proposed as a unit for wavenumber
balmer kayser # Even less common name than "kayser"
kine cm/s # velocity
bole g cm / s # momentum
pond gram force
glug gram force s^2 / cm # Mass which is accelerated at
# 1 cm/s^2 by 1 gram force
darcy centipoise cm^2 / s atm # Measures permeability to fluid flow.
# One darcy is the permeability of a
# medium that allows a flow of cc/s
# of a liquid of centipoise viscosity
# under a pressure gradient of
# atm/cm. Named for H. Darcy.
mobileohm cm / dyn s # mobile ohm, measure of mechanical
# mobility
mechanicalohm dyn s / cm # mechanical resistance
acousticalohm dyn s / cm^5 # ratio of the sound pressure of
# 1 dyn/cm^2 to a source of strength
# 1 cm^3/s
ray acousticalohm
rayl dyn s / cm^3 # Specific acoustical resistance
eotvos 1e-9 Gal/cm # Change in gravitational acceleration
# over horizontal distance
# Electromagnetic units derived from the abampere
abampere 10 A # Current which produces a force of
abamp abampere # 2 dyne/cm between two infinitely
aA abampere # long wires that are 1 cm apart
biot aA # alternative name for abamp
Bi biot
abcoulomb abamp sec
abcoul abcoulomb
abfarad abampere sec / abvolt
abhenry abvolt sec / abamp
abvolt dyne cm / abamp sec
abohm abvolt / abamp
abmho /abohm
gauss abvolt sec / cm^2
Gs gauss
maxwell abvolt sec # Also called the "line"
Mx maxwell
oersted gauss / mu0
Oe oersted
gilbert gauss cm / mu0
Gb gilbert
Gi gilbert
unitpole 4 pi maxwell
emu erg/gauss # "electro-magnetic unit", a measure of
# magnetic moment, often used as emu/cm^3
# to specify magnetic moment density.
# Gaussian system: electromagnetic units derived from statampere.
#
# Note that the Gaussian units are often used in such a way that Coulomb's law
# has the form F= q1 * q2 / r^2. The constant 1|4*pi*epsilon0 is incorporated
# into the units. From this, we can get the relation force=charge^2/dist^2.
# This means that the simplification esu^2 = dyne cm^2 can be used to simplify
# units in the Gaussian system, with the curious result that capacitance can be
# measured in cm, resistance in sec/cm, and inductance in sec^2/cm. These
# units are given the names statfarad, statohm and stathenry below.
statampere 10 A cm / s c
statamp statampere
statvolt dyne cm / statamp sec
statcoulomb statamp s
esu statcoulomb
statcoul statcoulomb
statfarad statamp sec / statvolt
cmcapacitance statfarad
stathenry statvolt sec / statamp
statohm statvolt / statamp
statmho /statohm
statmaxwell statvolt sec
franklin statcoulomb
debye 1e-18 statcoul cm # unit of electrical dipole moment
helmholtz debye/angstrom^2 # Dipole moment per area
jar 1000 statfarad # approx capacitance of Leyden jar
#
# Some historical electromagnetic units
#
intampere 0.999835 A # Defined as the current which in one
intamp intampere # second deposits .001118 gram of
# silver from an aqueous solution of
# silver nitrate.
intfarad 0.999505 F
intvolt 1.00033 V
intohm 1.000495 ohm # Defined as the resistance of a
# uniform column of mercury containing
# 14.4521 gram in a column 1.063 m
# long and maintained at 0 degC.
daniell 1.042 V # Meant to be electromotive force of a
# Daniell cell, but in error by .04 V
faraday N_A e mol # Charge that must flow to deposit or
faraday_phys 96521.9 C # liberate one gram equivalent of any
faraday_chem 96495.7 C # element. (The chemical and physical
# values are off slightly from what is
# obtained by multiplying by amu_chem
# or amu_phys. These values are from
# a 1991 NIST publication.) Note that
# there is a Faraday constant which is
# equal to N_A e and hence has units of
# C/mol.
kappline 6000 maxwell # Named by and for Gisbert Kapp
siemensunit 0.9534 ohm # Resistance of a meter long column of
# mercury with a 1 mm cross section.
#
# Printed circuit board units.
#
# http://www.ndt-ed.org/GeneralResources/IACS/IACS.htm.
#
# Conductivity is often expressed as a percentage of IACS. A copper wire a
# meter long with a 1 mm^2 cross section has a resistance of 1|58 ohm at
# 20 deg C. Copper density is also standarized at that temperature.
#
copperconductivity 58 siemens m / mm^2 # A wire a meter long with
IACS copperconductivity # a 1 mm^2 cross section
copperdensity 8.89 g/cm^3 # The "ounce" measures the
ouncecopper oz / ft^2 copperdensity # thickness of copper used
ozcu ouncecopper # in circuitboard fabrication
#
# Photometric units
#
LUMINOUS_INTENSITY candela
LUMINOUS_FLUX lumen
LUMINOUS_ENERGY talbot
ILLUMINANCE lux
EXITANCE lux
candle 1.02 candela # Standard unit for luminous intensity
hefnerunit 0.9 candle # in use before candela
hefnercandle hefnerunit #
violle 20.17 cd # luminous intensity of 1 cm^2 of
# platinum at its temperature of
# solidification (2045 K)
lumen cd sr # Luminous flux (luminous energy per
lm lumen # time unit)
talbot lumen s # Luminous energy
lumberg talbot # References give these values for
lumerg talbot # lumerg and lumberg both. Note that
# a paper from 1948 suggests that
# lumerg should be 1e-7 talbots so
# that lumergs/erg = talbots/joule.
# lumerg = luminous erg
lux lm/m^2 # Illuminance or exitance (luminous
lx lux # flux incident on or coming from
phot lumen / cm^2 # a surface)
ph phot #
footcandle lumen/ft^2 # Illuminance from a 1 candela source
# at a distance of one foot
metercandle lumen/m^2 # Illuminance from a 1 candela source
# at a distance of one meter
mcs metercandle s # luminous energy per area, used to
# measure photographic exposure
nox 1e-3 lux # These two units were proposed for
skot 1e-3 apostilb # measurements relating to dark adapted
# eyes.
# Luminance measures
LUMINANCE nit
nit cd/m^2 # Luminance: the intensity per projected
stilb cd / cm^2 # area of an extended luminous source.
sb stilb # (nit is from latin nitere = to shine.)
apostilb cd/pi m^2
asb apostilb
blondel apostilb # Named after a French scientist.
# Equivalent luminance measures. These units are units which measure
# the luminance of a surface with a specified exitance which obeys
# Lambert's law. (Lambert's law specifies that luminous intensity of
# a perfectly diffuse luminous surface is proportional to the cosine
# of the angle at which you view the luminous surface.)
equivalentlux cd / pi m^2 # luminance of a 1 lux surface
equivalentphot cd / pi cm^2 # luminance of a 1 phot surface
lambert cd / pi cm^2
footlambert cd / pi ft^2
# The bril is used to express "brilliance" of a source of light on a
# logarithmic scale to correspond to subjective perception. An increase of 1
# bril means doubling the luminance. A luminance of 1 lambert is defined to
# have a brilliance of 1 bril.
bril(x) units=[1;lambert] 2^(x+-100) lamberts ;log2(bril/lambert)+100
# Some luminance data from the IES Lighting Handbook, 8th ed, 1993
sunlum 1.6e9 cd/m^2 # at zenith
sunillum 100e3 lux # clear sky
sunillum_o 10e3 lux # overcast sky
sunlum_h 6e6 cd/m^2 # value at horizon
skylum 8000 cd/m^2 # average, clear sky
skylum_o 2000 cd/m^2 # average, overcast sky
moonlum 2500 cd/m^2
#
# Photographic Exposure Value
# This section by Jeff Conrad (jeff_conrad@msn.com)
#
# The Additive system of Photographic EXposure (APEX) proposed in ASA
# PH2.5-1960 was an attempt to simplify exposure determination for people who
# relied on exposure tables rather than exposure meters. Shortly thereafter,
# nearly all cameras incorporated exposure meters, so the APEX system never
# caught on, but the concept of exposure value remains in use. Though given as
# 'Ev' in ASA PH2.5-1960, it is now more commonly indicated by 'EV'. EV is
# related to exposure parameters by
#
# A^2 LS ES
# 2^EV = --- = -- = --
# t K C
#
# Where
# A = Relative aperture (f-number)
# t = Exposure time in seconds
# L = Scene luminance in cd/m2
# E = Scene illuminance in lux
# S = Arithmetic ISO speed
# K = Reflected-light meter calibration constant
# C = Incident-light meter calibration constant
#
# Strictly, an exposure value is a combination of aperture and exposure time,
# but it's also commonly used to indicate luminance (or illuminance).
# Conversion to luminance or illuminance units depends on the ISO speed and the
# meter calibration constant. Common practice is to use an ISO speed of 100.
# Calibration constants vary among camera and meter manufacturers: Canon,
# Nikon, and Sekonic use a value of 12.5 for reflected-light meters, while
# Kenko (formerly Minolta) and Pentax use a value of 14. Kenko and Sekonic use
# a value of 250 for incident-light meters with flat receptors.
#
# The values for in-camera meters apply only averaging, weighted-averaging, or
# spot metering--the multi-segment metering incorporated in most current
# cameras uses proprietary algorithms that evaluate many factors related to the
# luminance distribution of what is being metered; they are not amenable to
# simple conversions, and are usually not disclosed by the manufacturers.
s100 100 / lx s # ISO 100 speed
iso100 s100
# Reflected-light meter calibration constant with ISO 100 speed
k1250 12.5 (cd/m2) / lx s # For Canon, Nikon, and Sekonic
k1400 14 (cd/m2) / lx s # For Kenko (Minolta) and Pentax
# Incident-light meter calibration constant with ISO 100 film
c250 250 lx / lx s # flat-disc receptor
# Exposure value to scene luminance with ISO 100 imaging media
# For Kenko (Minolta) or Pentax
#ev100(x) units=[;cd/m^2] range=(0,) 2^x k1400 / s100; log2(ev100 s100/k1400)
# For Canon, Nikon, or Sekonic
ev100(x) units=[1;cd/m^2] range=(0,) 2^x k1250 / s100; log2(ev100 s100/k1250)
EV100() ev100
# Exposure value to scene illuminance with ISO 100 imaging media
iv100(x) units=[1;lx] range=(0,) 2^x c250 / s100; log2(iv100 s100 / c250)
# Other Photographic Exposure Conversions
#
# As part of APEX, ASA PH2.5-1960 proposed several logarithmic quantities
# related by
#
# Ev = Av + Tv = Bv + Sv
#
# where
# Av = log2(A^2) Aperture value
# Tv = log2(1/t) Time value
# Sv = log2(N Sx) Speed value
# Bv = log2(B S / K) Luminance ("brightness") value
# Iv = log2(I S / C) Illuminance value
#
# and
# A = Relative aperture (f-number)
# t = Exposure time in seconds
# Sx = Arithmetic ISO speed in 1/lux s
# B = luminance in cd/m2
# I = luminance in lux
# The constant N derives from the arcane relationship between arithmetic
# and logarithmic speed given in ASA PH2.5-1960. That relationship
# apparently was not obvious--so much so that it was thought necessary
# to explain it in PH2.12-1961. The constant has had several values
# over the years, usually without explanation for the changes. Although
# APEX had little impact on consumer cameras, it has seen a partial
# resurrection in the Exif standards published by the Camera & Imaging
# Products Association of Japan.
#N_apex 2^-1.75 lx s # precise value implied in ASA PH2.12-1961,
# derived from ASA PH2.5-1960.
#N_apex 0.30 lx s # rounded value in ASA PH2.5-1960,
# ASA PH2.12-1961, and ANSI PH2.7-1986
#N_apex 0.3162 lx s # value in ANSI PH2.7-1973
N_exif 1|3.125 lx s # value in Exif 2.3 (2010), making Sv(5) = 100
K_apex1961 11.4 (cd/m2) / lx s # value in ASA PH2.12-1961
K_apex1971 12.5 (cd/m2) / lx s # value in ANSI PH3.49-1971; more common
C_apex1961 224 lx / lx s # value in PH2.12-1961 (20.83 for I in
# footcandles; flat sensor?)
C_apex1971 322 lx / lx s # mean value in PH3.49-1971 (30 +/- 5 for I in
# footcandles; hemispherical sensor?)
N_speed N_exif
K_lum K_apex1971
C_illum C_apex1961
# Units for Photographic Exposure Variables
#
# Practical photography sometimes pays scant attention to units for exposure
# variables. In particular, the "speed" of the imaging medium is treated as if
# it were dimensionless when it should have units of reciprocal lux seconds;
# this practice works only because "speed" is almost invariably given in
# accordance with international standards (or similar ones used by camera
# manufacturers)--so the assumed units are invariant. In calculating
# logarithmic quantities--especially the time value Tv and the exposure value
# EV--the units for exposure time ("shutter speed") are often ignored; this
# practice works only because the units of exposure time are assumed to be in
# seconds, and the missing units that make the argument to the logarithmic
# function dimensionless are silently provided.
#
# In keeping with common practice, the definitions that follow treat "speeds"
# as dimensionless, so ISO 100 speed is given simply as '100'. When
# calculating the logarithmic APEX quantities Av and Tv, the definitions
# provide the missing units, so the times can be given with any appropriate
# units. For example, giving an exposure time of 1 minute as either '1 min' or
# '60 s' will result in Tv of -5.9068906.
#
# Exposure Value from f-number and Exposure Time
#
# Because nonlinear unit conversions only accept a single quantity,
# there is no direct conversion from f-number and exposure time to
# exposure value EV. But the EV can be obtained from a combination of
# Av and Tv. For example, the "sunny 16" rule states that correct
# exposure for a sunlit scene can achieved by using f/16 and an exposure
# time equal to the reciprocal of the ISO speed in seconds; this can be
# calculated as
#
# ~Av(16) + ~Tv(1|100 s),
#
# which gives 14.643856. These conversions may be combined with the
# ev100 conversion:
#
# ev100(~Av(16) + ~Tv(1|100 s))
#
# to yield the assumed average scene luminance of 3200 cd/m^2.
# convert relative aperture (f-number) to aperture value
Av(A) units=[1;1] domain=[-2,) range=[0.5,) 2^(A/2); 2 log2(Av)
# convert exposure time to time value
Tv(t) units=[1;s] range=(0,) 2^(-t) s; log2(s / Tv)
# convert logarithmic speed Sv in ASA PH2.5-1960 to ASA/ISO arithmetic speed;
# make arithmetic speed dimensionless
# 'Sv' conflicts with the symbol for sievert; you can uncomment this function
# definition if you don't need that symbol
#Sv(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sv)
Sval(S) units=[1;1] range=(0,) 2^S / (N_speed/lx s); log2((N_speed/lx s) Sval)
# convert luminance value Bv in ASA PH2.12-1961 to luminance
Bv(x) units=[1;cd/m^2] range=(0,) \
2^x K_lum N_speed ; log2(Bv / (K_lum N_speed))
# convert illuminance value Iv in ASA PH2.12-1961 to illuminance
Iv(x) units=[1;lx] range=(0,) \
2^x C_illum N_speed ; log2(Iv / (C_illum N_speed))
# convert ASA/ISO arithmetic speed Sx to ASA logarithmic speed in
# ASA PH2.5-1960; make arithmetic speed dimensionless
Sx(S) units=[1;1] domain=(0,) \
log2((N_speed/lx s) S); 2^Sx / (N_speed/lx s)
# convert DIN speed/ISO logarithmic speed in ISO 6:1993 to arithmetic speed
# for convenience, speed is treated here as if it were dimensionless
Sdeg(S) units=[1;1] range=(0,) 10^((S - 1) / 10) ; (1 + 10 log(Sdeg))
Sdin() Sdeg
# Numerical Aperture and f-Number of a Lens
#
# The numerical aperture (NA) is given by
#
# NA = n sin(theta)
#
# where n is the index of refraction of the medium and theta is half
# of the angle subtended by the aperture stop from a point in the image
# or object plane. For a lens in air, n = 1, and
#
# NA = 0.5 / f-number
#
# convert NA to f-number
numericalaperture(x) units=[1;1] domain=(0,1] range=[0.5,) \
0.5 / x ; 0.5 / numericalaperture
NA() numericalaperture
#
# convert f-number to itself; restrict values to those possible
fnumber(x) units=[1;1] domain=[0.5,) range=[0.5,) x ; fnumber
# Referenced Photographic Standards
#
# ASA PH-2.5-1960. USA Standard, Method for Determining (Monochrome,
# Continuous-Tone) Speed of Photographic Negative Materials.
# ASA PH2.12-1961. American Standard, General-Purpose Photographic
# Exposure Meters (photoelectric type).
# ANSI PH3.49-1971. American National Standard for general-purpose
# photographic exposure meters (photoelectric type).
# ANSI PH2.7-1973. American National Standard Photographic Exposure Guide.
# ANSI PH2.7-1986. American National Standard for Photography --
# Photographic Exposure Guide.
# CIPA DC-008-2010. Exchangeable image file format for digital still
# cameras: Exif Version 2.3
# ISO 6:1993. International Standard, Photography -- Black-and-white
# pictorial still camera negative film/process systems --
# Determination of ISO Speed.
#
# Astronomical time measurements
#
# Astronomical time measurement is a complicated matter. The length of the
# true day at a given place can be 21 seconds less than 24 hours or 30 seconds
# over 24 hours. The two main reasons for this are the varying speed of the
# earth in its elliptical orbit and the fact that the sun moves on the ecliptic
# instead of along the celestial equator. To devise a workable system for time
# measurement, Simon Newcomb (1835-1909) used a fictitious "mean sun".
# Consider a first fictitious sun traveling along the ecliptic at a constant
# speed and coinciding with the true sun at perigee and apogee. Then
# considering a second fictitious sun traveling along the celestial equator at
# a constant speed and coinciding with the first fictitious sun at the
# equinoxes. The second fictitious sun is the "mean sun". From this equations
# can be written out to determine the length of the mean day, and the tropical
# year. The length of the second was determined based on the tropical year
# from such a calculation and was officially used from 1960-1967 until atomic
# clocks replaced astronomical measurements for a standard of time. All of the
# values below give the mean time for the specified interval.
#
# See "Mathematical Astronomy Morsels" by Jean Meeus for more details
# and a description of how to compute the correction to mean time.
#
TIME second
anomalisticyear 365.2596 days # The time between successive
# perihelion passages of the
# earth.
siderealyear 365.256360417 day # The time for the earth to make
# one revolution around the sun
# relative to the stars.
tropicalyear 365.242198781 day # The time needed for the mean sun
# as defined above to increase
# its longitude by 360 degrees.
# Most references defined the
# tropical year as the interval
# between vernal equinoxes, but
# this is misleading. The length
# of the season changes over time
# because of the eccentricity of
# the earth's orbit. The time
# between vernal equinoxes is
# approximately 365.24237 days
# around the year 2000. See
# "Mathematical Astronomy
# Morsels" for more details.
eclipseyear 346.62 days # The line of nodes is the
# intersection of the plane of
# Earth's orbit around the sun
# with the plane of the moon's
# orbit around earth. Eclipses
# can only occur when the moon
# and sun are close to this
# line. The line rotates and
# appearances of the sun on the
# line of nodes occur every
# eclipse year.
saros 223 synodicmonth # The earth, moon and sun appear in
# the same arrangement every
# saros, so if an eclipse occurs,
# then one saros later, a similar
# eclipse will occur. (The saros
# is close to 19 eclipse years.)
# The eclipse will occur about
# 120 degrees west of the
# preceeding one because the
# saros is not an even number of
# days. After 3 saros, an
# eclipse will occur at
# approximately the same place.
siderealday 86164.09054 s # The sidereal day is the interval
siderealhour 1|24 siderealday # between two successive transits
siderealminute 1|60 siderealhour # of a star over the meridian,
siderealsecond 1|60 siderealminute # or the time required for the
# earth to make one rotation
# relative to the stars. The
# more usual solar day is the
# time required to make a
# rotation relative to the sun.
# Because the earth moves in its
# orbit, it has to turn a bit
# extra to face the sun again,
# hence the solar day is slightly
# longer.
anomalisticmonth 27.55454977 day # Time for the moon to travel from
# perigee to perigee
nodicalmonth 27.2122199 day # The nodes are the points where
draconicmonth nodicalmonth # an orbit crosses the ecliptic.
draconiticmonth nodicalmonth # This is the time required to
# travel from the ascending node
# to the next ascending node.
siderealmonth 27.321661 day # Time required for the moon to
# orbit the earth
lunarmonth 29 days + 12 hours + 44 minutes + 2.8 seconds
# Mean time between full moons.
synodicmonth lunarmonth # Full moons occur when the sun
lunation synodicmonth # and moon are on opposite sides
lune 1|30 lunation # of the earth. Since the earth
lunour 1|24 lune # moves around the sun, the moon
# has to revolve a bit extra to
# get into the full moon
# configuration.
year tropicalyear
yr year
month 1|12 year
mo month
lustrum 5 years # The Lustrum was a Roman
# purification ceremony that took
# place every five years.
# Classically educated Englishmen
# used this term.
decade 10 years
century 100 years
millennium 1000 years
millennia millennium
solaryear year
lunaryear 12 lunarmonth
calendaryear 365 day
commonyear 365 day
leapyear 366 day
julianyear 365.25 day
gregorianyear 365.2425 day
islamicyear 354 day # A year of 12 lunar months. They
islamicleapyear 355 day # began counting on July 16, AD 622
# when Muhammad emigrated to Medina
# (the year of the Hegira). They need
# 11 leap days in 30 years to stay in
# sync with the lunar year which is a
# bit longer than the 29.5 days of the
# average month. The months do not
# keep to the same seasons, but
# regress through the seasons every
# 32.5 years.
islamicmonth 1|12 islamicyear # They have 29 day and 30 day months.
