Great-circle distance

Great circle distance is the shortest distance between any two points on a sphere.

Because the Earth is approximately spherical, the great circle distance is commonly used to find the distance (e.g. in miles) between two coordinates (latitude/longitude pairs) on a map. First, some definitions:

Definitions

$R$ is the radius of the Earth ($\approx 6367000$ meters)

$\delta$ is latitude

$\lambda$ is longitude

The Formula

$gc(\delta ,\lambda ,\delta ',\lambda ')=$

$2\cdot R\cdot \arcsin {(\min {(1,{\sqrt {(\sin {({\frac {\delta '-\delta }{2}})})^{2}+\cos {\delta }\cdot \cos {\delta '}\cdot (\sin {({\frac {\lambda '-\lambda }{2}})})^{2}}})})}$

Practical Application

In order to use this formula for anything practical you will need two sets of coordinates. I'll provide the latitude and longitude of two airports:

• Nashville International Airport (BNA) in Nashville, TN, USA: W 86°40.2, N 36°7.2
• Los Angeles International Airport (LAX) in Los Angeles, CA, USA: W 118°24.0, N 33°56.4

See Also

http://mathworld.wolfram.com/GreatCircle.html

http://www.census.gov/cgi-bin/geo/gisfaq?Q5.1

http://williams.best.vwh.net/avform.htm