Great-circle distance

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

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

$R$ is the radius of the earth (6367000 meters)

$\delta$ is latitude

$\lambda$is longitude

The formula is:

$dlon=\lambda '-\lambda$

$dlat=\delta '-\delta$

$a=(\sin {({\frac {dlat}{2}})})^{2}+\cos {\delta }*\cos {\delta '}*(\sin {({\frac {dlon}{2}})})^{2}$

$c=2*\arcsin {(\min {(1,{\sqrt {a}})})}$

$d=R*c$