# The Hewbrew year is also based on lunar months, but synchronized to the solar
# calendar. The months vary irregularly between 29 and 30 days in length, and
# the years likewise vary. The regular year is 353, 354, or 355 days long. To
# keep up with the solar calendar, a leap month of 30 days is inserted every
# 3rd, 6th, 8th, 11th, 14th, 17th, and 19th years of a 19 year cycle. This
# gives leap years that last 383, 384, or 385 days.
# Sidereal days
mercuryday 58.6462 day
venusday 243.01 day # retrograde
earthday siderealday
marsday 1.02595675 day
jupiterday 0.41354 day
saturnday 0.4375 day
uranusday 0.65 day # retrograde
neptuneday 0.768 day
plutoday 6.3867 day
# Sidereal years from http://ssd.jpl.nasa.gov/phys_props_planets.html. Data
# was updated in May 2001 based on the 1992 Explanatory Supplement to the
# Astronomical Almanac and the mean longitude rates. Apparently the table of
# years in that reference is incorrect.
mercuryyear 0.2408467 julianyear
venusyear 0.61519726 julianyear
earthyear siderealyear
marsyear 1.8808476 julianyear
jupiteryear 11.862615 julianyear
saturnyear 29.447498 julianyear
uranusyear 84.016846 julianyear
neptuneyear 164.79132 julianyear
plutoyear 247.92065 julianyear
# Objects on the earth are charted relative to a perfect ellipsoid whose
# dimensions are specified by different organizations. The ellipsoid is
# specified by an equatorial radius and a flattening value which defines the
# polar radius. These values are the 1996 values given by the International
# Earth Rotation Service (IERS) whose reference documents can be found at
# http://maia.usno.navy.mil/
earthflattening 1|298.25642
earthradius_equatorial 6378136.49 m
earthradius_polar (-earthflattening+1) earthradius_equatorial
landarea 148.847e6 km^2
oceanarea 361.254e6 km^2
moonradius 1738 km # mean value
sunradius 6.96e8 m
# Many astronomical values can be measured most accurately in a system of units
# using the astronomical unit and the mass of the sun as base units. The
# uncertainty in the gravitational constant makes conversion to SI units
# significantly less accurate.
# The astronomical unit was defined to be the length of the of the semimajor
# axis of a massless object with the same year as the earth. With such a
# definition in force, and with the mass of the sun set equal to one, Kepler's
# third law can be used to solve for the value of the gravitational constant.
# Kepler's third law says that (2 pi / T)^2 a^3 = G M where T is the orbital
# period, a is the size of the semimajor axis, G is the gravitational constant
# and M is the mass. With M = 1 and T and a chosen for the earth's orbit, we
# find sqrt(G) = (2 pi / T) sqrt(AU^3). This constant is called the Gaussian
# gravitational constant, apparently because Gauss originally did the
# calculations. However, when the original calculation was done, the value
# for the length of the earth's year was inaccurate. The value used is called
# the Gaussian year. Changing the astronomical unit to bring it into
# agreement with more accurate values for the year would have invalidated a
# lot of previous work, so instead the astronomical unit has been kept equal
# to this original value. This is accomplished by using a standard value for
# the Gaussian gravitational constant. This constant is called k.
# Many values below are from http://ssd.jpl.nasa.gov/?constants
gauss_k 0.01720209895 # This beast has dimensions of
# au^(3|2) / day and is exact.
gaussianyear (2 pi / gauss_k) days # Year that corresponds to the Gaussian
# gravitational constant. This is a
# fictional year, and doesn't
# correspond to any celestial event.
astronomicalunit 149597870700 m # IAU definition from 2012, exact
au astronomicalunit # ephemeris for the above described
# astronomical unit. (See the NASA
# site listed above.)
solarmass 1.9891e30 kg
sunmass solarmass
sundist 1.0000010178 au # mean earth-sun distance
moondist 3.844e8 m # mean earth-moon distance
sundist_near 1.471e11 m # earth-sun distance at perihelion
sundist_far 1.521e11 m # earth-sun distance at aphelion
# The following are masses for planetary systems, not just the planet itself.
# The comments give the uncertainty in the denominators. As noted above,
# masses are given relative to the solarmass because this is more accurate.
# The conversion to SI is uncertain because of uncertainty in G, the
# gravitational constant.
#
# Values are from http://ssd.jpl.nasa.gov/astro_constants.html
mercurymass solarmass / 6023600 # 250
venusmass solarmass / 408523.71 # 0.06
earthmoonmass solarmass / 328900.56 # 0.02
marsmass solarmass / 3098708 # 9
jupitermass solarmass / 1047.3486 # 0.0008
saturnmass solarmass / 3497.898 # 0.018
uranusmass solarmass / 22902.98 # 0.03
neptunemass solarmass / 19412.24 # 0.04
plutomass solarmass / 1.35e8 # 0.07e8
moonearthmassratio 0.012300034 # uncertainty 3 x 10-9
earthmass earthmoonmass / ( 1 + moonearthmassratio)
moonmass moonearthmassratio earthmass
# These are the old values for the planetary masses. They may give
# the masses of the planets alone.
oldmercurymass 0.33022e24 kg
oldvenusmass 4.8690e24 kg
oldmarsmass 0.64191e24 kg
oldjupitermass 1898.8e24 kg
oldsaturnmass 568.5e24 kg
olduranusmass 86.625e24 kg
oldneptunemass 102.78e24 kg
oldplutomass 0.015e24 kg
# Mean radius from http://ssd.jpl.nsaa.gov/phys_props_planets.html which in
# turn cites Global Earth Physics by CF Yoder, 1995.
mercuryradius 2440 km
venusradius 6051.84 km
earthradius 6371.01 km
marsradius 3389.92 km
jupiterradius 69911 km
saturnradius 58232 km
uranusradius 25362 km
neptuneradius 24624 km
plutoradius 1151 km
moongravity 1.62 m/s^2
#
# The Hartree system of atomic units, derived from fundamental units
# of mass (of electron), action (planck's constant), charge, and
# the coulomb constant.
# Fundamental units
atomicmass electronmass
atomiccharge e
atomicaction hbar
# derived units (Warning: accuracy is lost from deriving them this way)
atomiclength bohrradius
atomictime hbar^3/coulombconst^2 atomicmass e^4 # Period of first
# bohr orbit
atomicvelocity atomiclength / atomictime
atomicenergy hbar / atomictime
hartree atomicenergy
#
# These thermal units treat entropy as charge, from [5]
#
thermalcoulomb J/K # entropy
thermalampere W/K # entropy flow
thermalfarad J/K^2
thermalohm K^2/W # thermal resistance
fourier thermalohm
thermalhenry J K^2/W^2 # thermal inductance
thermalvolt K # thermal potential difference
#
# United States units
#
# linear measure
# The US Metric Law of 1866 legalized the metric system in the USA and
# defined the meter in terms of the British system with the exact
# 1 meter = 39.37 inches. On April 5, 1893 Thomas Corwin Mendenhall,
# Superintendent of Weights and Measures, decided, in what has become
# known as the "Mendenhall Order" that the meter and kilogram would be the
# fundamental standards in the USA. The definition from 1866 was turned
# around to give an exact definition of the yard as 3600|3937 meters This
# definition was used until July of 1959 when the definition was changed
# to bring the US and other English-speaking countries into agreement; the
# Canadian value of 1 yard = 0.9144 meter (exactly) was chosen because it
# was approximately halfway between the British and US values; it had the
# added advantage of making 1 inch = 25.4 mm (exactly). Since 1959, the
# "international" foot has been exactly 0.3048 meters. At the same time,
# it was decided that any data expressed in feet derived from geodetic
# surveys within the US would continue to use the old definition and call
# the old unit the "survey foot." The US continues to define the statute
# mile, furlong, chain, rod, link, and fathom in terms of the US survey
# foot.
# Sources:
# NIST Special Publication 447, Sects. 5, 7, and 8.
# NIST Handbook 44, 2011 ed., Appendix C.
# Canadian Journal of Physics, 1959, 37:(1) 84, 10.1139/p59-014.
US 1200|3937 m/ft # These four values will convert
US- US # international measures to
survey- US # US Survey measures
geodetic- US
int 3937|1200 ft/m # Convert US Survey measures to
int- int # international measures
inch 2.54 cm
in inch
foot 12 inch
feet foot
ft foot
yard 3 ft
yd yard
mile 5280 ft # The mile was enlarged from 5000 ft
# to this number in order to make
# it an even number of furlongs.
# (The Roman mile is 5000 romanfeet.)
line 1|12 inch # Also defined as '.1 in' or as '1e-8 Wb'
rod 5.5 yard
perch rod
furlong 40 rod # From "furrow long"
statutemile mile
league 3 mile # Intended to be an an hour's walk
# surveyor's measure
surveyorschain 66 surveyft
surveychain surveyorschain
surveyorspole 1|4 surveyorschain
surveyorslink 1|100 surveyorschain
chain 66 ft
link 1|100 chain
ch chain
USacre 10 surveychain^2
intacre 10 chain^2 # Acre based on international ft
intacrefoot acre foot
USacrefoot USacre surveyfoot
acrefoot intacrefoot
acre intacre
section mile^2
township 36 section
homestead 160 acre # Area of land granted by the 1862 Homestead
# Act of the United States Congress
gunterschain surveyorschain
engineerschain 100 ft
engineerslink 1|100 engineerschain
ramsdenschain engineerschain
ramsdenslink engineerslink
gurleychain 33 feet # Andrew Ellicott chain is the
gurleylink 1|50 gurleychain # same length
wingchain 66 feet # Chain from 1664, introduced by
winglink 1|80 wingchain # Vincent Wing, also found in a
# 33 foot length with 40 links.
# early US length standards
# The US has had four standards for the yard: one by Troughton of London
# (1815); bronze yard #11 (1856); the Mendhall yard (1893), consistent
# with the definition of the meter in the metric joint resolution of
# Congress in 1866, but defining the yard in terms of the meter; and the
# international yard (1959), which standardized definitions for Australia,
# Canada, New Zealand, South Africa, the UK, and the US.
# Sources: Pat Naughtin (2009), Which Inch?, www.metricationmatters.com;
# Lewis E. Barbrow and Lewis V. Judson (1976). NBS Special Publication
# 447, Weights and Measures Standards of the United States: A Brief
# History.
troughtonyard 914.42190 mm
bronzeyard11 914.39980 mm
mendenhallyard surveyyard
internationalyard yard
# nautical measure
fathom 6 ft # Originally defined as the distance from
# fingertip to fingertip with arms fully
# extended.
nauticalmile 1852 m # Supposed to be one minute of latitude at
# the equator. That value is about 1855 m.
# Early estimates of the earth's circumference
# were a bit off. The value of 1852 m was
# made the international standard in 1929.
# The US did not accept this value until
# 1954. The UK switched in 1970.
cable 1|10 nauticalmile
intcable cable # international cable
cablelength cable
UScable 100 USfathom
navycablelength 720 USft # used for depth in water
marineleague 3 nauticalmile
geographicalmile brnauticalmile
knot nauticalmile / hr
click km # US military slang
klick click
# Avoirdupois weight
pound 0.45359237 kg # The one normally used
lb pound # From the latin libra
grain 1|7000 pound # The grain is the same in all three
# weight systems. It was originally
# defined as the weight of a barley
# corn taken from the middle of the
# ear.
ounce 1|16 pound
oz ounce
dram 1|16 ounce
dr dram
ushundredweight 100 pounds
cwt hundredweight
shorthundredweight ushundredweight
uston shortton
shortton 2000 lb
quarterweight 1|4 uston
shortquarterweight 1|4 shortton
shortquarter shortquarterweight
# Troy Weight. In 1828 the troy pound was made the first United States
# standard weight. It was to be used to regulate coinage.
troypound 5760 grain
troyounce 1|12 troypound
ozt troyounce
pennyweight 1|20 troyounce # Abbreviated "d" in reference to a
dwt pennyweight # Frankish coin called the "denier"
# minted in the late 700's. There
# were 240 deniers to the pound.
assayton mg ton / troyounce # mg / assayton = troyounce / ton
usassayton mg uston / troyounce
brassayton mg brton / troyounce
fineounce troyounce # A troy ounce of 99.5% pure gold
# Some other jewelers units
metriccarat 0.2 gram # Defined in 1907
metricgrain 50 mg
carat metriccarat
ct carat
jewelerspoint 1|100 carat
silversmithpoint 1|4000 inch
momme 3.75 grams # Traditional Japanese unit based
# on the chinese mace. It is used for
# pearls in modern times and also for
# silk density. The definition here
# was adopted in 1891.
# Apothecaries' weight
appound troypound
apounce troyounce
apdram 1|8 apounce
apscruple 1|3 apdram
# Liquid measure
usgallon 231 in^3 # US liquid measure is derived from
gal gallon # the British wine gallon of 1707.
quart 1|4 gallon # See the "winegallon" entry below
pint 1|2 quart # more historical information.
gill 1|4 pint
usquart 1|4 usgallon
uspint 1|2 usquart
usgill 1|4 uspint
usfluidounce 1|16 uspint
fluiddram 1|8 usfloz
minimvolume 1|60 fluiddram
qt quart
pt pint
floz fluidounce
usfloz usfluidounce
fldr fluiddram
liquidbarrel 31.5 usgallon
usbeerbarrel 2 beerkegs
beerkeg 15.5 usgallon # Various among brewers
ponykeg 1|2 beerkeg
winekeg 12 usgallon
petroleumbarrel 42 usgallon # Originated in Pennsylvania oil
barrel petroleumbarrel # fields, from the winetierce
bbl barrel
ushogshead 2 liquidbarrel
usfirkin 9 usgallon
# Dry measures: The Winchester Bushel was defined by William III in 1702 and
# legally adopted in the US in 1836.
usbushel 2150.42 in^3 # Volume of 8 inch cylinder with 18.5
bu bushel # inch diameter (rounded)
peck 1|4 bushel
uspeck 1|4 usbushel
brpeck 1|4 brbushel
pk peck
drygallon 1|2 uspeck
dryquart 1|4 drygallon
drypint 1|2 dryquart
drybarrel 7056 in^3 # Used in US for fruits, vegetables,
# and other dry commodities except for
# cranberries.
cranberrybarrel 5826 in^3 # US cranberry barrel
heapedbushel 1.278 usbushel# The following explanation for this
# value was provided by Wendy Krieger
# <os2fan2@yahoo.com> based on
# guesswork. The cylindrical vessel is
# 18.5 inches in diameter and 1|2 inch
# thick. A heaped bushel includes the
# contents of this cylinder plus a heap
# on top. The heap is a cone 19.5
# inches in diameter and 6 inches
# high. With these values, the volume
# of the bushel is 684.5 pi in^3 and
# the heap occupies 190.125 pi in^3.
# Therefore, the heaped bushel is
# 874.625|684.5 bushels. This value is
# approximately 1.2777575 and it rounds
# to the value listed for the size of
# the heaped bushel. Sometimes the
# heaped bushel is reported as 1.25
# bushels. This same explanation gives
# that value if the heap is taken to
# have an 18.5 inch diameter.
# Grain measures. The bushel as it is used by farmers in the USA is actually
# a measure of mass which varies for different commodities. Canada uses the
# same bushel masses for most commodities, but not for oats.
wheatbushel 60 lb
soybeanbushel 60 lb
cornbushel 56 lb
ryebushel 56 lb
barleybushel 48 lb
oatbushel 32 lb
ricebushel 45 lb
canada_oatbushel 34 lb
# Wine and Spirits measure
ponyvolume 1 usfloz
jigger 1.5 usfloz # Can vary between 1 and 2 usfloz
shot jigger # Sometimes 1 usfloz
eushot 25 ml # EU standard spirits measure
fifth 1|5 usgallon
winebottle 750 ml # US industry standard, 1979
winesplit 1|4 winebottle
wineglass 4 usfloz
magnum 1.5 liter # Standardized in 1979, but given
# as 2 qt in some references
metrictenth 375 ml
metricfifth 750 ml
metricquart 1 liter
# Old British bottle size
reputedquart 1|6 brgallon
reputedpint 1|2 reputedquart
brwinebottle reputedquart # Very close to 1|5 winegallon
# French champagne bottle sizes
split 200 ml
jeroboam 2 magnum
rehoboam 3 magnum
methuselah 4 magnum
salmanazar 6 magnum
balthazar 8 magnum
nebuchadnezzar 10 magnum
#
# Water is "hard" if it contains various minerals, expecially calcium
# carbonate.
#
clarkdegree grains/brgallon # Content by weigh of calcium carbonate
gpg grains/usgallon # Divide by water's density to convert to
# a dimensionless concentration measure
#
# Shoe measures
#
shoeiron 1|48 inch # Used to measure leather in soles
shoeounce 1|64 inch # Used to measure non-sole shoe leather
# USA shoe sizes. These express the length of the shoe or the length
# of the "last", the form that the shoe is made on. But note that
# this only captures the length. It appears that widths change 1/4
# inch for each letter within the same size, and if you change the
# length by half a size then the width changes between 1/8 inch and
# 1/4 inch. But this may not be standard. If you know better, please
# contact me.
shoesize_delta 1|3 inch # USA shoe sizes differ by this amount
shoe_men0 8.25 inch
shoe_women0 (7+11|12) inch
shoe_boys0 (3+11|12) inch
shoe_girls0 (3+7|12) inch
shoesize_men(n) units=[1;inch] shoe_men0 + n shoesize_delta ; \
(shoesize_men+(-shoe_men0))/shoesize_delta
shoesize_women(n) units=[1;inch] shoe_women0 + n shoesize_delta ; \
(shoesize_women+(-shoe_women0))/shoesize_delta
shoesize_boys(n) units=[1;inch] shoe_boys0 + n shoesize_delta ; \
(shoesize_boys+(-shoe_boys0))/shoesize_delta
shoesize_girls(n) units=[1;inch] shoe_girls0 + n shoesize_delta ; \
(shoesize_girls+(-shoe_girls0))/shoesize_delta
# European shoe size. According to
# http://www.shoeline.com/footnotes/shoeterm.shtml
# shoe sizes in Europe are measured with Paris points which simply measure
# the length of the shoe.
europeshoesize 2|3 cm
#
# USA slang units
#
buck US$
fin 5 US$
sawbuck 10 US$
usgrand 1000 US$
greenback US$
key kg # usually of marijuana, 60's
lid 1 oz # Another 60's weed unit
footballfield usfootballfield
usfootballfield 100 yards
canadafootballfield 110 yards # And 65 yards wide
marathon 26 miles + 385 yards
#
# British
#
# The length measure in the UK was defined by a bronze bar manufactured in
# 1844. Various conversions were sanctioned for convenience at different
# times, which makes conversions before 1963 a confusing matter. Apparently
# previous conversions were never explicitly revoked. Four different
# conversion factors appear below. Multiply them times an imperial length
# units as desired. The Weights and Measures Act of 1963 switched the UK away
# from their bronze standard and onto a definition of the yard in terms of the
# meter. This happened after an international agreement in 1959 to align the
# world's measurement systems.
UK UKlength_SJJ
UK- UK
british- UK
UKlength_B 0.9143992 meter / yard # Benoit found the yard to be
# 0.9143992 m at a weights and
# measures conference around
# 1896. Legally sanctioned
# in 1898.
UKlength_SJJ 0.91439841 meter / yard # In 1922, Seers, Jolly and
# Johnson found the yard to be
# 0.91439841 meters.
# Used starting in the 1930's.
UKlength_K meter / 39.37079 inch # In 1816 Kater found this ratio
# for the meter and inch. This
# value was used as the legal
# conversion ratio when the
# metric system was legalized
# for contract in 1864.
UKlength_C meter / 1.09362311 yard # In 1866 Clarke found the meter
# to be 1.09362311 yards. This
# conversion was legalized
# around 1878.
brnauticalmile 6080 ft # Used until 1970 when the UK
brknot brnauticalmile / hr # switched to the international
brcable 1|10 brnauticalmile # nautical mile.
