Haversine Distance Formulas

Haversine.md

Haversine Formula

used to calculate the great circle distance between two points on the earth (specified in decimal degrees)

Earth's Radius

• Miles: 3956
• Kilometers: 6371

Javascript

// Convert numeric degrees to radians
if (typeof(Number.prototype.toRad) === 'undefined') {
  Number.prototype.toRad = function() {
    return this * Math.PI / 180;
  }
}

function distance(lat1, lng1, lat2, lng2) {
  var dLat = (lat2-lat1).toRad(),
      dLng = (lng2-lng1).toRad(),
      lat1 = lat1.toRad(),
      lat2 = lat2.toRad();

  var a = Math.sin(dLat / 2) * Math.sin(dLat / 2) +
          Math.sin(dLng / 2) * Math.sin(dLng / 2) * 
          Math.cos(lat1) * Math.cos(lat2),
      c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1 - a));

  return 3956 * c;
}

Coffeescript

toRad = (val) ->
  val * Math.PI / 180

distance = (lat1, lng1, lat2, lng2) ->
  dLat = toRad(lat2-lat1)
  dLng = toRad(lng2-lng1)
  a = Math.sin(dLat/2) * Math.sin(dLat/2) + Math.cos(toRad(lat1)) * Math.cos(toRad(lat2)) * Math.sin(dLng/2) * Math.sin(dLng/2)
  c = 2 * Math.atan2(Math.sqrt(a), Math.sqrt(1-a))
  3956 * c

PHP

function distance($lat1, $lng1, $lat2, $lng2) {

    // convert decimal degrees to radians
    $dLat = deg2rad($lat2 - $lat1);
    $dLng = deg2rad($lng2 - $lng1);
    $lat1 = deg2rad($lat1);
    $lat2 = deg2rad($lat2);

    // haversine formula
    $a = sin($dLat / 2) * sin($dLat / 2) +
         sin($dLng / 2) * sin($dLng / 2) *
         cos($lat1) * cos($lat2);
    $c = 2 * atan2(sqrt($a), sqrt(1 - $a));
    return 3956 * $c;
}

Python

def distance(self, lat1, lng1, lat2, lng2):
    """
    Calculate the great circle distance (in miles) between two points
    on the earth (specified in decimal degrees)
    """

    # convert decimal degrees to radians
    lng1, lat1, lng2, lat2 = map(radians, [lng1, lat1, lng2, lat2])
    dlng = lng2 - lng1
    dlat = lat2 - lat1

    # haversine formula
    a = sin(dlat/2)**2 + cos(lat1) * cos(lat2) * sin(dlng/2)**2
    c = 2 * asin(sqrt(a))
    return 3956 * c

Ruby

class Geo
  EARTH_RADIUS = 3956
  RADIANS_PER_DEGREE = 0.017453293

  # Uses the haversine formula to calculate the great-circle distance between two points (in miles)
  def self.distance( lat1, lng1, lat2, lng2 )
    dlng = lng2 - lng1
    dlat = lat2 - lat1

    dlng_rad = dlng * RADIANS_PER_DEGREE
    dlat_rad = dlat * RADIANS_PER_DEGREE

    lat1_rad = lat1 * RADIANS_PER_DEGREE
    lat2_rad = lat2 * RADIANS_PER_DEGREE

    a = (Math.sin(dlat_rad/2))**2 + Math.cos(lat1_rad) * Math.cos(lat2_rad) * (Math.sin(dlng_rad/2))**2
    c = 2 * Math.atan2( Math.sqrt(a), Math.sqrt(1-a))

    EARTH_RADIUS * c
  end
end