Google Apps Script for converting UTM coordinates to [latitude, longitude].

LICENSE

Copyright 2018 Google LLC.

Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at

https://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.

UTM2LL.gs

// Heavily based on https://gis.stackexchange.com/a/278112/4412.
function UTM2LL(easting, northing, utm_zone, is_north) {
  // First some validation:
  if (easting < 160000 || easting > 840000) {
    throw 'Outside permissible range of easting values.';
  }
  if (northing < 0) {
    throw 'Negative values are not allowed for northing.';
  }
  if (northing > 10000000) {
    throw 'Northing may not exceed 10,000,000.';
  }

  // Symbols as used in USGS PP 1395: Map Projections - A Working Manual
  const DatumEqRad = [
    6378137.0, 6378137.0, 6378137.0, 6378135.0, 6378160.0, 6378245.0, 6378206.4,
    6378388.0, 6378388.0, 6378249.1, 6378206.4, 6377563.4, 6377397.2, 6377276.3
  ];
  const DatumFlat = [
    298.2572236, 298.2572236, 298.2572215, 298.2597208, 298.2497323,
    298.2997381, 294.9786982, 296.9993621, 296.9993621, 293.4660167,
    294.9786982, 299.3247788, 299.1527052, 300.8021499
  ];

  const Item = 0;                              // default
  const a = DatumEqRad[Item];                  // equatorial radius (meters)
  const f = 1 / DatumFlat[Item];               // polar flattening
  const drad = Math.PI / 180;                  // convert degrees to radians
  const k0 = 0.9996;                           // scale on central meridian
  const b = a * (1 - f);                       // polar axis
  const e = Math.sqrt(1 - (b / a) * (b / a));  // eccentricity
  const esq = (1 - (b / a) * (b / a));         // e² for use in expansions
  const e0sq = e * e / (1 - e * e);            // e0² — always even powers

  // Now the actual calculation:
  const zcm = 3 + 6 * (utm_zone - 1) - 180;  // central meridian of zone
  const e1 = (1 - Math.sqrt(1 - e * e)) / (1 + Math.sqrt(1 - e * e));
  const M0 = 0;  // in case origin other than zero lat

  const M = is_north ?  // arc length along standard meridian
      M0 + northing / k0 :
      M0 + (northing - 10000000) / k;
  const mu = M / (a * (1 - esq * (1 / 4 + esq * (3 / 64 + 5 * esq / 256))));
  var phi1 = mu + e1 * (3 / 2 - 27 * e1 * e1 / 32) * Math.sin(2 * mu) + e1 * e1 * (21 / 16 - 55 * e1 * e1 / 32) * Math.sin(4 * mu);
  phi1 = phi1 + e1 * e1 * e1 * (Math.sin(6 * mu) * 151 / 96 + e1 * Math.sin(8 * mu) * 1097 / 512);
  const C1 = e0sq * Math.pow(Math.cos(phi1), 2);
  const T1 = Math.pow(Math.tan(phi1), 2);
  const N1 = a / Math.sqrt(1 - Math.pow(e * Math.sin(phi1), 2));
  const R1 = N1 * (1 - e * e) / (1 - Math.pow(e * Math.sin(phi1), 2));
  const D = (easting - 500000) / (N1 * k0);
  var phi = (D * D) * (1 / 2 - D * D * (5 + 3 * T1 + 10 * C1 - 4 * C1 * C1 - 9 * e0sq) / 24);
  phi = phi + Math.pow(D, 6) * (61 + 90 * T1 + 298 * C1 + 45 * T1 * T1 - 252 * e0sq - 3 * C1 * C1) / 720;
  phi = phi1 - (N1 * Math.tan(phi1) / R1) * phi;

  const lon = D * (1 + D * D * ((-1 - 2 * T1 - C1) / 6 + D * D * (5 - 2 * C1 + 28 * T1 - 3 * C1 * C1 + 8 * e0sq + 24 * T1 * T1) / 120)) / Math.cos(phi1);

  return [
    phi / drad,
    zcm + lon / drad,
  ];
}

function UTM34N2LL(easting, northing) {
  return UTM2LL(easting, northing, 34, true);
}