admiraltymile brnauticalmile
admiraltyknot brknot
admiraltycable brcable
seamile 6000 ft
shackle 15 fathoms # Adopted 1949 by British navy
# British Imperial weight is mostly the same as US weight. A few extra
# units are added here.
clove 7 lb
stone 14 lb
tod 28 lb
brquarterweight 1|4 brhundredweight
brhundredweight 8 stone
longhundredweight brhundredweight
longton 20 brhundredweight
brton longton
# British Imperial volume measures
brminim 1|60 brdram
brscruple 1|3 brdram
fluidscruple brscruple
brdram 1|8 brfloz
brfluidounce 1|20 brpint
brfloz brfluidounce
brgill 1|4 brpint
brpint 1|2 brquart
brquart 1|4 brgallon
brgallon 4.54609 l # The British Imperial gallon was
# defined in 1824 to be the volume of
# water which weighed 10 pounds at 62
# deg F with a pressure of 30 inHg.
# It was also defined as 277.274 in^3,
# Which is slightly in error. In
# 1963 it was defined to be the volume
# occupied by 10 pounds of distilled
# water of density 0.998859 g/ml weighed
# in air of density 0.001217 g/ml
# against weights of density 8.136 g/ml.
# This gives a value of approximately
# 4.5459645 liters, but the old liter
# was in force at this time. In 1976
# the definition was changed to exactly
# 4.54609 liters using the new
# definition of the liter (1 dm^3).
brbarrel 36 brgallon # Used for beer
brbushel 8 brgallon
brheapedbushel 1.278 brbushel
brquarter 8 brbushel
brchaldron 36 brbushel
# Obscure British volume measures. These units are generally traditional
# measures whose definitions have fluctuated over the years. Often they
# depended on the quantity being measured. They are given here in terms of
# British Imperial measures. For example, the puncheon may have historically
# been defined relative to the wine gallon or beer gallon or ale gallon
# rather than the British Imperial gallon.
bag 4 brbushel
bucket 4 brgallon
kilderkin 2 brfirkin
last 40 brbushel
noggin brgill
pottle 0.5 brgallon
pin 4.5 brgallon
puncheon 72 brgallon
seam 8 brbushel
coomb 4 brbushel
boll 6 brbushel
firlot 1|4 boll
brfirkin 9 brgallon # Used for ale and beer
cran 37.5 brgallon # measures herring, about 750 fish
brwinehogshead 52.5 brgallon # This value is approximately equal
brhogshead brwinehogshead # to the old wine hogshead of 63
# wine gallons. This adjustment
# is listed in the OED and in
# "The Weights and Measures of
# England" by R. D. Connor
brbeerhogshead 54 brgallon
brbeerbutt 2 brbeerhogshead
registerton 100 ft^3 # Used for internal capacity of ships
shippington 40 ft^3 # Used for ship's cargo freight or timber
brshippington 42 ft^3 #
freightton shippington # Both register ton and shipping ton derive
# from the "tun cask" of wine.
displacementton 35 ft^3 # Approximate volume of a longton weight of
# sea water. Measures water displaced by
# ships.
waterton 224 brgallon
strike 70.5 l # 16th century unit, sometimes
# defined as .5, 2, or 4 bushels
# depending on the location. It
# probably doesn't make a lot of
# sense to define in terms of imperial
# bushels. Zupko gives a value of
# 2 Winchester grain bushels or about
# 70.5 liters.
amber 4 brbushel# Used for dry and liquid capacity [18]
# British volume measures with "imperial"
imperialminim brminim
imperialscruple brscruple
imperialdram brdram
imperialfluidounce brfluidounce
imperialfloz brfloz
imperialgill brgill
imperialpint brpint
imperialquart brquart
imperialgallon brgallon
imperialbarrel brbarrel
imperialbushel brbushel
imperialheapedbushel brheapedbushel
imperialquarter brquarter
imperialchaldron brchaldron
imperialwinehogshead brwinehogshead
imperialhogshead brhogshead
imperialbeerhogshead brbeerhogshead
imperialbeerbutt brbeerbutt
imperialfirkin brfirkin
# obscure British lengths
barleycorn 1|3 UKinch # Given in Realm of Measure as the
# difference between successive shoe sizes
nail 1|16 UKyard # Originally the width of the thumbnail,
# or 1|16 ft. This took on the general
# meaning of 1|16 and settled on the
# nail of a yard or 1|16 yards as its
# final value. [12]
pole 16.5 UKft # This was 15 Saxon feet, the Saxon
rope 20 UKft # foot (aka northern foot) being longer
englishell 45 UKinch
flemishell 27 UKinch
ell englishell # supposed to be measure from elbow to
# fingertips
span 9 UKinch # supposed to be distance from thumb
# to pinky with full hand extension
goad 4.5 UKft # used for cloth, possibly named after the
# stick used for prodding animals.
# misc obscure British units
hide 120 acre # English unit of land area dating to the 7th
# century, originally the amount of land
# that a single plowman could cultivate,
# which varied from 60-180 acres regionally.
# Standardized at Normon conquest.
virgate 1|4 hide
nook 1|2 virgate
rood furlong rod # Area of a strip a rod by a furlong
englishcarat troyounce/151.5 # Originally intended to be 4 grain
# but this value ended up being
# used in the London diamond market
mancus 2 oz
mast 2.5 lb
nailkeg 100 lbs
basebox 31360 in^2 # Used in metal plating
# alternate spellings
metre meter
gramme gram
litre liter
dioptre diopter
aluminium aluminum
sulphur sulfur
#
# Units derived the human body (may not be very accurate)
#
geometricpace 5 ft # distance between points where the same
# foot hits the ground
pace 2.5 ft # distance between points where alternate
# feet touch the ground
USmilitarypace 30 in # United States official military pace
USdoubletimepace 36 in # United States official doubletime pace
fingerbreadth 7|8 in # The finger is defined as either the width
fingerlength 4.5 in # or length of the finger
finger fingerbreadth
palmwidth hand # The palm is a unit defined as either the width
palmlength 8 in # or the length of the hand
hand 4 inch # width of hand
shaftment 6 inch # Distance from tip of outstretched thumb to the
# opposite side of the palm of the hand. The
# ending -ment is from the old English word
# for hand. [18]
smoot 5 ft + 7 in # Created as part of an MIT fraternity prank.
# In 1958 Oliver Smoot was used to measure
# the length of the Harvard Bridge, which was
# marked off in Smoot lengths. These
# markings have been maintained on the bridge
# since then and repainted by subsequent
# incoming fraternity members. During a
# bridge renovation the new sidewalk was
# scored every Smoot rather than at the
# customary 6 ft spacing.
#
# Cooking measures
#
# Common abbreviations
tbl tablespoon
tbsp tablespoon
tblsp tablespoon
Tb tablespoon
tsp teaspoon
saltspoon 1|4 tsp
# US measures
uscup 8 usfloz
ustablespoon 1|16 uscup
usteaspoon 1|3 ustablespoon
ustbl ustablespoon
ustbsp ustablespoon
ustblsp ustablespoon
ustsp usteaspoon
metriccup 250 ml
stickbutter 1|4 lb # Butter in the USA is sold in one
# pound packages that contain four
# individually wrapped pieces. The
# pieces are marked into tablespoons,
# making it possible to measure out
# butter by volume by slicing the
# butter.
legalcup 240 ml # The cup used on nutrition labeling
legaltablespoon 1|16 legalcup
legaltbsp legaltablespoon
# Scoop size. Ice cream scoops in the US are marked with numbers
# indicating the number of scoops requird to fill a US quart.
scoop(n) units=[1;cup] domain=[4,100] range=[0.04,1] \
32 usfloz / n ; 32 usfloz / scoop
# US can sizes.
number1can 10 usfloz
number2can 19 usfloz
number2.5can 3.5 uscups
number3can 4 uscups
number5can 7 uscups
number10can 105 usfloz
# British measures
brcup 1|2 brpint
brteacup 1|3 brpint
brtablespoon 15 ml # Also 5|8 brfloz, approx 17.7 ml
brteaspoon 1|3 brtablespoon # Also 1|4 brtablespoon
brdessertspoon 2 brteaspoon
dessertspoon brdessertspoon
dsp dessertspoon
brtsp brteaspoon
brtbl brtablespoon
brtbsp brtablespoon
brtblsp brtablespoon
# Australian
australiatablespoon 20 ml
austbl australiatablespoon
austbsp australiatablespoon
austblsp australiatablespoon
australiateaspoon 1|4 australiatablespoon
austsp australiateaspoon
# Italian
etto 100 g # Used for buying items like meat and
etti etto # cheese.
# Chinese
catty 0.5 kg
oldcatty 4|3 lbs # Before metric conversion.
tael 1|16 oldcatty # Should the tael be defined both ways?
mace 0.1 tael
oldpicul 100 oldcatty
picul 100 catty # Chinese usage
# Indian
seer 14400 grain # British Colonial standard
ser seer
maund 40 seer
pakistanseer 1 kg
pakistanmaund 40 pakistanseer
chittak 1|16 seer
tola 1|5 chittak
ollock 1|4 liter # Is this right?
# Japanese
japancup 200 ml
# densities of cooking ingredients from The Cake Bible by Rose Levy Beranbaum
# so you can convert '2 cups sugar' to grams, for example, or in the other
# direction grams could be converted to 'cup flour_scooped'.
butter 8 oz/uscup
butter_clarified 6.8 oz/uscup
cocoa_butter 9 oz/uscup
shortening 6.75 oz/uscup # vegetable shortening
oil 7.5 oz/uscup
cakeflour_sifted 3.5 oz/uscup # The density of flour depends on the
cakeflour_spooned 4 oz/uscup # measuring method. "Scooped", or
cakeflour_scooped 4.5 oz/uscup # "dip and sweep" refers to dipping a
flour_sifted 4 oz/uscup # measure into a bin, and then sweeping
flour_spooned 4.25 oz/uscup # the excess off the top. "Spooned"
flour_scooped 5 oz/uscup # means to lightly spoon into a measure
breadflour_sifted 4.25 oz/uscup # and then sweep the top. Sifted means
breadflour_spooned 4.5 oz/uscup # sifting the flour directly into a
breadflour_scooped 5.5 oz/uscup # measure and then sweeping the top.
cornstarch 120 grams/uscup
dutchcocoa_sifted 75 g/uscup # These are for Dutch processed cocoa
dutchcocoa_spooned 92 g/uscup
dutchcocoa_scooped 95 g/uscup
cocoa_sifted 75 g/uscup # These are for nonalkalized cocoa
cocoa_spooned 82 g/uscup
cocoa_scooped 95 g/uscup
heavycream 232 g/uscup
milk 242 g/uscup
sourcream 242 g/uscup
molasses 11.25 oz/uscup
cornsyrup 11.5 oz/uscup
honey 11.75 oz/uscup
sugar 200 g/uscup
powdered_sugar 4 oz/uscup
brownsugar_light 217 g/uscup # packed
brownsugar_dark 239 g/uscup
baking_powder 4.6 grams / ustsp
salt 6 g / ustsp
koshersalt 2.8 g / ustsp # Diamond Crystal kosher salt
koshersalt_morton 4.8 g / ustsp # Morton kosher salt
# Values are from the nutrition info
# on the packages
# Egg weights and volumes for a USA large egg
egg 50 grams # without shell
eggwhite 30 grams
eggyolk 18.6 grams
eggvolume 3 ustablespoons + 1|2 ustsp
eggwhitevolume 2 ustablespoons
eggyolkvolume 3.5 ustsp
# Alcohol density
ethanoldensity 0.7893 g/cm^3 # From CRC Handbook, 91st Edition
alcoholdensity ethanoldensity
#
# Density measures. Density has traditionally been measured on a variety of
# bizarre nonlinear scales.
#
# Density of a sugar syrup is frequently measured in candy making procedures.
# In the USA the boiling point of the syrup is measured. Some recipes instead
# specify the density using degrees Baume. Conversion between degrees Baume
# and the boiling point measure has proved elusive. This table appeared in one
# text, and provides a fragmentary relationship to the concentration.
#
# temp(C) conc (%)
# 100 30
# 101 40
# 102 50
# 103 60
# 106 70
# 112 80
# 123 90
# 140 95
# 151 97
# 160 98.2
# 166 99.5
# 171 99.6
#
# The best source identified to date came from "Boiling point elevation of
# technical sugarcane solutions and its use in automatic pan boiling" by
# Michael Saska. International Sugar Journal, 2002, 104, 1247, pp 500-507.
#
# But I'm using equation (3) which is credited to Starzak and Peacock,
# "Water activity coefficient in aqueous solutions of sucrose--A comprehensive
# data analyzis. Zuckerindustrie, 122, 380-387. (I couldn't find this
# document.)
#
# Note that the range of validity is uncertain, but answers are in agreement
# with the above table all the way to 99.6.
#
# The original equation has a parameter for the boiling point of water, which
# of course varies with altitude. It also includes various other model
# parameters. The input is the molar concentration of sucrose in the solution,
# (moles sucrose) / (total moles).
#
# Bsp 3797.06 degC
# Csp 226.28 degC
# QQ -17638 J/mol
# asp -1.0038
# bsp -0.24653
# tbw 100 degC # boiling point of water
# sugar_bpe_orig(x) ((1-QQ/R Bsp * x^2 (1+asp x + bsp x^2) (tbw + Csp) \
# /(tbw+stdtemp)) / (1+(tbw + Csp)/Bsp *ln(1-x))-1) * (tbw + Csp)
#
# To convert mass concentration (brix) to molar concentration
#
# sc(x) (x / 342.3) / (( x/342.3) + (100-x)/18.02); \
# 100 sc 342.3|18.02 / (sc (342.3|18.02-1)+1)
#
# Here is a simplfied version of this equation where the temperature of boiling
# water has been fixed at 100 degrees Celcius and the argument is now the
# concentration (brix).
#
# sugar_bpe(x) ((1+ 0.48851085 * sc(x)^2 (1+ -1.0038 sc(x) + -0.24653 sc(x)^2)) \
# / (1+0.08592964 ln(1-sc(x)))-1) 326.28 K
#
#
# The formula is not invertible, so to implement it in units we unfortunately
# must turn it into a table.
# This table gives the boiling point elevation as a function of the sugar syrup
# concentration expressed as a percentage.
sugar_conc_bpe[K] \
0 0.0000 5 0.0788 10 0.1690 15 0.2729 20 0.3936 25 0.5351 \
30 0.7027 35 0.9036 40 1.1475 42 1.2599 44 1.3825 46 1.5165 \
48 1.6634 50 1.8249 52 2.0031 54 2.2005 56 2.4200 58 2.6651 \
60 2.9400 61 3.0902 62 3.2499 63 3.4198 64 3.6010 65 3.7944 \
66 4.0012 67 4.2227 68 4.4603 69 4.7156 70 4.9905 71 5.2870 \
72 5.6075 73 5.9546 74 6.3316 75 6.7417 76 7.1892 77 7.6786 \
78.0 8.2155 79.0 8.8061 80.0 9.4578 80.5 9.8092 81.0 10.1793 \
81.5 10.5693 82.0 10.9807 82.5 11.4152 83.0 11.8743 83.5 12.3601 \
84.0 12.8744 84.5 13.4197 85.0 13.9982 85.5 14.6128 86.0 15.2663 \
86.5 15.9620 87.0 16.7033 87.5 17.4943 88.0 18.3391 88.5 19.2424 \
89.0 20.2092 89.5 21.2452 90.0 22.3564 90.5 23.5493 91.0 24.8309 \
91.5 26.2086 92.0 27.6903 92.5 29.2839 93.0 30.9972 93.5 32.8374 \
94.0 34.8104 94.5 36.9195 95.0 39.1636 95.5 41.5348 96.0 44.0142 \
96.5 46.5668 97.0 49.1350 97.5 51.6347 98.0 53.9681 98.1 54.4091 \
98.2 54.8423 98.3 55.2692 98.4 55.6928 98.5 56.1174 98.6 56.5497 \
98.7 56.9999 98.8 57.4828 98.9 58.0206 99.0 58.6455 99.1 59.4062 \
99.2 60.3763 99.3 61.6706 99.4 63.4751 99.5 66.1062 99.6 70.1448 \
99.7 76.7867
# Using the brix table we can use this to produce a mapping from boiling point
# to density which makes all of the units interconvertible. Because the brix
# table stops at 95 this approach works up to a boiling point elevation of 39 K
# or a boiling point of 139 C / 282 F, which is the "soft crack" stage in candy
# making. The "hard crack" stage continues up to 310 F.
# Boiling point elevation
sugar_bpe(T) units=[K;g/cm^3] domain=[0,39.1636] range=[0.99717,1.5144619] \
brix(~sugar_conc_bpe(T)); sugar_conc_bpe(~brix(sugar_bpe))
# Absolute boiling point (produces an absolute temperature)
sugar_bp(T) units=[K;g/cm^3] domain=[373.15,412.3136] \
range=[0.99717,1.5144619] \
brix(~sugar_conc_bpe(T-tempC(100))) ;\
sugar_conc_bpe(~brix(sugar_bp))+tempC(100)
# In practice dealing with the absolute temperature is annoying because it is
# not possible to convert to a nested function, so you're stuck retyping the
# absolute temperature in Kelvins to convert to celsius or Fahrenheit. To
# prevent this we supply definitions that build in the temperature conversion
# and produce results in the Fahrenheit and Celcius scales. So using these
# measures, to convert 46 degrees Baume to a Fahrenheit boiling point:
#
# You have: baume(45)
# You want: sugar_bpF
# 239.05647
#
sugar_bpF(T) units=[1;g/cm^3] domain=[212,282.49448] range=[0.99717,1.5144619]\
brix(~sugar_conc_bpe(tempF(T)+-tempC(100))) ;\
~tempF(sugar_conc_bpe(~brix(sugar_bpF))+tempC(100))
sugar_bpC(T) units=[1;g/cm^3] domain=[100,139.1636] range=[0.99717,1.5144619]\
brix(~sugar_conc_bpe(tempC(T)+-tempC(100))) ;\
~tempC(sugar_conc_bpe(~brix(sugar_bpC))+tempC(100))
# Degrees Baume is used in European recipes to specify the density of a sugar
# syrup. An entirely different definition is used for densities below
# 1 g/cm^3. An arbitrary constant appears in the definition. This value is
# equal to 145 in the US, but was according to [], the old scale used in
# Holland had a value of 144, and the new scale or Gerlach scale used 146.78.
baumeconst 145 # US value
baume(d) units=[1;g/cm^3] domain=[0,145) range=[1,) \
(baumeconst/(baumeconst+-d)) g/cm^3 ; \
(baume+((-g)/cm^3)) baumeconst / baume
# It's not clear if this value was ever used with negative degrees.
twaddell(x) units=[1;g/cm^3] domain=[-200,) range=[0,) \
(1 + 0.005 x) g / cm^3 ; \
200 (twaddell / (g/cm^3) +- 1)
