Vincenty

Calculate the geographical distance (in meters) between 2 points with extreme accuracy.

This library implements Vincenty's solution to the inverse geodetic problem. It is based on the WGS 84 reference ellipsoid and is accurate to within 1 mm (!) or better.

This formula is widely used in geographic information systems (GIS) and is much more accurate than methods for computing the great-circle distance (which assume a spherical Earth).

Include the gem in your Gemfile:

gem 'vincenty_distance'

or

$ gem install vincenty_distance

and

require 'vincenty'

require 'vincenty'

boston  = { latitude: 42.3541165, longitude: -71.0693514 }
newyork = { latitude: 40.7791472, longitude: -73.9680804 }

distance = Vincenty.distance_between_points(boston, newyork)

# distance =  298_396.057 m

Wikipedia: Vincenty's formulae

Wikipedia: World Geodetic System

Python implementation