# The degree quevenne is a unit for measuring the density of milk.
# Similarly it's unclear if negative values were allowed here.
quevenne(x) units=[1;g/cm^3] domain=[-1000,) range=[0,) \
(1 + 0.001 x) g / cm^3 ; \
1000 (quevenne / (g/cm^3) +- 1)
# Degrees brix measures sugar concentration by weigh as a percentage, so a
# solution that is 3 degrees brix is 3% sugar by weight. This unit was named
# after Adolf Brix who invented a hydrometer that read this percentage
# directly. This data is from Table 114 of NIST Circular 440, "Polarimetry,
# Saccharimetry and the Sugars". It gives apparent specific gravity at 20
# degrees Celsius of various sugar concentrations. As rendered below this
# data is converted to apparent density at 20 degrees Celsius using the
# density figure for water given in the same NIST reference. They use the
# word "apparent" to refer to measurements being made in air with brass
# weights rather than vacuum.
brix[0.99717g/cm^3]\
0 1.00000 1 1.00390 2 1.00780 3 1.01173 4 1.01569 5 1.01968 \
6 1.02369 7 1.02773 8 1.03180 9 1.03590 10 1.04003 11 1.04418 \
12 1.04837 13 1.05259 14 1.05683 15 1.06111 16 1.06542 17 1.06976 \
18 1.07413 19 1.07853 20 1.08297 21 1.08744 22 1.09194 23 1.09647 \
24 1.10104 25 1.10564 26 1.11027 27 1.11493 28 1.11963 29 1.12436 \
30 1.12913 31 1.13394 32 1.13877 33 1.14364 34 1.14855 35 1.15350 \
36 1.15847 37 1.16349 38 1.16853 39 1.17362 40 1.17874 41 1.18390 \
42 1.18910 43 1.19434 44 1.19961 45 1.20491 46 1.21026 47 1.21564 \
48 1.22106 49 1.22652 50 1.23202 51 1.23756 52 1.24313 53 1.24874 \
54 1.25439 55 1.26007 56 1.26580 57 1.27156 58 1.27736 59 1.28320 \
60 1.28909 61 1.29498 62 1.30093 63 1.30694 64 1.31297 65 1.31905 \
66 1.32516 67 1.33129 68 1.33748 69 1.34371 70 1.34997 71 1.35627 \
72 1.36261 73 1.36900 74 1.37541 75 1.38187 76 1.38835 77 1.39489 \
78 1.40146 79 1.40806 80 1.41471 81 1.42138 82 1.42810 83 1.43486 \
84 1.44165 85 1.44848 86 1.45535 87 1.46225 88 1.46919 89 1.47616 \
90 1.48317 91 1.49022 92 1.49730 93 1.50442 94 1.51157 95 1.51876
# Density measure invented by the American Petroleum Institute. Lighter
# petroleum products are more valuable, and they get a higher API degree.
#
# The intervals of range and domain should be open rather than closed.
#
apidegree(x) units=[1;g/cm^3] domain=[-131.5,) range=[0,) \
141.5 g/cm^3 / (x+131.5) ; \
141.5 (g/cm^3) / apidegree + (-131.5)
#
# Units derived from imperial system
#
ouncedal oz ft / s^2 # force which accelerates an ounce
# at 1 ft/s^2
poundal lb ft / s^2 # same thing for a pound
tondal longton ft / s^2 # and for a ton
pdl poundal
osi ounce force / inch^2 # used in aviation
psi pound force / inch^2
psia psi # absolute pressure
# Note that gauge pressure can be given
# using the gaugepressure() and
# psig() nonlinear unit definitions
tsi ton force / inch^2
reyn psi sec
slug lbf s^2 / ft
slugf slug force
slinch lbf s^2 / inch # Mass unit derived from inch second
slinchf slinch force # pound-force system. Used in space
# applications where in/sec^2 was a
# natural acceleration measure.
geepound slug
lbf lb force
tonf ton force
lbm lb
kip 1000 lbf # from kilopound
ksi kip / in^2
mil 0.001 inch
thou 0.001 inch
tenth 0.0001 inch # one tenth of one thousandth of an inch
millionth 1e-6 inch # one millionth of an inch
circularinch 1|4 pi in^2 # area of a one-inch diameter circle
circleinch circularinch # A circle with diameter d inches has
# an area of d^2 circularinches
cylinderinch circleinch inch # Cylinder h inch tall, d inches diameter
# has volume d^2 h cylinder inches
circularmil 1|4 pi mil^2 # area of one-mil diameter circle
cmil circularmil
cental 100 pound
centner cental
caliber 0.01 inch # for measuring bullets
duty ft lbf
celo ft / s^2
jerk ft / s^3
australiapoint 0.01 inch # The "point" is used to measure rainfall
# in Australia
sabin ft^2 # Measure of sound absorption equal to the
# absorbing power of one square foot of
# a perfectly absorbing material. The
# sound absorptivity of an object is the
# area times a dimensionless
# absorptivity coefficient.
standardgauge 4 ft + 8.5 in # Standard width between railroad track
flag 5 ft^2 # Construction term referring to sidewalk.
rollwallpaper 30 ft^2 # Area of roll of wall paper
fillpower in^3 / ounce # Density of down at standard pressure.
# The best down has 750-800 fillpower.
pinlength 1|16 inch # A #17 pin is 17/16 in long in the USA.
buttonline 1|40 inch # The line was used in 19th century USA
# to measure width of buttons.
beespace 1|4 inch # Bees will fill any space that is smaller
# than the bee space and leave open
# spaces that are larger. The size of
# the space varies with species.
diamond 8|5 ft # Marking on US tape measures that is
# useful to carpenters who wish to place
# five studs in an 8 ft distance. Note
# that the numbers appear in red every
# 16 inches as well, giving six
# divisions in 8 feet.
retmaunit 1.75 in # Height of rack mountable equipment.
U retmaunit # Equipment should be 1|32 inch narrower
RU U # than its U measurement indicates to
# allow for clearance, so 4U=(6+31|32)in
# RETMA stands for the former name of
# the standardizing organization, Radio
# Electronics Television Manufacturers
# Association. This organization is now
# called the Electronic Industries
# Alliance (EIA) and the rack standard
# is specified in EIA RS-310-D.
count per pound # For measuring the size of shrimp
#
# Other units of work, energy, power, etc
#
ENERGY joule
WORK joule
# Calorie: approximate energy to raise a gram of water one degree celsius
calorie cal_th # Default is the thermochemical calorie
cal calorie
calorie_th 4.184 J # Thermochemical calorie, defined in 1930
thermcalorie calorie_th # by Frederick Rossini as 4.1833 J to
cal_th calorie_th # avoid difficulties associated with the
# uncertainty in the heat capacity of
# water. In 1948 the value of the joule
# was changed, so the thermochemical
# calorie was redefined to 4.184 J.
# This kept the energy measured by this
# unit the same.
calorie_IT 4.1868 J # International (Steam) Table calorie,
cal_IT calorie_IT # defined in 1929 as watt-hour/860 or
# equivalently 180|43 joules. At this
# time the international joule had a
# different value than the modern joule,
# and the values were different in the
# USA and in Europe. In 1956 at the
# Fifth International Conference on
# Properties of Steam the exact
# definition given here was adopted.
calorie_15 4.18580 J # Energy to go from 14.5 to 15.5 degC
cal_15 calorie_15
calorie_fifteen cal_15
calorie_20 4.18190 J # Energy to go from 19.5 to 20.5 degC
cal_20 calorie_20
calorie_twenty calorie_20
cal_mean 4.19002 J # 1|100 energy to go from 0 to 100 degC
Calorie kilocalorie # the food Calorie
thermie 1e6 cal_15 # Heat required to raise the
# temperature of a tonne of
# water from 14.5 to 15.5 degC.
# btu definitions: energy to raise a pound of water 1 degF
btu btu_IT # International Table BTU is the default
britishthermalunit btu
btu_IT cal_IT lb degF / gram K
btu_th cal_th lb degF / gram K
btu_mean cal_mean lb degF / gram K
quad quadrillion btu
ECtherm 1.05506e8 J # Exact definition, close to 1e5 btu
UStherm 1.054804e8 J # Exact definition
therm UStherm
# Water latent heat from [23]
water_fusion_heat 6.01 kJ/mol / (18.015 g/mol) # At 0 deg C
water_vaporization_heat 2256.4 J/g # At saturation, 100 deg C, 101.42 kPa
# Specific heat capacities of various substances
specificheat_water calorie / g K
water_specificheat specificheat_water
# Values from www.engineeringtoolbox.com/specific-heat-metals-d_152.html
specificheat_aluminum 0.91 J/g K
specificheat_antimony 0.21 J/g K
specificheat_barium 0.20 J/g K
specificheat_beryllium 1.83 J/g K
specificheat_bismuth 0.13 J/g K
specificheat_cadmium 0.23 J/g K
specificheat_cesium 0.24 J/g K
specificheat_chromium 0.46 J/g K
specificheat_cobalt 0.42 J/g K
specificheat_copper 0.39 J/g K
specificheat_gallium 0.37 J/g K
specificheat_germanium 0.32 J/g K
specificheat_gold 0.13 J/g K
specificheat_hafnium 0.14 J/g K
specificheat_indium 0.24 J/g K
specificheat_iridium 0.13 J/g K
specificheat_iron 0.45 J/g K
specificheat_lanthanum 0.195 J/g K
specificheat_lead 0.13 J/g K
specificheat_lithium 3.57 J/g K
specificheat_lutetium 0.15 J/g K
specificheat_magnesium 1.05 J/g K
specificheat_manganese 0.48 J/g K
specificheat_mercury 0.14 J/g K
specificheat_molybdenum 0.25 J/g K
specificheat_nickel 0.44 J/g K
specificheat_osmium 0.13 J/g K
specificheat_palladium 0.24 J/g K
specificheat_platinum 0.13 J/g K
specificheat_plutonum 0.13 J/g K
specificheat_potassium 0.75 J/g K
specificheat_rhenium 0.14 J/g K
specificheat_rhodium 0.24 J/g K
specificheat_rubidium 0.36 J/g K
specificheat_ruthenium 0.24 J/g K
specificheat_scandium 0.57 J/g K
specificheat_selenium 0.32 J/g K
specificheat_silicon 0.71 J/g K
specificheat_silver 0.23 J/g K
specificheat_sodium 1.21 J/g K
specificheat_strontium 0.30 J/g K
specificheat_tantalum 0.14 J/g K
specificheat_thallium 0.13 J/g K
specificheat_thorium 0.13 J/g K
specificheat_tin 0.21 J/g K
specificheat_titanium 0.54 J/g K
specificheat_tungsten 0.13 J/g K
specificheat_uranium 0.12 J/g K
specificheat_vanadium 0.39 J/g K
specificheat_yttrium 0.30 J/g K
specificheat_zinc 0.39 J/g K
specificheat_zirconium 0.27 J/g K
specificheat_ethanol 2.3 J/g K
specificheat_ammonia 4.6 J/g K
specificheat_freon 0.91 J/g K # R-12 at 0 degrees Fahrenheit
specificheat_gasoline 2.22 J/g K
specificheat_iodine 2.15 J/g K
specificheat_oliveoil 1.97 J/g K
# en.wikipedia.org/wiki/Heat_capacity#Table_of_specific_heat_capacities
specificheat_hydrogen 14.3 J/g K
specificheat_helium 5.1932 J/g K
specificheat_argon 0.5203 J/g K
specificheat_tissue 3.5 J/g K
specificheat_diamond 0.5091 J/g K
specificheat_granite 0.79 J/g K
specificheat_graphite 0.71 J/g K
specificheat_ice 2.11 J/g K
specificheat_asphalt 0.92 J/g K
specificheat_brick 0.84 J/g K
specificheat_concrete 0.88 J/g K
specificheat_glass_silica 0.84 J/g K
specificheat_glass_flint 0.503 J/g K
specificheat_glass_pyrex 0.753 J/g K
specificheat_gypsum 1.09 J/g K
specificheat_marble 0.88 J/g K
specificheat_sand 0.835 J/g K
specificheat_soil 0.835 J/g K
specificheat_wood 1.7 J/g K
specificheat_sucrose 1.244 J/g K #www.sugartech.co.za/heatcapacity/index.php
# Energy densities of various fuels
#
# Most of these fuels have varying compositions or qualities and hence their
# actual energy densities vary. These numbers are hence only approximate.
#
# E1. http://bioenergy.ornl.gov/papers/misc/energy_conv.html
# E2. http://www.aps.org/policy/reports/popa-reports/energy/units.cfm
# E3. http://www.ior.com.au/ecflist.html
tonoil 1e10 cal_IT # Ton oil equivalent. A conventional
# value for the energy released by
toe tonoil # burning one metric ton of oil. [18,E2]
# Note that energy per mass of petroleum
# products is fairly constant.
# Variations in volumetric energy
# density result from variations in the
# density (kg/m^3) of different fuels.
# This definition is given by the
# IEA/OECD.
toncoal 7e9 cal_IT # Energy in metric ton coal from [18].
# This is a nominal value which
# is close to the heat content
# of coal used in the 1950's
barreloil 5.8 Mbtu # Conventional value for barrel of crude
# oil [E2]. Actual range is 5.6 - 6.3.
naturalgas_HHV 1027 btu/ft3 # Energy content of natural gas. HHV
naturalgas_LHV 930 btu/ft3 # is for Higher Heating Value and
naturalgas naturalgas_HHV # includes energy from condensation
# combustion products. LHV is for Lower
# Heating Value and excludes these.
# American publications typically report
# HHV whereas European ones report LHV.
charcoal 30 GJ/tonne
woodenergy_dry 20 GJ/tonne # HHV, a cord weights about a tonne
woodenergy_airdry 15 GJ/tonne # 20% moisture content
coal_bituminous 27 GJ / tonne
coal_lignite 15 GJ / tonne
coal_US 22 GJ / uston # Average for US coal (short ton), 1995
ethanol_HHV 84000 btu/usgallon
ethanol_LHV 75700 btu/usgallon
diesel 130500 btu/usgallon
gasoline_LHV 115000 btu/usgallon
gasoline_HHV 125000 btu/usgallon
gasoline gasoline_HHV
heating 37.3 MJ/liter
fueloil 39.7 MJ/liter # low sulphur
propane 93.3 MJ/m^3
butane 124 MJ/m^3
# These values give total energy from uranium fission. Actual efficiency
# of nuclear power plants is around 30%-40%. Note also that some reactors
# use enriched uranium around 3% U-235. Uranium during processing or use
# may be in a compound of uranium oxide or uranium hexafluoride, in which
# case the energy density would be lower depending on how much uranium is
# in the compound.
uranium_pure 200 MeV avogadro / (235.0439299 g/mol) # Pure U-235
uranium_natural 0.7% uranium_pure # Natural uranium: 0.7% U-235
# Celsius heat unit: energy to raise a pound of water 1 degC
celsiusheatunit cal lb degC / gram K
chu celsiusheatunit
POWER watt
# "Apparent" average power in an AC circuit, the product of rms voltage
# and rms current, equal to the true power in watts when voltage and
# current are in phase. In a DC circuit, always equal to the true power.
VA volt ampere
kWh kilowatt hour
# The horsepower is supposedly the power of one horse pulling. Obviously
# different people had different horses.
horsepower 550 foot pound force / sec # Invented by James Watt
mechanicalhorsepower horsepower
hp horsepower
metrichorsepower 75 kilogram force meter / sec # PS=Pferdestaerke in
electrichorsepower 746 W # Germany
boilerhorsepower 9809.50 W
waterhorsepower 746.043 W
brhorsepower 745.70 W
donkeypower 250 W
chevalvapeur metrichorsepower
#
# Heat Transfer
#
# Thermal conductivity, K, measures the rate of heat transfer across
# a material. The heat transfered is
# Q = K dT A t / L
# where dT is the temperature difference across the material, A is the
# cross sectional area, t is the time, and L is the length (thickness).
# Thermal conductivity is a material property.
THERMAL_CONDUCTIVITY POWER / AREA (TEMPERATURE_DIFFERENCE/LENGTH)
THERMAL_RESISTIVITY 1/THERMAL_CONDUCTIVITY
# Thermal conductance is the rate at which heat flows across a given
# object, so the area and thickness have been fixed. It depends on
# the size of the object and is hence not a material property.
THERMAL_CONDUCTANCE POWER / TEMPERATURE_DIFFERENCE
THERMAL_RESISTANCE 1/THERMAL_CONDUCTANCE
# Thermal admittance is the rate of heat flow per area across an
# object whose thickness has been fixed. Its reciprocal, thermal
# insulation, is used to for measuring the heat transfer per area
# of sheets of insulation or cloth that are of specified thickness.
THERMAL_ADMITTANCE THERMAL_CONDUCTIVITY / LENGTH
THERMAL_INSULANCE THERMAL_RESISTIVITY LENGTH
THERMAL_INSULATION THERMAL_RESISTIVITY LENGTH
Rvalue degF ft^2 hr / btu
Uvalue 1/Rvalue
europeanUvalue watt / m^2 K
RSI degC m^2 / W
clo 0.155 degC m^2 / W # Supposed to be the insulance
# required to keep a resting person
# comfortable indoors. The value
# given is from NIST and the CRC,
# but [5] gives a slightly different
# value of 0.875 ft^2 degF hr / btu.
tog 0.1 degC m^2 / W # Also used for clothing.
# The bel was defined by engineers of Bell Laboratories to describe the
# reduction in audio level over a length of one mile. It was originally
# called the transmission unit (TU) but was renamed around 1923 to honor
# Alexander Graham Bell. The bel proved inconveniently large so the decibel
# has become more common. The decibel is dimensionless since it reports a
# ratio, but it is used in various contexts to report a signal's power
# relative to some reference level.
bel(x) units=[1;1] range=(0,) 10^(x); log(bel) # Basic bel definition
decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel) # Basic decibel
dB() decibel # Abbreviation
dBW(x) units=[1;W] range=(0,) dB(x) W ; ~dB(dBW/W) # Reference = 1 W
dBk(x) units=[1;W] range=(0,) dB(x) kW ; ~dB(dBk/kW) # Reference = 1 kW
dBf(x) units=[1;W] range=(0,) dB(x) fW ; ~dB(dBf/fW) # Reference = 1 fW
dBm(x) units=[1;W] range=(0,) dB(x) mW ; ~dB(dBm/mW) # Reference = 1 mW
dBmW(x) units=[1;W] range=(0,) dBm(x) ; ~dBm(dBmW) # Reference = 1 mW
dBJ(x) units=[1;J] range=(0,) dB(x) J; ~dB(dBJ/J) # Energy relative
# to 1 joule. Used for power spectral
# density since W/Hz = J
# When used to measure amplitude, voltage, or current the signal is squared
# because power is proportional to the square of these measures. The root
# mean square (RMS) voltage is typically used with these units.
dBV(x) units=[1;V] range=(0,) dB(0.5 x) V;~dB(dBV^2 / V^2) # Reference = 1 V
dBmV(x) units=[1;V] range=(0,) dB(0.5 x) mV;~dB(dBmV^2/mV^2)# Reference = 1 mV
dBuV(x) units=[1;V] range=(0,) dB(0.5 x) microV ; ~dB(dBuV^2 / microV^2)
# Reference = 1 microvolt
# Referenced to the voltage that causes 1 mW dissipation in a 600 ohm load.
# Originally defined as dBv but changed to prevent confusion with dBV.
# The "u" is for unloaded.
dBu(x) units=[1;V] range=(0,) dB(0.5 x) sqrt(mW 600 ohm) ; \
~dB(dBu^2 / mW 600 ohm)
dBv(x) units=[1;V] range=(0,) dBu(x) ; ~dBu(dBv) # Synonym for dBu
# Measurements for sound in air, referenced to the threshold of human hearing
# Note that sound in other media typically uses 1 micropascal as a reference
# for sound pressure. Units dBA, dBB, dBC, refer to different frequency
# weightings meant to approximate the human ear's response.
dBSPL(x) units=[1;Pa] range=(0,) dB(0.5 x) 20 microPa ; \
~dB(dBSPL^2 / (20 microPa)^2) # pressure
dBSIL(x) units=[1;W/m^2] range=(0,) dB(x) 1e-12 W/m^2; \
~dB(dBSIL / (1e-12 W/m^2)) # intensity
dBSWL(x) units=[1;W] range=(0,) dB(x) 1e-12 W; ~dB(dBSWL/1e-12 W)
# Misc other measures
ENTROPY ENERGY / TEMPERATURE
clausius 1e3 cal/K # A unit of physical entropy
langley thermcalorie/cm^2 # Used in radiation theory
poncelet 100 kg force m / s
tonrefrigeration uston 144 btu / lb day # One ton refrigeration is
# the rate of heat extraction required
# turn one ton of water to ice in
# a day. Ice is defined to have a
# latent heat of 144 btu/lb.
tonref tonrefrigeration
refrigeration tonref / ton
frigorie 1000 cal_15 # Used in refrigeration engineering.
tnt 1e9 cal_th / ton# So you can write tons tnt. This
# is a defined, not measured, value.
airwatt 8.5 (ft^3/min) inH2O # Measure of vacuum power as
# pressure times air flow.
#
# Permeability: The permeability or permeance, n, of a substance determines
# how fast vapor flows through the substance. The formula W = n A dP
# holds where W is the rate of flow (in mass/time), n is the permeability,
# A is the area of the flow path, and dP is the vapor pressure difference.
#
perm_0C grain / hr ft^2 inHg
perm_zero perm_0C
perm_0 perm_0C
perm perm_0C
perm_23C grain / hr ft^2 in Hg23C
perm_twentythree perm_23C
#
# Counting measures
#
pair 2
brace 2
nest 3 # often used for items like bowls that
# nest together
hattrick 3 # Used in sports, especially cricket and ice
# hockey to report the number of goals.
dicker 10
dozen 12
bakersdozen 13
score 20
flock 40
timer 40
shock 60
toncount 100 # Used in sports in the UK
longhundred 120 # From a germanic counting system
gross 144
greatgross 12 gross
tithe 1|10 # From Anglo-Saxon word for tenth
# Paper counting measure
shortquire 24
quire 25
shortream 480
ream 500
perfectream 516
bundle 2 reams
bale 5 bundles
#
# Paper measures
#
# USA paper sizes
lettersize 8.5 inch 11 inch
legalsize 8.5 inch 14 inch
ledgersize 11 inch 17 inch
executivesize 7.25 inch 10.5 inch
Apaper 8.5 inch 11 inch
Bpaper 11 inch 17 inch
Cpaper 17 inch 22 inch
Dpaper 22 inch 34 inch
Epaper 34 inch 44 inch
# Correspondence envelope sizes. #10 is the standard business
# envelope in the USA.
envelope6_25size 3.5 inch 6 inch
envelope6_75size 3.625 inch 6.5 inch
envelope7size 3.75 inch 6.75 inch
envelope7_75size 3.875 inch 7.5 inch
envelope8_625size 3.625 inch 8.625 inch
envelope9size 3.875 inch 8.875 inch
envelope10size 4.125 inch 9.5 inch
envelope11size 4.5 inch 10.375 inch
envelope12size 4.75 inch 11 inch
envelope14size 5 inch 11.5 inch
envelope16size 6 inch 12 inch
# Announcement envelope sizes (no relation to metric paper sizes like A4)
envelopeA1size 3.625 inch 5.125 inch # same as 4bar
envelopeA2size 4.375 inch 5.75 inch
envelopeA6size 4.75 inch 6.5 inch
envelopeA7size 5.25 inch 7.25 inch
envelopeA8size 5.5 inch 8.125 inch
envelopeA9size 5.75 inch 8.75 inch
envelopeA10size 6 inch 9.5 inch
# Baronial envelopes
envelope4bar 3.625 inch 5.125 inch # same as A1
envelope5_5bar 4.375 inch 5.75 inch
envelope6bar 4.75 inch 6.5 inch
# Coin envelopes
envelope1baby 2.25 inch 3.5 inch # same as #1 coin
envelope00coin 1.6875 inch 2.75 inch
envelope1coin 2.25 inch 3.5 inch
envelope3coin 2.5 inch 4.25 inch
envelope4coin 3 inch 4.5 inch
envelope4_5coin 3 inch 4.875 inch
envelope5coin 2.875 inch 5.25 inch
envelope5_5coin 3.125 inch 5.5 inch
envelope6coin 3.375 inch 6 inch
envelope7coin 3.5 inch 6.5 inch
# The metric paper sizes are defined so that if a sheet is cut in half
# along the short direction, the result is two sheets which are
# similar to the original sheet. This means that for any metric size,
# the long side is close to sqrt(2) times the length of the short
# side. Each series of sizes is generated by repeated cuts in half,
# with the values rounded down to the nearest millimeter.
A0paper 841 mm 1189 mm # The basic size in the A series
A1paper 594 mm 841 mm # is defined to have an area of
A2paper 420 mm 594 mm # one square meter.
A3paper 297 mm 420 mm
A4paper 210 mm 297 mm
A5paper 148 mm 210 mm
A6paper 105 mm 148 mm
A7paper 74 mm 105 mm
A8paper 52 mm 74 mm
A9paper 37 mm 52 mm
A10paper 26 mm 37 mm
B0paper 1000 mm 1414 mm # The basic B size has an area
B1paper 707 mm 1000 mm # of sqrt(2) square meters.
B2paper 500 mm 707 mm
B3paper 353 mm 500 mm
B4paper 250 mm 353 mm
B5paper 176 mm 250 mm
B6paper 125 mm 176 mm
B7paper 88 mm 125 mm
B8paper 62 mm 88 mm
B9paper 44 mm 62 mm
B10paper 31 mm 44 mm
C0paper 917 mm 1297 mm # The basic C size has an area
C1paper 648 mm 917 mm # of sqrt(sqrt(2)) square meters.
C2paper 458 mm 648 mm
C3paper 324 mm 458 mm # Intended for envelope sizes
C4paper 229 mm 324 mm
C5paper 162 mm 229 mm
C6paper 114 mm 162 mm
C7paper 81 mm 114 mm
C8paper 57 mm 81 mm
C9paper 40 mm 57 mm
C10paper 28 mm 40 mm
# gsm (Grams per Square Meter), a sane, metric paper weight measure
gsm grams / meter^2
# In the USA, a collection of crazy historical paper measures are used. Paper
# is measured as a weight of a ream of that particular type of paper. This is
# sometimes called the "substance" or "basis" (as in "substance 20" paper).
# The standard sheet size or "basis size" varies depending on the type of
# paper. As a result, 20 pound bond paper and 50 pound text paper are actually
# about the same weight. The different sheet sizes were historically the most
# convenient for printing or folding in the different applications. These
# different basis weights are standards maintained by American Society for
# Testing Materials (ASTM) and the American Forest and Paper Association
# (AF&PA).
poundbookpaper lb / 25 inch 38 inch ream
lbbook poundbookpaper
poundtextpaper poundbookpaper
lbtext poundtextpaper
poundoffsetpaper poundbookpaper # For offset printing
lboffset poundoffsetpaper
poundbiblepaper poundbookpaper # Designed to be lightweight, thin,
lbbible poundbiblepaper # strong and opaque.
poundtagpaper lb / 24 inch 36 inch ream
lbtag poundtagpaper
poundbagpaper poundtagpaper
lbbag poundbagpaper
poundnewsprintpaper poundtagpaper
lbnewsprint poundnewsprintpaper
poundposterpaper poundtagpaper
lbposter poundposterpaper
poundtissuepaper poundtagpaper
lbtissue poundtissuepaper
poundwrappingpaper poundtagpaper
lbwrapping poundwrappingpaper
poundwaxingpaper poundtagpaper
lbwaxing poundwaxingpaper
poundglassinepaper poundtagpaper
lbglassine poundglassinepaper
poundcoverpaper lb / 20 inch 26 inch ream
lbcover poundcoverpaper
poundindexpaper lb / 25.5 inch 30.5 inch ream
lbindex poundindexpaper
poundindexbristolpaper poundindexpaper
lbindexbristol poundindexpaper
poundbondpaper lb / 17 inch 22 inch ream # Bond paper is stiff and
lbbond poundbondpaper # durable for repeated
poundwritingpaper poundbondpaper # filing, and it resists
lbwriting poundwritingpaper # ink penetration.
poundledgerpaper poundbondpaper
lbledger poundledgerpaper
poundcopypaper poundbondpaper
lbcopy poundcopypaper
poundblottingpaper lb / 19 inch 24 inch ream
lbblotting poundblottingpaper
poundblankspaper lb / 22 inch 28 inch ream
lbblanks poundblankspaper
poundpostcardpaper lb / 22.5 inch 28.5 inch ream
lbpostcard poundpostcardpaper
poundweddingbristol poundpostcardpaper
lbweddingbristol poundweddingbristol
poundbristolpaper poundweddingbristol
lbbristol poundbristolpaper
poundboxboard lb / 1000 ft^2
lbboxboard poundboxboard
poundpaperboard poundboxboard
lbpaperboard poundpaperboard
# When paper is marked in units of M, it means the weight of 1000 sheets of the
# given size of paper. To convert this to paper weight, divide by the size of
# the paper in question.
paperM lb / 1000
# In addition paper weight is reported in "caliper" which is simply the
# thickness of one sheet, typically in inches. Thickness is also reported in
# "points" where a point is 1|1000 inch. These conversions are supplied to
# convert these units roughly (using an approximate density) into the standard
# paper weight values.
pointthickness 0.001 in
paperdensity 0.8 g/cm^3 # approximate--paper densities vary!
papercaliper in paperdensity
paperpoint pointthickness paperdensity
#
# Printing
#
fournierpoint 0.1648 inch / 12 # First definition of the printers
# point made by Pierre Fournier who
# defined it in 1737 as 1|12 of a
# cicero which was 0.1648 inches.
olddidotpoint 1|72 frenchinch # François Ambroise Didot, one of
# a family of printers, changed
# Fournier's definition around 1770
# to fit to the French units then in
# use.
bertholdpoint 1|2660 m # H. Berthold tried to create a
# metric version of the didot point
# in 1878.
INpoint 0.4 mm # This point was created by a
# group directed by Fermin Didot in
# 1881 and is associated with the
# imprimerie nationale. It doesn't
# seem to have been used much.
germandidotpoint 0.376065 mm # Exact definition appears in DIN
# 16507, a German standards document
# of 1954. Adopted more broadly in
# 1966 by ???
metricpoint 3|8 mm # Proposed in 1977 by Eurograf
oldpoint 1|72.27 inch # The American point was invented
printerspoint oldpoint # by Nelson Hawks in 1879 and
texpoint oldpoint # dominates USA publishing.
# It was standardized by the American
# Typefounders Association at the
# value of 0.013837 inches exactly.
# Knuth uses the approximation given
# here (which is very close). The
# comp.fonts FAQ claims that this
# value is supposed to be 1|12 of a
# pica where 83 picas is equal to 35
# cm. But this value differs from
# the standard.
texscaledpoint 1|65536 texpoint # The TeX typesetting system uses
texsp texscaledpoint # this for all computations.
computerpoint 1|72 inch # The American point was rounded
point computerpoint
computerpica 12 computerpoint # to an even 1|72 inch by computer
postscriptpoint computerpoint # people at some point.
pspoint postscriptpoint
twip 1|20 point # TWentieth of an Imperial Point
Q 1|4 mm # Used in Japanese phototypesetting
# Q is for quarter
frenchprinterspoint olddidotpoint
didotpoint germandidotpoint # This seems to be the dominant value
europeanpoint didotpoint # for the point used in Europe
cicero 12 didotpoint
stick 2 inches
# Type sizes
excelsior 3 oldpoint
brilliant 3.5 oldpoint
diamondtype 4 oldpoint
pearl 5 oldpoint
agate 5.5 oldpoint # Originally agate type was 14 lines per
# inch, giving a value of 1|14 in.
ruby agate # British
nonpareil 6 oldpoint
mignonette 6.5 oldpoint
emerald mignonette # British
minion 7 oldpoint
brevier 8 oldpoint
bourgeois 9 oldpoint
longprimer 10 oldpoint
smallpica 11 oldpoint
pica 12 oldpoint
english 14 oldpoint
columbian 16 oldpoint
greatprimer 18 oldpoint
paragon 20 oldpoint
meridian 44 oldpoint
canon 48 oldpoint
# German type sizes
nonplusultra 2 didotpoint
brillant 3 didotpoint
diamant 4 didotpoint
perl 5 didotpoint
nonpareille 6 didotpoint
kolonel 7 didotpoint
petit 8 didotpoint
borgis 9 didotpoint
korpus 10 didotpoint
corpus korpus
garamond korpus
mittel 14 didotpoint
tertia 16 didotpoint
text 18 didotpoint
kleine_kanon 32 didotpoint
kanon 36 didotpoint
grobe_kanon 42 didotpoint
missal 48 didotpoint
kleine_sabon 72 didotpoint
grobe_sabon 84 didotpoint
#
# Information theory units. Note that the name "entropy" is used both
# to measure information and as a physical quantity.
#
INFORMATION bit
nat (1/ln(2)) bits # Entropy measured base e
hartley log2(10) bits # Entropy of a uniformly
ban hartley # distributed random variable
# over 10 symbols.
dit hartley # from Decimal digIT
#
# Computer
#
bps bit/sec # Sometimes the term "baud" is
# incorrectly used to refer to
# bits per second. Baud refers
# to symbols per second. Modern
# modems transmit several bits
# per symbol.
byte 8 bit # Not all machines had 8 bit
B byte # bytes, but these days most of
# them do. But beware: for
# transmission over modems, a
# few extra bits are used so
# there are actually 10 bits per
# byte.
octet 8 bits # The octet is always 8 bits
nybble 4 bits # Half of a byte. Sometimes
# equal to different lengths
# such as 3 bits.
nibble nybble
nyp 2 bits # Donald Knuth asks in an exercise
# for a name for a 2 bit
# quantity and gives the "nyp"
# as a solution due to Gregor
# Purdy. Not in common use.
meg megabyte # Some people consider these
# units along with the kilobyte
gig gigabyte # to be defined according to
# powers of 2 with the kilobyte
# equal to 2^10 bytes, the
# megabyte equal to 2^20 bytes and
# the gigabyte equal to 2^30 bytes
# but these usages are forbidden
# by SI. Binary prefixes have
# been defined by IEC to replace
# the SI prefixes. Use them to
# get the binary values: KiB, MiB,
# and GiB.
jiffy 0.01 sec # This is defined in the Jargon File
jiffies jiffy # (http://www.jargon.org) as being the
# duration of a clock tick for measuring
# wall-clock time. Supposedly the value
# used to be 1|60 sec or 1|50 sec
# depending on the frequency of AC power,
# but then 1|100 sec became more common.
# On linux systems, this term is used and
# for the Intel based chips, it does have
# the value of .01 sec. The Jargon File
# also lists two other definitions:
# millisecond, and the time taken for
# light to travel one foot.
cdaudiospeed 44.1 kHz 2*16 bits # CD audio data rate at 44.1 kHz with 2
# samples of sixteen bits each.
cdromspeed 75 2048 bytes / sec # For data CDs (mode1) 75 sectors are read
# each second with 2048 bytes per sector.
# Audio CDs do not have sectors, but
# people sometimes divide the bit rate by
# 75 and claim a sector length of 2352.
# Data CDs have a lower rate due to
# increased error correction overhead.
# There is a rarely used mode (mode2) with
# 2336 bytes per sector that has fewer
# error correction bits than mode1.
dvdspeed 1385 kB/s # This is the "1x" speed of a DVD using
# constant linear velocity (CLV) mode.
# Modern DVDs may vary the linear velocity
# as they go from the inside to the
# outside of the disc.
# See http://www.osta.org/technology/dvdqa/dvdqa4.htm
#
# Musical measures. Musical intervals expressed as ratios. Multiply
# two intervals together to get the sum of the interval. The function
# musicalcent can be used to convert ratios to cents.
#
# Perfect intervals
octave 2
majorsecond musicalfifth^2 / octave
majorthird 5|4
minorthird 6|5
musicalfourth 4|3
musicalfifth 3|2
majorsixth musicalfourth majorthird
minorsixth musicalfourth minorthird
majorseventh musicalfifth majorthird
minorseventh musicalfifth minorthird
pythagoreanthird majorsecond musicalfifth^2 / octave
syntoniccomma pythagoreanthird / majorthird
pythagoreancomma musicalfifth^12 / octave^7
# Equal tempered definitions
semitone octave^(1|12)
musicalcent(x) units=[1;1] range=(0,) semitone^(x/100) ; \
100 log(musicalcent)/log(semitone)
#
# Musical note lengths.
#
wholenote !
MUSICAL_NOTE_LENGTH wholenote
halfnote 1|2 wholenote
quarternote 1|4 wholenote
eighthnote 1|8 wholenote
sixteenthnote 1|16 wholenote
thirtysecondnote 1|32 wholenote
sixtyfourthnote 1|64 wholenote
dotted 3|2
doubledotted 7|4
breve doublewholenote
semibreve wholenote
minimnote halfnote
crotchet quarternote
quaver eighthnote
semiquaver sixteenthnote
demisemiquaver thirtysecondnote
hemidemisemiquaver sixtyfourthnote
semidemisemiquaver hemidemisemiquaver
#
# yarn and cloth measures
#
# yarn linear density
woolyarnrun 1600 yard/pound # 1600 yds of "number 1 yarn" weighs
# a pound.
yarncut 300 yard/pound # Less common system used in
# Pennsylvania for wool yarn
cottonyarncount 840 yard/pound
linenyarncount 300 yard/pound # Also used for hemp and ramie
worstedyarncount 1680 ft/pound
metricyarncount meter/gram
denier 1|9 tex # used for silk and rayon
manchesteryarnnumber drams/1000 yards # old system used for silk
pli lb/in
typp 1000 yd/lb # abbreviation for Thousand Yard Per Pound
asbestoscut 100 yd/lb # used for glass and asbestos yarn
tex gram / km # rational metric yarn measure, meant
drex 0.1 tex # to be used for any kind of yarn
poumar lb / 1e6 yard
# yarn and cloth length
skeincotton 80*54 inch # 80 turns of thread on a reel with a
# 54 in circumference (varies for other
# kinds of thread)
cottonbolt 120 ft # cloth measurement
woolbolt 210 ft
bolt cottonbolt
heer 600 yards
cut 300 yards # used for wet-spun linen yarn
lea 300 yards
sailmakersyard 28.5 in
sailmakersounce oz / sailmakersyard 36 inch
silkmomme momme / 25 yards 1.49 inch # Traditional silk weight
silkmm silkmomme # But it is also defined as
# lb/100 yd 45 inch. The two
# definitions are slightly different
# and neither one seems likely to be
# the true source definition.
#
# drug dosage
#
mcg microgram # Frequently used for vitamins
iudiptheria 62.8 microgram # IU is for international unit
iupenicillin 0.6 microgram
iuinsulin 41.67 microgram
drop 1|20 ml # The drop was an old "unit" that was
# replaced by the minim. But I was
# told by a pharmacist that in his
# profession, the conversion of 20
# drops per ml is actually used.
bloodunit 450 ml # For whole blood. For blood
# components, a blood unit is the
# quanity of the component found in a
# blood unit of whole blood. The
# human body contains about 12 blood
# units of whole blood.
#
# misc medical measure
#
frenchcathetersize 1|3 mm # measure used for the outer diameter
# of a catheter
charriere frenchcathetersize
#
# fixup units for times when prefix handling doesn't do the job
#
hectare hectoare
megohm megaohm
kilohm kiloohm
microhm microohm
megalerg megaerg # 'L' added to make it pronounceable [18].
#
# Money
#
# Note that US$ is the primitive unit so other currencies are
# generally given in US$.
#
unitedstatesdollar US$
usdollar US$
$ dollar
mark germanymark
bolivar venezuelabolivar
venezuelanbolivarfuerte venezuelabolivar
bolivarfuerte bolivar # The currency was revalued by
oldbolivar 1|1000 bolivar # a factor of 1000.
peseta spainpeseta
rand southafricarand
escudo portugalescudo
guilder netherlandsguilder
hollandguilder netherlandsguilder
peso mexicopeso
yen japanyen
lira italylira
rupee indiarupee
drachma greecedrachma
franc francefranc
markka finlandmarkka
britainpound unitedkingdompound
greatbritainpound unitedkingdompound
unitedkingdompound ukpound
poundsterling britainpound
yuan chinayuan
# Some European currencies have permanent fixed exchange rates with
# the Euro. These rates were taken from the EC's web site:
# http://ec.europa.eu/economy_finance/euro/adoption/conversion/index_en.htm
austriaschilling 1|13.7603 euro
belgiumfranc 1|40.3399 euro
estoniakroon 1|15.6466 euro # Equal to 1|8 germanymark
finlandmarkka 1|5.94573 euro
francefranc 1|6.55957 euro
germanymark 1|1.95583 euro
greecedrachma 1|340.75 euro
irelandpunt 1|0.787564 euro
italylira 1|1936.27 euro
luxembourgfranc 1|40.3399 euro
netherlandsguilder 1|2.20371 euro
portugalescudo 1|200.482 euro
spainpeseta 1|166.386 euro
cypruspound 1|0.585274 euro
maltalira 1|0.429300 euro
sloveniatolar 1|239.640 euro
slovakiakoruna 1|30.1260 euro
UKP GBP # Not an ISO code, but looks like one, and
# sometimes used on usenet.
VEB 1|1000 VEF # old venezuelan bolivar
!include currency.units
# Money on the gold standard, used in the late 19th century and early
# 20th century.
olddollargold 23.22 grains goldprice # Used until 1934
newdollargold 96|7 grains goldprice # After Jan 31, 1934
dollargold newdollargold
poundgold 113 grains goldprice
goldounce goldprice troyounce
silverounce silverprice troyounce
platinumounce platinumprice troyounce
XAU goldounce
XPT platinumounce
XAG silverounce
# Nominal masses of US coins. Note that dimes, quarters and half dollars
# have weight proportional to value. Before 1965 it was $40 / kg.
USpennyweight 2.5 grams # Since 1982, 48 grains before
USnickelweight 5 grams
USdimeweight US$ 0.10 / (20 US$ / lb) # Since 1965
USquarterweight US$ 0.25 / (20 US$ / lb) # Since 1965
UShalfdollarweight US$ 0.50 / (20 US$ / lb) # Since 1971
USdollarmass 8.1 grams
# British currency
quid britainpound # Slang names
fiver 5 quid
tenner 10 quid
monkey 500 quid
brgrand 1000 quid
bob shilling
shilling 1|20 britainpound # Before decimalisation, there
oldpence 1|12 shilling # were 20 shillings to a pound,
farthing 1|4 oldpence # each of twelve old pence
guinea 21 shilling # Still used in horse racing
crown 5 shilling
florin 2 shilling
groat 4 oldpence
tanner 6 oldpence
brpenny 0.01 britainpound
pence brpenny
tuppence 2 pence
tuppenny tuppence
ha'penny halfbrpenny
hapenny ha'penny
oldpenny oldpence
oldtuppence 2 oldpence
oldtuppenny oldtuppence
threepence 3 oldpence # threepence never refers to new money
threepenny threepence
oldthreepence threepence
oldthreepenny threepence
oldhalfpenny halfoldpenny
oldha'penny oldhalfpenny
oldhapenny oldha'penny
brpony 25 britainpound
# Canadian currency
loony 1 canadadollar # This coin depicts a loon
toony 2 canadadollar
#
# Units used for measuring volume of wood
#
cord 4*4*8 ft^3 # 4 ft by 4 ft by 8 ft bundle of wood
facecord 1|2 cord
cordfoot 1|8 cord # One foot long section of a cord
cordfeet cordfoot
housecord 1|3 cord # Used to sell firewood for residences,
# often confusingly called a "cord"
boardfoot ft^2 inch # Usually 1 inch thick wood
boardfeet boardfoot
fbm boardfoot # feet board measure
stack 4 yard^3 # British, used for firewood and coal [18]
rick 4 ft 8 ft 16 inches # Stack of firewood, supposedly
# sometimes called a face cord, but this
# value is equal to 1|3 cord. Name
# comes from an old Norse word for a
# stack of wood.
stere m^3
timberfoot ft^3 # Used for measuring solid blocks of wood
standard 120 12 ft 11 in 1.5 in # This is the St Petersburg or
# Pittsburg standard. Apparently the
# term is short for "standard hundred"
# which was meant to refer to 100 pieces
# of wood (deals). However, this
# particular standard is equal to 120
# deals which are 12 ft by 11 in by 1.5
# inches (not the standard deal).
hoppusfoot (4/pi) ft^3 # Volume calculation suggested in 1736
hoppusboardfoot 1|12 hoppusfoot # forestry manual by Edward Hoppus, for
hoppuston 50 hoppusfoot # estimating the usable volume of a log.
# It results from computing the volume
# of a cylindrical log of length, L, and
# girth (circumference), G, by V=L(G/4)^2.
# The hoppus ton is apparently still in
# use for shipments from Southeast Asia.
# In Britain, the deal is apparently any piece of wood over 6 feet long, over
# 7 wide and 2.5 inches thick. The OED doesn't give a standard size. A piece
# of wood less than 7 inches wide is called a "batten". This unit is now used
# exclusively for fir and pine.
deal 12 ft 11 in 2.5 in # The standard North American deal [OED]
wholedeal 12 ft 11 in 1.25 in # If it's half as thick as the standard
# deal it's called a "whole deal"!
splitdeal 12 ft 11 in 5|8 in # And half again as thick is a split deal.
# Used for shellac mixing rate
poundcut pound / gallon
lbcut poundcut
#
# Gas and Liquid flow units
#
FLUID_FLOW VOLUME / TIME
# Some obvious volumetric gas flow units (cu is short for cubic)
cumec m^3/s
cusec ft^3/s
# Conventional abbreviations for fluid flow units
gph gal/hr
gpm gal/min
mgd megagal/day
cfs ft^3/s
cfh ft^3/hour
cfm ft^3/min
lpm liter/min
lfm ft/min # Used to report air flow produced by fans.
# Multiply by cross sectional area to get a
# flow in cfm.
pru mmHg / (ml/min) # peripheral resistance unit, used in
# medicine to assess blood flow in
# the capillaries.
# Miner's inch: This is an old historic unit used in the Western United
# States. It is generally defined as the rate of flow through a one square
# inch hole at a specified depth such as 4 inches. In the late 19th century,
# volume of water was sometimes measured in the "24 hour inch". Values for the
# miner's inch were fixed by state statues. (This information is from a web
# site operated by the Nevada Division of Water Planning: The Water Words
# Dictionary at http://www.state.nv.us/cnr/ndwp/dict-1/waterwds.htm.)
minersinchAZ 1.5 ft^3/min
minersinchCA 1.5 ft^3/min
minersinchMT 1.5 ft^3/min
minersinchNV 1.5 ft^3/min
minersinchOR 1.5 ft^3/min
minersinchID 1.2 ft^3/min
minersinchKS 1.2 ft^3/min
minersinchNE 1.2 ft^3/min
minersinchNM 1.2 ft^3/min
minersinchND 1.2 ft^3/min
minersinchSD 1.2 ft^3/min
minersinchUT 1.2 ft^3/min
minersinchCO 1 ft^3/sec / 38.4 # 38.4 miner's inches = 1 ft^3/sec
minersinchBC 1.68 ft^3/min # British Columbia
# Oceanographic flow
sverdrup 1e6 m^3 / sec # Used to express flow of ocean
# currents. Named after Norwegian
# oceanographer H. Sverdrup.
# In vacuum science and some other applications, gas flow is measured
# as the product of volumetric flow and pressure. This is useful
# because it makes it easy to compare with the flow at standard
# pressure (one atmosphere). It also directly relates to the number
# of gas molecules per unit time, and hence to the mass flow if the
# molecular mass is known.
GAS_FLOW PRESSURE FLUID_FLOW
sccm atm cc/min # 's' is for "standard" to indicate
sccs atm cc/sec # flow at standard pressure
scfh atm ft^3/hour #
scfm atm ft^3/min
slpm atm liter/min
slph atm liter/hour
lusec liter micron Hg / s # Used in vacuum science
# US Standard Atmosphere (1976)
# Atmospheric temperature and pressure vs. geometric height above sea level
# This definition covers only the troposphere (the lowest atmospheric
# layer, up to 11 km), and assumes the layer is polytropic.
# A polytropic process is one for which PV^k = const, where P is the
# pressure, V is the volume, and k is the polytropic exponent. The
# polytropic index is n = 1 / (k - 1). As noted in the Wikipedia article
# https://en.wikipedia.org/wiki/Polytropic_process, some authors reverse
# the definitions of "exponent" and "index." The functions below assume
# the following parameters:
# temperature lapse rate, -dT/dz, in troposphere
lapserate 6.5 K/km # US Std Atm (1976)
# air molecular weight, including constituent mol wt, given
# in Table 3, p. 3
air_1976 78.084 % 28.0134 \
+ 20.9476 % 31.9988 \
+ 9340 ppm 39.948 \
+ 314 ppm 44.00995 \
+ 18.18 ppm 20.183 \
+ 5.24 ppm 4.0026 \
+ 2 ppm 16.04303 \
+ 1.14 ppm 83.80 \
+ 0.55 ppm 2.01594 \
+ 0.087 ppm 131.30
# universal gas constant
R_1976 8.31432e3 N m/(kmol K)
# polytropic index n
polyndx_1976 air_1976 (kg/kmol) gravity/(R_1976 lapserate) - 1
# If desired, redefine using current values for air mol wt and R
polyndx polyndx_1976
# polyndx air (kg/kmol) gravity/(R lapserate) - 1
# for comparison with various references
polyexpnt (polyndx + 1) / polyndx
# The model assumes the following reference values:
# sea-level temperature and pressure
stdatmT0 288.15 K
stdatmP0 atm
# "effective radius" for relation of geometric to geopotential height,
# at a latitude at which g = 9.80665 m/s (approximately 45.543 deg); no
# relation to actual radius
earthradUSAtm 6356766 m
# Temperature vs. geopotential height h
# Assumes 15 degC at sea level
# Based on approx 45 deg latitude
# Lower limits of domain and upper limits of range are those of the
# tables in US Standard Atmosphere (NASA 1976)
stdatmTH(h) units=[m;K] domain=[-5000,11e3] range=[217,321] \
stdatmT0+(-lapserate h) ; (stdatmT0+(-stdatmTH))/lapserate
# Temperature vs. geometric height z; based on approx 45 deg latitude
stdatmT(z) units=[m;K] domain=[-5000,11e3] range=[217,321] \
stdatmTH(geop_ht(z)) ; ~geop_ht(~stdatmTH(stdatmT))
# Pressure vs. geopotential height h
# Assumes 15 degC and 101325 Pa at sea level
# Based on approx 45 deg latitude
# Lower limits of domain and upper limits of range are those of the
# tables in US Standard Atmosphere (NASA 1976)
stdatmPH(h) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \
atm (1 - (lapserate/stdatmT0) h)^(polyndx + 1) ; \
(stdatmT0/lapserate) (1+(-(stdatmPH/stdatmP0)^(1/(polyndx + 1))))
# Pressure vs. geometric height z; based on approx 45 deg latitude
stdatmP(z) units=[m;Pa] domain=[-5000,11e3] range=[22877,177764] \
stdatmPH(geop_ht(z)); ~geop_ht(~stdatmPH(stdatmP))
# Geopotential height from geometric height
# Based on approx 45 deg latitude
# Lower limits of domain and range are somewhat arbitrary; they
# correspond to the limits in the US Std Atm tables
geop_ht(z) units=[m;m] domain=[-5000,) range=[-5004,) \
(earthradUSAtm z) / (earthradUSAtm + z) ; \
(earthradUSAtm geop_ht) / (earthradUSAtm + (-geop_ht))
# The standard value for the sea-level acceleration due to gravity is
# 9.80665 m/s^2, but the actual value varies with latitude (Harrison 1949)
# R_eff = 2 g_phi / denom
# g_phi = 978.0356e-2 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2)
# or
# g_phi = 980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2)
# denom = 3.085462e-6+2.27e-9 cos(2 lat)+(-2e-12) cos(4 lat) (minutes?)
# There is no inverse function; the standard value applies at a latitude
# of about 45.543 deg
g_phi(lat) units=[deg;m/s2] domain=[0,90] noerror \
980.6160e-2 (1+(-0.0026373) cos(2 lat)+0.0000059 cos(2 lat)^2) m/s2
# effective Earth radius for relation of geometric height to
# geopotential height, as function of latitude (Harrison 1949)
earthradius_eff(lat) units=[deg;m] domain=[0,90] noerror \
m 2 9.780356 (1+0.0052885 sin(lat)^2+(-0.0000059) sin(2 lat)^2) / \
(3.085462e-6 + 2.27e-9 cos(2 lat) + (-2e-12) cos(4 lat))
# References
# Harrison, L.P. 1949. Relation Between Geopotential and Geometric
# Height. In Smithsonian Meteorological Tables. List, Robert J., ed.
# 6th ed., 4th reprint, 1968. Washington, DC: Smithsonian Institution.
# NASA. US National Aeronautics and Space Administration. 1976.
# US Standard Atmosphere 1976. Washington, DC: US Government Printing Office.
# Gauge pressure functions
#
# Gauge pressure is measured relative to atmospheric pressure. In the English
# system, where pressure is often given in pounds per square inch, gauge
# pressure is often indicated by 'psig' to distinguish it from absolute
# pressure, often indicated by 'psia'. At the standard atmospheric pressure
# of 14.696 psia, a gauge pressure of 0 psig is an absolute pressure of 14.696
# psia; an automobile tire inflated to 31 psig has an absolute pressure of
# 45.696 psia.
#
# With gaugepressure(), the units must be specified (e.g., gaugepressure(1.5
# bar)); with psig(), the units are taken as psi, so the example above of tire
# pressure could be given as psig(31).
#
# If the normal elevation is significantly different from sea level, change
# Patm appropriately, and adjust the lower domain limit on the gaugepressure
# definition.
Patm atm
gaugepressure(x) units=[Pa;Pa] domain=[-101325,) range=[0,) \
x + Patm ; gaugepressure+(-Patm)
psig(x) units=[1;Pa] domain=[-14.6959487755135,) range=[0,) \
gaugepressure(x psi) ; ~gaugepressure(psig) / psi
#
# Wire Gauge
#
# This area is a nightmare with huge charts of wire gauge diameters
# that usually have no clear origin. There are at least 5 competing wire gauge
# systems to add to the confusion. The use of wire gauge is related to the
# manufacturing method: a metal rod is heated and drawn through a hole. The
# size change can't be too big. To get smaller wires, the process is repeated
# with a series of smaller holes. Generally larger gauges mean smaller wires.
# The gauges often have values such as "00" and "000" which are larger sizes
# than simply "0" gauge. In the tables that appear below, these gauges must be
# specified as negative numbers (e.g. "00" is -1, "000" is -2, etc).
# Alternatively, you can use the following units:
#
g00 (-1)
g000 (-2)
g0000 (-3)
g00000 (-4)
g000000 (-5)
g0000000 (-6)
# American Wire Gauge (AWG) or Brown & Sharpe Gauge appears to be the most
# important gauge. ASTM B-258 specifies that this gauge is based on geometric
# interpolation between gauge 0000, which is 0.46 inches exactly, and gauge 36
# which is 0.005 inches exactly. Therefore, the diameter in inches of a wire
# is given by the formula 1|200 92^((36-g)/39). Note that 92^(1/39) is close
# to 2^(1/6), so diameter is approximately halved for every 6 gauges. For the
# repeated zero values, use negative numbers in the formula. The same document
# also specifies rounding rules which seem to be ignored by makers of tables.
# Gauges up to 44 are to be specified with up to 4 significant figures, but no
# closer than 0.0001 inch. Gauges from 44 to 56 are to be rounded to the
# nearest 0.00001 inch.
#
# In addition to being used to measure wire thickness, this gauge is used to
# measure the thickness of sheets of aluminum, copper, and most metals other
# than steel, iron and zinc.
wiregauge(g) units=[1;m] range=(0,) \
1|200 92^((36+(-g))/39) in; 36+(-39)ln(200 wiregauge/in)/ln(92)
awg() wiregauge
# Next we have the SWG, the Imperial or British Standard Wire Gauge. This one
# is piecewise linear. It was used for aluminum sheets.
brwiregauge[in] \
-6 0.5 \
-5 0.464 \
-3 0.4 \
-2 0.372 \
3 0.252 \
6 0.192 \
10 0.128 \
14 0.08 \
19 0.04 \
23 0.024 \
26 0.018 \
28 0.0148 \
30 0.0124 \
39 0.0052 \
49 0.0012 \
50 0.001
# The following is from the Appendix to ASTM B 258
#
# For example, in U.S. gage, the standard for sheet metal is based on the
# weight of the metal, not on the thickness. 16-gage is listed as
# approximately .0625 inch thick and 40 ounces per square foot (the original
# standard was based on wrought iron at .2778 pounds per cubic inch; steel
# has almost entirely superseded wrought iron for sheet use, at .2833 pounds
# per cubic inch). Smaller numbers refer to greater thickness. There is no
# formula for converting gage to thickness or weight.
#
# It's rather unclear from the passage above whether the plate gauge values are
# therefore wrong if steel is being used. Reference [15] states that steel is
# in fact measured using this gauge (under the name Manufacturers' Standard
# Gauge) with a density of 501.84 lb/ft3 = 0.2904 lb/in3 used for steel.
# But this doesn't seem to be the correct density of steel (.2833 lb/in3 is
# closer).
#
# This gauge was established in 1893 for purposes of taxation.
# Old plate gauge for iron
plategauge[(oz/ft^2)/(480*lb/ft^3)] \
-5 300 \
1 180 \
14 50 \
16 40 \
17 36 \
20 24 \
26 12 \
31 7 \
36 4.5 \
38 4
# Manufacturers Standard Gage
stdgauge[(oz/ft^2)/(501.84*lb/ft^3)] \
-5 300 \
1 180 \
14 50 \
16 40 \
17 36 \
20 24 \
26 12 \
31 7 \
36 4.5 \
38 4
# A special gauge is used for zinc sheet metal. Notice that larger gauges
# indicate thicker sheets.
zincgauge[in] \
1 0.002 \
10 0.02 \
15 0.04 \
19 0.06 \
23 0.1 \
24 0.125 \
27 0.5 \
28 1
#
# Screw sizes
#
# In the USA, screw diameters are reported using a gauge number.
# Metric screws are reported as Mxx where xx is the diameter in mm.
#
screwgauge(g) units=[1;m] range=[0,) \
(.06 + .013 g) in ; (screwgauge/in + (-.06)) / .013
#
# Abrasive grit size
#
# Standards governing abrasive grit sizes are complicated, specifying
# fractions of particles that are passed or retained by different mesh
# sizes. As a result, it is not possible to make precise comparisons
# of different grit standards. The tables below allow the
# determination of rough equivlants by using median particle size.
#
# Standards in the USA are determined by the Unified Abrasives
# Manufacturers' Association (UAMA), which resulted from the merger of
# several previous organizations. One of the old organizations was
# CAMI (Coated Abrasives Manufacturers' Institute).
#
# UAMA has a web page with plots showing abrasive particle ranges for
# various different grits and comparisons between standards.
#
# http://www.uama.org/Abrasives101/101Standards.html
#
# Abrasives are grouped into "bonded" abrasives for use with grinding
# wheels and "coated" abrasives for sandpapers and abrasive films.
# The industry uses different grit standards for these two
# categories.
#
# Another division is between "macrogrits", grits below 240 and
# "microgrits", which are above 240. Standards differ, as do methods
# for determining particle size. In the USA, ANSI B74.12 is the
# standard governing macrogrits. ANSI B74.10 covers bonded microgrit
# abrasives, and ANSI B74.18 covers coated microgrit abrasives. It
# appears that the coated standard is identical to the bonded standard
# for grits up through 600 but then diverges significantly.
#
# European grit sizes are determined by the Federation of European
# Producers of Abrasives. http://www.fepa-abrasives.org
#
# They give two standards, the "F" grit for bonded abrasives and the
# "P" grit for coated abrasives. This data is taken directly from
# their web page.
# FEPA P grit for coated abrasives is commonly seen on sandpaper in
# the USA where the paper will be marked P600, for example. FEPA P
# grits are said to be more tightly constrained than comparable ANSI
# grits so that the particles are more uniform in size and hence give
# a better finish.
grit_P[micron] \
12 1815 \
16 1324 \
20 1000 \
24 764 \
30 642 \
36 538 \
40 425 \
50 336 \
60 269 \
80 201 \
100 162 \
120 125 \
150 100 \
180 82 \
220 68 \
240 58.5 \
280 52.2 \
320 46.2 \
360 40.5 \
400 35 \
500 30.2 \
600 25.8 \
800 21.8 \
1000 18.3 \
1200 15.3 \
1500 12.6 \
2000 10.3 \
2500 8.4
# The F grit is the European standard for bonded abrasives such as
# grinding wheels
grit_F[micron] \
4 4890 \
5 4125 \
6 3460 \
7 2900 \
8 2460 \
10 2085 \
12 1765 \
14 1470 \
16 1230 \
20 1040 \
22 885 \
24 745 \
30 625 \
36 525 \
40 438 \
46 370 \
54 310 \
60 260 \
70 218 \
80 185 \
90 154 \
100 129 \
120 109 \
150 82 \
180 69 \
220 58 \
230 53 \
240 44.5 \
280 36.5 \
320 29.2 \
360 22.8 \
400 17.3 \
500 12.8 \
600 9.3 \
800 6.5 \
1000 4.5 \
1200 3 \
1500 2.0 \
2000 1.2
# According to the UAMA web page, the ANSI bonded and ANSI coated standards
# are identical to FEPA F in the macrogrit range (under 240 grit), so these
# values are taken from the FEPA F table. The values for 240 and above are
# from the UAMA web site and represent the average of the "d50" range
# endpoints listed there.
ansibonded[micron] \
4 4890 \
5 4125 \
6 3460 \
7 2900 \
8 2460 \
10 2085 \
12 1765 \
14 1470 \
16 1230 \
20 1040 \
22 885 \
24 745 \
30 625 \
36 525 \
40 438 \
46 370 \
54 310 \
60 260 \
70 218 \
80 185 \
90 154 \
100 129 \
120 109 \
150 82 \
180 69 \
220 58 \
240 50 \
280 39.5 \
320 29.5 \
360 23 \
400 18.25 \
500 13.9 \
600 10.55 \
800 7.65 \
1000 5.8 \
1200 3.8
grit_ansibonded() ansibonded
# Like the bonded grit, the coated macrogrits below 240 are taken from the
# FEPA F table. Data above this is from the UAMA site. Note that the coated
# and bonded standards are evidently the same from 240 up to 600 grit, but
# starting at 800 grit, the coated standard diverges. The data from UAMA show
# that 800 grit coated has an average size slightly larger than the average
# size of 600 grit coated/bonded. However, the 800 grit has a significantly
# smaller particle size variation.
#
# Because of this non-monotonicity from 600 grit to 800 grit this definition
# produces a warning about the lack of a unique inverse.
ansicoated[micron] noerror \
4 4890 \
5 4125 \
6 3460 \
7 2900 \
8 2460 \
10 2085 \
12 1765 \
14 1470 \
16 1230 \
20 1040 \
22 885 \
24 745 \
30 625 \
36 525 \
40 438 \
46 370 \
54 310 \
60 260 \
70 218 \
80 185 \
90 154 \
100 129 \
120 109 \
150 82 \
180 69 \
220 58 \
240 50 \
280 39.5 \
320 29.5 \
360 23 \
400 18.25 \
500 13.9 \
600 10.55 \
800 11.5 \
1000 9.5 \
2000 7.2 \
2500 5.5 \
3000 4 \
4000 3 \
6000 2 \
8000 1.2
grit_ansicoated() ansicoated
#
# Is this correct? This is the JIS Japanese standard used on waterstones
#
jisgrit[micron] \
150 75 \
180 63 \
220 53 \
280 48 \
320 40 \
360 35 \
400 30 \
600 20 \
700 17 \
800 14 \
1000 11.5 \
1200 9.5 \
1500 8 \
2000 6.7 \
2500 5.5 \
3000 4 \
4000 3 \
6000 2 \
8000 1.2
# The "Finishing Scale" marked with an A (e.g. A75). This information
# is from the web page of the sand paper manufacturer Klingspor
# http://www.klingspor.com/gritgradingsystems.htm
#
# I have no information about what this scale is used for.
grit_A[micron]\
16 15.3 \
25 21.8 \
30 23.6 \
35 25.75 \
45 35 \
60 46.2 \
65 53.5 \
75 58.5 \
90 65 \
110 78 \
130 93 \
160 127 \
200 156
#
# Grits for DMT brand diamond sharpening stones from
# http://dmtsharp.com/products/colorcode.htm
#
dmtxxcoarse 120 micron # 120 mesh
dmtsilver dmtxxcoarse
dmtxx dmtxxcoarse
dmtxcoarse 60 micron # 220 mesh
dmtx dmtxcoarse
dmtblack dmtxcoarse
dmtcoarse 45 micron # 325 mesh
dmtc dmtcoarse
dmtblue dmtcoarse
dmtfine 25 micron # 600 mesh
dmtred dmtfine
dmtf dmtfine
dmtefine 9 micron # 1200 mesh
dmte dmtefine
dmtgreen dmtefine
dmtceramic 7 micron # 2200 mesh
dmtcer dmtceramic
dmtwhite dmtceramic
dmteefine 3 micron # 8000 mesh
dmttan dmteefine
dmtee dmteefine
#
# The following values come from a page in the Norton Stones catalog,
# available at their web page, http://www.nortonstones.com.
#
hardtranslucentarkansas 6 micron # Natural novaculite (silicon quartz)
softarkansas 22 micron # stones
extrafineindia 22 micron # India stones are Norton's manufactured
fineindia 35 micron # aluminum oxide product
mediumindia 53.5 micron
coarseindia 97 micron
finecrystolon 45 micron # Crystolon stones are Norton's
mediumcrystalon 78 micron # manufactured silicon carbide product
coarsecrystalon 127 micron
# The following are not from the Norton catalog
hardblackarkansas 6 micron
hardwhitearkansas 11 micron
washita 35 micron
#
# Ring size. All ring sizes are given as the circumference of the ring.
#
# USA ring sizes. Several slightly different definitions seem to be in
# circulation. According to [15], the interior diameter of size n ring in
# inches is 0.32 n + 0.458 for n ranging from 3 to 13.5 by steps of 0.5. The
# size 2 ring is inconsistently 0.538in and no 2.5 size is listed.
#
# However, other sources list 0.455 + 0.0326 n and 0.4525 + 0.0324 n as the
# diameter and list no special case for size 2. (Or alternatively they are
# 1.43 + .102 n and 1.4216+.1018 n for measuring circumference in inches.) One
# reference claimed that the original system was that each size was 1|10 inch
# circumference, but that source doesn't have an explanation for the modern
# system which is somewhat different.
ringsize(n) units=[1;in] domain=[2,) range=[1.6252,) \
(1.4216+.1018 n) in ; (ringsize/in + (-1.4216))/.1018
# Old practice in the UK measured rings using the "Wheatsheaf gauge" with sizes
# specified alphabetically and based on the ring inside diameter in steps of
# 1|64 inch. This system was replaced in 1987 by British Standard 6820 which
# specifies sizes based on circumference. Each size is 1.25 mm different from
# the preceding size. The baseline is size C which is 40 mm circumference.
# The new sizes are close to the old ones. Sometimes it's necessary to go
# beyond size Z to Z+1, Z+2, etc.
sizeAring 37.50 mm
sizeBring 38.75 mm
sizeCring 40.00 mm
sizeDring 41.25 mm
sizeEring 42.50 mm
sizeFring 43.75 mm
sizeGring 45.00 mm
sizeHring 46.25 mm
sizeIring 47.50 mm
sizeJring 48.75 mm
sizeKring 50.00 mm
sizeLring 51.25 mm
sizeMring 52.50 mm
sizeNring 53.75 mm
sizeOring 55.00 mm
sizePring 56.25 mm
sizeQring 57.50 mm
sizeRring 58.75 mm
sizeSring 60.00 mm
sizeTring 61.25 mm
sizeUring 62.50 mm
sizeVring 63.75 mm
sizeWring 65.00 mm
sizeXring 66.25 mm
sizeYring 67.50 mm
sizeZring 68.75 mm
# Japanese sizes start with size 1 at a 13mm inside diameter and each size is
# 1|3 mm larger in diameter than the previous one. They are multiplied by pi
# to give circumference.
jpringsize(n) units=[1;mm] domain=[1,) range=[0.040840704,) \
(38|3 + n/3) pi mm ; 3 jpringsize/ pi mm + (-38)
# The European ring sizes are the length of the circumference in mm minus 40.
euringsize(n) units=[1;mm] (n+40) mm ; euringsize/mm + (-40)
#
# Abbreviations
#
mph mile/hr
mpg mile/gal
kph km/hr
fL footlambert
fpm ft/min
fps ft/s
rpm rev/min
rps rev/sec
mi mile
smi mile
nmi nauticalmile
mbh 1e3 btu/hour
mcm 1e3 circularmil
ipy inch/year # used for corrosion rates
ccf 100 ft^3 # used for selling water [18]
Mcf 1000 ft^3 # not million cubic feet [18]
kp kilopond
kpm kp meter
Wh W hour
hph hp hour
plf lb / foot # pounds per linear foot
#
# Compatibility units with unix version
#
pa Pa
ev eV
hg Hg
oe Oe
mh mH
rd rod
pf pF
gr grain
nt N
hz Hz
hd hogshead
dry drygallon/gallon
nmile nauticalmile
beV GeV
bev beV
coul C
#
# Radioactivity units
#
becquerel /s # Activity of radioactive source
Bq becquerel #
curie 3.7e10 Bq # Defined in 1910 as the radioactivity
Ci curie # emitted by the amount of radon that is
# in equilibrium with 1 gram of radium.
rutherford 1e6 Bq #
RADIATION_DOSE gray
gray J/kg # Absorbed dose of radiation
Gy gray #
rad 1e-2 Gy # From Radiation Absorbed Dose
rep 8.38 mGy # Roentgen Equivalent Physical, the amount
# of radiation which , absorbed in the
# body, would liberate the same amount
# of energy as 1 roentgen of X rays
# would, or 97 ergs.
sievert J/kg # Dose equivalent: dosage that has the
Sv sievert # same effect on human tissues as 200
rem 1e-2 Sv # keV X-rays. Different types of
# radiation are weighted by the
# Relative Biological Effectiveness
# (RBE).
#
# Radiation type RBE
# X-ray, gamma ray 1
# beta rays, > 1 MeV 1
# beta rays, < 1 MeV 1.08
# neutrons, < 1 MeV 4-5
# neutrons, 1-10 MeV 10
# protons, 1 MeV 8.5
# protons, .1 MeV 10
# alpha, 5 MeV 15
# alpha, 1 MeV 20
#
# The energies are the kinetic energy
# of the particles. Slower particles
# interact more, so they are more
# effective ionizers, and hence have
# higher RBE values.
#
# rem stands for Roentgen Equivalent
# Mammal
banana_dose 0.1e-6 sievert # Informal measure of the dose due to
# eating one average sized banana
roentgen 2.58e-4 C / kg # Ionizing radiation that produces
# 1 statcoulomb of charge in 1 cc of
# dry air at stp.
rontgen roentgen # Sometimes it appears spelled this way
sievertunit 8.38 rontgen # Unit of gamma ray dose delivered in one
# hour at a distance of 1 cm from a
# point source of 1 mg of radium
# enclosed in platinum .5 mm thick.
eman 1e-7 Ci/m^3 # radioactive concentration
mache 3.7e-7 Ci/m^3
#
# Atomic weights. The atomic weight of an element is the ratio of the mass of
# a mole of the element to 1|12 of a mole of Carbon 12. The Standard Atomic
# Weights apply to the elements as they occur naturally on earth. Elements
# which do not occur naturally or which occur with wide isotopic variability do
# not have Standard Atomic Weights. For these elements, the atomic weight is
# based on the longest lived isotope, as marked in the comments. In some
# cases, the comment for these entries also gives a number which is an atomic
# weight for a different isotope that may be of more interest than the longest
# lived isotope.
#
actinium 227.0278
aluminum 26.981539
americium 243.0614 # Longest lived. 241.06
antimony 121.760
argon 39.948
arsenic 74.92159
astatine 209.9871 # Longest lived
barium 137.327
berkelium 247.0703 # Longest lived. 249.08
beryllium 9.012182
bismuth 208.98037
boron 10.811
bromine 79.904
cadmium 112.411
calcium 40.078
californium 251.0796 # Longest lived. 252.08
carbon 12.011
cerium 140.115
cesium 132.90543
chlorine 35.4527
chromium 51.9961
cobalt 58.93320
copper 63.546
curium 247.0703
deuterium 2.0141017778
dysprosium 162.50
einsteinium 252.083 # Longest lived
erbium 167.26
europium 151.965
fermium 257.0951 # Longest lived
fluorine 18.9984032
francium 223.0197 # Longest lived
gadolinium 157.25
gallium 69.723
germanium 72.61
gold 196.96654
hafnium 178.49
helium 4.002602
holmium 164.93032
hydrogen 1.00794
indium 114.818
iodine 126.90447
iridium 192.217
iron 55.845
krypton 83.80
lanthanum 138.9055
lawrencium 262.11 # Longest lived
lead 207.2
lithium 6.941
lutetium 174.967
magnesium 24.3050
manganese 54.93805
mendelevium 258.10 # Longest lived
mercury 200.59
molybdenum 95.94
neodymium 144.24
neon 20.1797
neptunium 237.0482
nickel 58.6934
niobium 92.90638
nitrogen 14.00674
nobelium 259.1009 # Longest lived
osmium 190.23
oxygen 15.9994
palladium 106.42
phosphorus 30.973762
platinum 195.08
plutonium 244.0642 # Longest lived. 239.05
polonium 208.9824 # Longest lived. 209.98
potassium 39.0983
praseodymium 140.90765
promethium 144.9127 # Longest lived. 146.92
protactinium 231.03588
radium 226.0254
radon 222.0176 # Longest lived
rhenium 186.207
rhodium 102.90550
rubidium 85.4678
ruthenium 101.07
samarium 150.36
scandium 44.955910
selenium 78.96
silicon 28.0855
silver 107.8682
sodium 22.989768
strontium 87.62
sulfur 32.066
tantalum 180.9479
technetium 97.9072 # Longest lived. 98.906
tellurium 127.60
terbium 158.92534
thallium 204.3833
thorium 232.0381
thullium 168.93421
tin 118.710
titanium 47.867
tungsten 183.84
uranium 238.0289
vanadium 50.9415
xenon 131.29
ytterbium 173.04
yttrium 88.90585
zinc 65.39
zirconium 91.224
# Average molecular weight of air
#
# The atmospheric composition listed is from NASA Earth Fact Sheet (accessed
# 28 August 2015)
# http://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html
# Numbers do not add up to exactly 100% due to roundoff and uncertainty Water
# is highly variable, typically makes up about 1%
air 78.08% nitrogen 2 \
+ 20.95% oxygen 2 \
+ 9340 ppm argon \
+ 400 ppm (carbon + oxygen 2) \
+ 18.18 ppm neon \
+ 5.24 ppm helium \
+ 1.7 ppm (carbon + 4 hydrogen) \
+ 1.14 ppm krypton \
+ 0.55 ppm hydrogen 2
#
# population units
#
people 1
person people
death people
capita people
percapita per capita
# TGM dozen based unit system listed on the "dozenal" forum
# http://www.dozenalsociety.org.uk/apps/tgm.htm. These units are
# proposed as an allegedly more rational alternative to the SI system.
Tim 12^-4 hour # Time
Grafut gravity Tim^2 # Length based on gravity
Surf Grafut^2 # area
Volm Grafut^3 # volume
Vlos Grafut/Tim # speed
Denz Maz/Volm # density
Mag Maz gravity # force
Maz Volm kg / oldliter # mass based on water
Tm Tim # Abbreviations
Gf Grafut
Sf Surf
Vm Volm
Vl Vlos
Mz Maz
Dz Denz
# Dozen based unit prefixes
Zena- 12
Duna- 12^2
Trina- 12^3
Quedra- 12^4
Quena- 12^5
Hesa- 12^6
Seva- 12^7
Aka- 12^8
Neena- 12^9
Dexa- 12^10
Lefa- 12^11
Zennila- 12^12
Zeni- 12^-1
Duni- 12^-2
Trini- 12^-3
Quedri- 12^-4
Queni- 12^-5
Hesi- 12^-6
Sevi- 12^-7
Aki- 12^-8
Neeni- 12^-9
Dexi- 12^-10
Lefi- 12^-11
Zennili- 12^-12
#
# Traditional Japanese units (shakkanhou)
#
# The traditional system of weights and measures is called shakkanhou from the
# shaku and the ken. Japan accepted SI units in 1891 and legalized conversions
# to the traditional system. In 1909 the inch-pound system was also legalized,
# so Japan had three legally approved systems. A change to the metric system
# started in 1921 but there was a lot of resistance. The Measurement Law of
# October 1999 prohibits sales in anything but SI units. However, the old
# units still live on in construction and as the basis for paper sizes of books
# and tools used for handicrafts.
#
# Note that units below use the Hepburn romanization system. Some other
# systems would render "mou", "jou", and "chou" as "mo", "jo" and "cho".
#
#
# http://hiramatu-hifuka.com/onyak/onyindx.html
# Japanese Proportions. These are still in everyday use. They also
# get used as units to represent the proportion of the standard unit.
wari_proportion 1|10
wari wari_proportion
bu_proportion 1|100 # The character bu can also be read fun or bun
# but usually "bu" is used for units.
rin_proportion 1|1000
mou_proportion 1|10000
# Japanese Length Measures
#
# The length system is called kanejaku or
# square and originated in China. It was
# adopted as Japan's official measure in 701
# by the Taiho Code. This system is still in
# common use in architecture and clothing.
shaku 1|3.3 m
mou 1|10000 shaku
rin 1|1000 shaku
bu_distance 1|100 shaku
sun 1|10 shaku
jou_distance 10 shaku
jou jou_distance
kanejakusun sun # Alias to emphasize architectural name
kanejaku shaku
kanejakujou jou
# http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
taichi shaku # http://zh.wikipedia.org/wiki/台尺
taicun sun # http://zh.wikipedia.org/wiki/台制
!utf8
台尺 taichi # via Hanyu Pinyin romanizations
台寸 taicun
!endutf8
# In context of clothing, shaku is different from architecture
# http://www.scinet.co.jp/sci/sanwa/kakizaki-essay54.html
kujirajaku 10|8 shaku
kujirajakusun 1|10 kujirajaku
kujirajakubu 1|100 kujirajaku
kujirajakujou 10 kujirajaku
tan_distance 3 kujirajakujou
ken 6 shaku # Also sometimes 6.3, 6.5, or 6.6
# http://www.homarewood.co.jp/syakusun.htm
# mostly unused
chou_distance 60 ken
chou chou_distance
ri 36 chou
# Japanese Area Measures
# Tsubo is still used for land size, though the others are more
# recognized by their homonyms in the other measurements.
gou_area 1|10 tsubo
tsubo 36 shaku^2 # Size of two tatami = ken^2 ??
se 30 tsubo
tan_area 10 se
chou_area 10 tan_area
# http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
ping tsubo # http://zh.wikipedia.org/wiki/坪
jia 2934 ping # http://zh.wikipedia.org/wiki/甲_(单位)
fen 1|10 jia # http://zh.wikipedia.org/wiki/分
fen_area 1|10 jia # Protection against future collisions
!utf8
坪 ping # via Hanyu Pinyin romanizations
甲 jia
分 fen
分地 fen_area # Protection against future collisions
!endutf8
# Japanese architecture is based on a "standard" size of tatami mat.
# Room sizes today are given in number of tatami, and this number
# determines the spacing between colums and hence sizes of sliding
# doors and paper screens. However, every region has its own slightly
# different tatami size. Edoma, used in and around Tokyo and
# Hokkaido, is becoming a nationwide standard. Kyouma is used around
# Kyoto, Osaka and Kyuushu, and Chuukyouma is used around Nagoya.
# Note that the tatami all have the aspect ratio 2:1 so that the mats
# can tile the room with some of them turned 90 degrees.
#
# http://www.moon2.net/tatami/infotatami/structure.html
edoma (5.8*2.9) shaku^2
kyouma (6.3*3.15) shaku^2
chuukyouma (6*3) shaku^2
jou_area edoma
tatami jou_area
# Japanese Volume Measures
# The "shou" is still used for such things as alcohol and seasonings.
# Large quantities of paint are still purchased in terms of "to".
shaku_volume 1|10 gou_volume
gou_volume 1|10 shou
gou gou_volume
shou (4.9*4.9*2.7) sun^3 # The character shou which is
# the same as masu refers to a
# rectangular wooden cup used to
# measure liquids and cereal.
# Sake is sometimes served in a masu
# Note that it happens to be
# EXACTLY 7^4/11^3 liters.
to 10 shou
koku 10 to # No longer used; historically a measure of rice
# Japanese Weight Measures
#
# http://wyoming.hp.infoseek.co.jp/zatugaku/zamoney.html
# Not really used anymore.
rin_weight 1|10 bu_weight
bu_weight 1|10 monme
fun 1|10 monme
monme momme
kin 160 monme
kan 1000 monme
kwan kan # This was the old pronounciation of the unit.
# The old spelling persisted a few centuries
# longer and was not changed until around
# 1950.
# http://en.wikipedia.org/wiki/Taiwanese_units_of_measurement
# says: "Volume measure in Taiwan is largely metric".
taijin kin # http://zh.wikipedia.org/wiki/台斤
tailiang 10 monme # http://zh.wikipedia.org/wiki/台斤
taiqian monme # http://zh.wikipedia.org/wiki/台制
!utf8
台斤 taijin # via Hanyu Pinyin romanizations
台兩 tailiang
台錢 taiqian
!endutf8
#
# Australian unit
#
australiasquare (10 ft)^2 # Used for house area
#
# A few German units as currently in use.
#
zentner 50 kg
doppelzentner 2 zentner
pfund 500 g
#
# Some traditional Russian measures
#
# If you would like to help expand this section and understand
# cyrillic transliteration, let me know. These measures are meant to
# reflect common usage, e.g. in translated literature.
#
dessiatine 2400 sazhen^2 # Land measure
dessjatine dessiatine
funt 409.51718 grams # similar to pound
zolotnik 1|96 funt # used for precious metal measure
pood 40 funt # common in agricultural measure
arshin (2 + 1|3) feet
sazhen 3 arshin # analogous to fathom
verst 500 sazhen # of similar use to mile
versta verst
borderverst 1000 sazhen
russianmile 7 verst
#
# Old French distance measures, from French Weights and Measures
# Before the Revolution by Zupko
#
frenchfoot 144|443.296 m # pied de roi, the standard of Paris.
pied frenchfoot # Half of the hashimicubit,
frenchfeet frenchfoot # instituted by Charlemagne.
frenchinch 1|12 frenchfoot # This exact definition comes from
frenchthumb frenchinch # a law passed on 10 Dec 1799 which
pouce frenchthumb # fixed the meter at
# 3 frenchfeet + 11.296 lignes.
frenchline 1|12 frenchinch # This is supposed to be the size
ligne frenchline # of the average barleycorn
frenchpoint 1|12 frenchline
toise 6 frenchfeet
arpent 180^2 pied^2 # The arpent is 100 square perches,
# but the perche seems to vary a lot
# and can be 18 feet, 20 feet, or 22
# feet. This measure was described
# as being in common use in Canada in
# 1934 (Websters 2nd). The value
# given here is the Paris standard
# arpent.
frenchgrain 1|18827.15 kg # Weight of a wheat grain, hence
# smaller than the British grain.
frenchpound 9216 frenchgrain
#
# Before the Imperial Weights and Measures Act of 1824, various different
# weights and measures were in use in different places.
#
# Scots linear measure
scotsinch 1.00540054 UKinch
scotslink 1|100 scotschain
scotsfoot 12 scotsinch
scotsfeet scotsfoot
scotsell 37 scotsinch
scotsfall 6 scotsell
scotschain 4 scotsfall
scotsfurlong 10 scotschain
scotsmile 8 scotsfurlong
# Scots area measure
scotsrood 40 scotsfall^2
scotsacre 4 scotsrood
# Irish linear measure
irishinch UKinch
irishpalm 3 irishinch
irishspan 3 irishpalm
irishfoot 12 irishinch
irishfeet irishfoot
irishcubit 18 irishinch
irishyard 3 irishfeet
irishpace 5 irishfeet
irishfathom 6 irishfeet
irishpole 7 irishyard # Only these values
irishperch irishpole # are different from
irishchain 4 irishperch # the British Imperial
irishlink 1|100 irishchain # or English values for
irishfurlong 10 irishchain # these lengths.
irishmile 8 irishfurlong #
# Irish area measure
irishrood 40 irishpole^2
irishacre 4 irishrood
# English wine capacity measures (Winchester measures)
winepint 1|2 winequart
winequart 1|4 winegallon
winegallon 231 UKinch^3 # Sometimes called the Winchester Wine Gallon,
# it was legalized in 1707 by Queen Anne, and
# given the definition of 231 cubic inches. It
# had been in use for a while as 8 pounds of wine
# using a merchant's pound, but the definition of
# the merchant's pound had become uncertain. A
# pound of 15 tower ounces (6750 grains) had been
# common, but then a pound of 15 troy ounces
# (7200 grains) gained popularity. Because of
# the switch in the value of the merchants pound,
# the size of the wine gallon was uncertain in
# the market, hence the official act in 1707.
# The act allowed that a six inch tall cylinder
# with a 7 inch diameter was a lawful wine
# gallon. (This comes out to 230.9 in^3.)
# Note also that in Britain a legal conversion
# was established to the 1824 Imperial gallon
# then taken as 277.274 in^3 so that the wine
# gallon was 0.8331 imperial gallons. This is
# 231.1 cubic inches (using the international
# inch).
winerundlet 18 winegallon
winebarrel 31.5 winegallon
winetierce 42 winegallon
winehogshead 2 winebarrel
winepuncheon 2 winetierce
winebutt 2 winehogshead
winepipe winebutt
winetun 2 winebutt
# English beer and ale measures used 1803-1824 and used for beer before 1688
beerpint 1|2 beerquart
beerquart 1|4 beergallon
beergallon 282 UKinch^3
beerbarrel 36 beergallon
beerhogshead 1.5 beerbarrel
# English ale measures used from 1688-1803 for both ale and beer
alepint 1|2 alequart
alequart 1|4 alegallon
alegallon beergallon
alebarrel 34 alegallon
alehogshead 1.5 alebarrel
# Scots capacity measure
scotsgill 1|4 mutchkin
mutchkin 1|2 choppin
choppin 1|2 scotspint
scotspint 1|2 scotsquart
scotsquart 1|4 scotsgallon
scotsgallon 827.232 UKinch^3
scotsbarrel 8 scotsgallon
jug scotspint
# Scots dry capacity measure
scotswheatlippy 137.333 UKinch^3 # Also used for peas, beans, rye, salt
scotswheatlippies scotswheatlippy
scotswheatpeck 4 scotswheatlippy
scotswheatfirlot 4 scotswheatpeck
scotswheatboll 4 scotswheatfirlot
scotswheatchalder 16 scotswheatboll
scotsoatlippy 200.345 UKinch^3 # Also used for barley and malt
scotsoatlippies scotsoatlippy
scotsoatpeck 4 scotsoatlippy
scotsoatfirlot 4 scotsoatpeck
scotsoatboll 4 scotsoatfirlot
scotsoatchalder 16 scotsoatboll
# Scots Tron weight
trondrop 1|16 tronounce
tronounce 1|20 tronpound
tronpound 9520 grain
tronstone 16 tronpound
# Irish liquid capacity measure
irishnoggin 1|4 irishpint
irishpint 1|2 irishquart
irishquart 1|2 irishpottle
irishpottle 1|2 irishgallon
irishgallon 217.6 UKinch^3
irishrundlet 18 irishgallon
irishbarrel 31.5 irishgallon
irishtierce 42 irishgallon
irishhogshead 2 irishbarrel
irishpuncheon 2 irishtierce
irishpipe 2 irishhogshead
irishtun 2 irishpipe
# Irish dry capacity measure
irishpeck 2 irishgallon
irishbushel 4 irishpeck
irishstrike 2 irishbushel
irishdrybarrel 2 irishstrike
irishquarter 2 irishbarrel
# English Tower weights, abolished in 1528
towerpound 5400 grain
towerounce 1|12 towerpound
towerpennyweight 1|20 towerounce
towergrain 1|32 towerpennyweight
# English Mercantile weights, used since the late 12th century
mercpound 6750 grain
mercounce 1|15 mercpound
mercpennyweight 1|20 mercounce
# English weights for lead
leadstone 12.5 lb
fotmal 70 lb
leadwey 14 leadstone
fothers 12 leadwey
# English Hay measure
newhaytruss 60 lb # New and old here seem to refer to "new"
newhayload 36 newhaytruss # hay and "old" hay rather than a new unit
oldhaytruss 56 lb # and an old unit.
oldhayload 36 oldhaytruss
# English wool measure
woolclove 7 lb
woolstone 2 woolclove
wooltod 2 woolstone
woolwey 13 woolstone
woolsack 2 woolwey
woolsarpler 2 woolsack
woollast 6 woolsarpler
#
# Ancient history units: There tends to be uncertainty in the definitions
# of the units in this section
# These units are from [11]
# Roman measure. The Romans had a well defined distance measure, but their
# measures of weight were poor. They adopted local weights in different
# regions without distinguishing among them so that there are half a dozen
# different Roman "standard" weight systems.
romanfoot 296 mm # There is some uncertainty in this definition
romanfeet romanfoot # from which all the other units are derived.
pes romanfoot # This value appears in numerous sources. In "The
pedes romanfoot # Roman Land Surveyors", Dilke gives 295.7 mm.
romaninch 1|12 romanfoot # The subdivisions of the Roman foot have the
romandigit 1|16 romanfoot # same names as the subdivisions of the pound,
romanpalm 1|4 romanfoot # but we can't have the names for different
romancubit 18 romaninch # units.
romanpace 5 romanfeet # Roman double pace (basic military unit)
passus romanpace
romanperch 10 romanfeet
stade 125 romanpaces
stadia stade
stadium stade
romanmile 8 stadia # 1000 paces
romanleague 1.5 romanmile
schoenus 4 romanmile
# Other values for the Roman foot (from Dilke)
earlyromanfoot 29.73 cm
pesdrusianus 33.3 cm # or 33.35 cm, used in Gaul & Germany in 1st c BC
lateromanfoot 29.42 cm
# Roman areas
actuslength 120 romanfeet # length of a Roman furrow
actus 120*4 romanfeet^2 # area of the furrow
squareactus 120^2 romanfeet^2 # actus quadratus
acnua squareactus
iugerum 2 squareactus
iugera iugerum
jugerum iugerum
jugera iugerum
heredium 2 iugera # heritable plot
heredia heredium
centuria 100 heredia
centurium centuria
# Roman volumes
sextarius 35.4 in^3 # Basic unit of Roman volume. As always,
sextarii sextarius # there is uncertainty. Six large Roman
# measures survive with volumes ranging from
# 34.4 in^3 to 39.55 in^3. Three of them
# cluster around the size given here.
#
# But the values for this unit vary wildly
# in other sources. One reference gives 0.547
# liters, but then says the amphora is a
# cubic Roman foot. This gives a value for the
# sextarius of 0.540 liters. And the
# encyclopedia Brittanica lists 0.53 liters for
# this unit. Both [7] and [11], which were
# written by scholars of weights and measures,
# give the value of 35.4 cubic inches.
cochlearia 1|48 sextarius
cyathi 1|12 sextarius
acetabula 1|8 sextarius
quartaria 1|4 sextarius
quartarius quartaria
heminae 1|2 sextarius
hemina heminae
cheonix 1.5 sextarii
# Dry volume measures (usually)
semodius 8 sextarius
semodii semodius
modius 16 sextarius
modii modius
# Liquid volume measures (usually)
congius 12 heminae
congii congius
amphora 8 congii
amphorae amphora # Also a dry volume measure
culleus 20 amphorae
quadrantal amphora
# Roman weights
libra 5052 grain # The Roman pound varied significantly
librae libra # from 4210 grains to 5232 grains. Most of
romanpound libra # the standards were obtained from the weight
uncia 1|12 libra # of particular coins. The one given here is
unciae uncia # based on the Gold Aureus of Augustus which
romanounce uncia # was in use from BC 27 to AD 296.
deunx 11 uncia
dextans 10 uncia
dodrans 9 uncia
bes 8 uncia
seprunx 7 uncia
semis 6 uncia
quincunx 5 uncia
triens 4 uncia
quadrans 3 uncia
sextans 2 uncia
sescuncia 1.5 uncia
semuncia 1|2 uncia
siscilius 1|4 uncia
sextula 1|6 uncia
semisextula 1|12 uncia
scriptulum 1|24 uncia
scrupula scriptulum
romanobol 1|2 scrupula
romanaspound 4210 grain # Old pound based on bronze coinage, the
# earliest money of Rome BC 338 to BC 268.
# Egyptian length measure
egyptianroyalcubit 20.63 in # plus or minus .2 in
egyptianpalm 1|7 egyptianroyalcubit
egyptiandigit 1|4 egyptianpalm
egyptianshortcubit 6 egyptianpalm
doubleremen 29.16 in # Length of the diagonal of a square with
remendigit 1|40 doubleremen # side length of 1 royal egyptian cubit.
# This is divided into 40 digits which are
# not the same size as the digits based on
# the royal cubit.
# Greek length measures
greekfoot 12.45 in # Listed as being derived from the
greekfeet greekfoot # Egyptian Royal cubit in [11]. It is
greekcubit 1.5 greekfoot # said to be 3|5 of a 20.75 in cubit.
pous greekfoot
podes greekfoot
orguia 6 greekfoot
greekfathom orguia
stadion 100 orguia
akaina 10 greekfeet
plethron 10 akaina
greekfinger 1|16 greekfoot
homericcubit 20 greekfingers # Elbow to end of knuckles.
shortgreekcubit 18 greekfingers # Elbow to start of fingers.
ionicfoot 296 mm
doricfoot 326 mm
olympiccubit 25 remendigit # These olympic measures were not as
olympicfoot 2|3 olympiccubit # common as the other greek measures.
olympicfinger 1|16 olympicfoot # They were used in agriculture.
olympicfeet olympicfoot
olympicdakylos olympicfinger
olympicpalm 1|4 olympicfoot
olympicpalestra olympicpalm
olympicspithame 3|4 foot
olympicspan olympicspithame
olympicbema 2.5 olympicfeet
olympicpace olympicbema
olympicorguia 6 olympicfeet
olympicfathom olympicorguia
olympiccord 60 olympicfeet
olympicamma olympiccord
olympicplethron 100 olympicfeet
olympicstadion 600 olympicfeet
# Greek capacity measure
greekkotyle 270 ml # This approximate value is obtained
xestes 2 greekkotyle # from two earthenware vessels that
khous 12 greekkotyle # were reconstructed from fragments.
metretes 12 khous # The kotyle is a day's corn ration
choinix 4 greekkotyle # for one man.
hekteos 8 choinix
medimnos 6 hekteos
# Greek weight. Two weight standards were used, an Aegina standard based
# on the Beqa shekel and an Athens (attic) standard.
aeginastater 192 grain # Varies up to 199 grain
aeginadrachmae 1|2 aeginastater
aeginaobol 1|6 aeginadrachmae
aeginamina 50 aeginastaters
aeginatalent 60 aeginamina # Supposedly the mass of a cubic foot
# of water (whichever foot was in use)
atticstater 135 grain # Varies 134-138 grain
atticdrachmae 1|2 atticstater
atticobol 1|6 atticdrachmae
atticmina 50 atticstaters
attictalent 60 atticmina # Supposedly the mass of a cubic foot
# of water (whichever foot was in use)
# "Northern" cubit and foot. This was used by the pre-Aryan civilization in
# the Indus valley. It was used in Mesopotamia, Egypt, North Africa, China,
# central and Western Europe until modern times when it was displaced by
# the metric system.
northerncubit 26.6 in # plus/minus .2 in
northernfoot 1|2 northerncubit
sumeriancubit 495 mm
kus sumeriancubit
sumerianfoot 2|3 sumeriancubit
assyriancubit 21.6 in
assyrianfoot 1|2 assyriancubit
assyrianpalm 1|3 assyrianfoot
assyriansusi 1|20 assyrianpalm
susi assyriansusi
persianroyalcubit 7 assyrianpalm
# Arabic measures. The arabic standards were meticulously kept. Glass weights
# accurate to .2 grains were made during AD 714-900.
hashimicubit 25.56 in # Standard of linear measure used
# in Persian dominions of the Arabic
# empire 7-8th cent. Is equal to two
# French feet.
blackcubit 21.28 in
arabicfeet 1|2 blackcubit
arabicfoot arabicfeet
arabicinch 1|12 arabicfoot
arabicmile 4000 blackcubit
silverdirhem 45 grain # The weights were derived from these two
tradedirhem 48 grain # units with two identically named systems
# used for silver and used for trade purposes
silverkirat 1|16 silverdirhem
silverwukiyeh 10 silverdirhem
silverrotl 12 silverwukiyeh
arabicsilverpound silverrotl
tradekirat 1|16 tradedirhem
tradewukiyeh 10 tradedirhem
traderotl 12 tradewukiyeh
arabictradepound traderotl
# Miscellaneous ancient units
parasang 3.5 mile # Persian unit of length usually thought
# to be between 3 and 3.5 miles
biblicalcubit 21.8 in
hebrewcubit 17.58 in
li 10|27.8 mile # Chinese unit of length
# 100 li is considered a day's march
liang 11|3 oz # Chinese weight unit
# Medieval time units. According to the OED, these appear in Du Cange
# by Papias.
timepoint 1|5 hour # also given as 1|4
timeminute 1|10 hour
timeostent 1|60 hour
timeounce 1|8 timeostent
timeatom 1|47 timeounce
# Given in [15], these subdivisions of the grain were supposedly used
# by jewelers. The mite may have been used but the blanc could not
# have been accurately measured.
mite 1|20 grain
droit 1|24 mite
periot 1|20 droit
blanc 1|24 periot
#
# Localization
#
!var UNITS_ENGLISH US
hundredweight ushundredweight
ton uston
scruple apscruple
fluidounce usfluidounce
gallon usgallon
bushel usbushel
quarter quarterweight
cup uscup
tablespoon ustablespoon
teaspoon usteaspoon
dollar US$
cent $ 0.01
penny cent
minim minimvolume
pony ponyvolume
grand usgrand
firkin usfirkin
hogshead ushogshead
!endvar
!var UNITS_ENGLISH GB
hundredweight brhundredweight
ton brton
scruple brscruple
fluidounce brfluidounce
gallon brgallon
bushel brbushel
quarter brquarter
chaldron brchaldron
cup brcup
teacup brteacup
tablespoon brtablespoon
teaspoon brteaspoon
dollar US$
cent $ 0.01
penny brpenny
minim minimnote
pony brpony
grand brgrand
firkin brfirkin
hogshead brhogshead
!endvar
!varnot UNITS_ENGLISH GB US
!message Unknown value for environment variable UNITS_ENGLISH. Should be GB or US.
!endvar
!utf8
⅛- 1|8
¼- 1|4
⅜- 3|8
½- 1|2
⅝- 5|8
¾- 3|4
⅞- 7|8
⅙- 1|6
⅓- 1|3
⅔- 2|3
⅚- 5|6
⅕- 1|5
⅖- 2|5
⅗- 3|5
⅘- 4|5
# U+2150- 1|7 For some reason these characters are getting
# U+2151- 1|9 flagged as invalid UTF8.
# U+2152- 1|10
ℯ exp(1) # U+212F, base of natural log
µ- micro # micro sign U+00B5
μ- micro # small mu U+03BC
ångström angstrom
Å angstrom # angstrom symbol U+212B
Å angstrom # A with ring U+00C5
röntgen roentgen
°C degC
°F degF
°K K # °K is incorrect notation
°R degR
° degree
℃ degC
℉ degF
K K # Kelvin symbol, U+212A
ℓ liter # unofficial abbreviation used in some places
¢ cent
£ britainpound
¥ japanyen
€ euro
₩ southkoreawon
₪ israelnewshekel
₤ lira
₨ rupee
Ω ohm # Ohm symbol U+2126
Ω ohm # Greek capital omega U+03A9
℧ mho
ʒ dram # U+0292
℈ scruple
℥ ounce
℔ lb
ℎ h
ℏ hbar
‰ 1|1000
‱ 1|10000
′ ' # U+2032
″ " # U+2033
#
# Square unicode symbols starting at U+3371
#
㍱ hPa
㍲ da
㍳ au
㍴ bar
# ㍵ oV???
㍶ pc
#㍷ dm invalid on Mac
#㍸ dm^2 invalid on Mac
#㍹ dm^3 invalid on Mac
㎀ pA
㎁ nA
㎂ µA
㎃ mA
㎄ kA
㎅ kB
㎆ MB
㎇ GB
㎈ cal
㎉ kcal
㎊ pF
㎋ nF
㎌ µF
㎍ µg
㎎ mg
㎏ kg
㎐ Hz
㎑ kHz
㎒ MHz
㎓ GHz
㎔ THz
㎕ µL
㎖ mL
㎗ dL
㎘ kL
㎙ fm
㎚ nm
㎛ µm
㎜ mm
㎝ cm
㎞ km
㎟ mm^2
㎠ cm^2
㎡ m^2
㎢ km^2
㎣ mm^3
㎤ cm^3
㎥ m^3
㎦ km^3
㎧ m/s
㎨ m/s^2
㎩ Pa
㎪ kPa
㎫ MPa
㎬ GPa
㎭ rad
㎮ rad/s
㎯ rad/s^2
㎰ ps
㎱ ns
㎲ µs
㎳ ms
㎴ pV
㎵ nV
㎶ µV
㎷ mV
㎸ kV
㎹ MV
㎺ pW
㎻ nW
㎼ µW
㎽ mW
㎾ kW
㎿ MW
㏀ kΩ
㏁ MΩ
㏃ Bq
㏄ cc
㏅ cd
㏆ C/kg
㏈() dB
㏉ Gy
㏊ ha
# ㏋ HP??
㏌ in
# ㏍ KK??
# ㏎ KM???
㏏ kt
㏐ lm
# ㏑ ln
# ㏒ log
㏓ lx
㏔ mb
㏕ mil
㏖ mol
㏗() pH
㏙ ppm
# ㏚ PR???
㏛ sr
㏜ Sv
㏝ Wb
#㏞ V/m Invalid on Mac
#㏟ A/m Invalid on Mac
#㏿ gal Invalid on Mac
!endutf8
############################################################################
#
# Unit list aliases
#
# These provide a shorthand for conversions to unit lists.
#
############################################################################
!unitlist hms hr;min;sec
!unitlist time year;day;hr;min;sec
!unitlist dms deg;arcmin;arcsec
!unitlist ftin ft;in;1|8 in
!unitlist inchfine in;1|8 in;1|16 in;1|32 in;1|64 in
!unitlist usvol cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\
tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp
############################################################################
#
# The following units were in the unix units database but do not appear in
# this file:
#
# wey used for cheese, salt and other goods. Measured mass or
# waymass volume depending on what was measured and where the measuring
# took place. A wey of cheese ranged from 200 to 324 pounds.
#
# sack No precise definition
#
# spindle The length depends on the type of yarn
#
# block Defined variously on different computer systems
#
# erlang A unit of telephone traffic defined variously.
# Omitted because there are no other units for this
# dimension. Is this true? What about CCS = 1/36 erlang?
# Erlang is supposed to be dimensionless. One erlang means
# a single channel occupied for one hour.
#
############################################################################
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