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.

latitude is $\delta$ longitude is $\lambda$

The formula is:

dlon = <math>\lambda\sub{2}</math - lon1

dlat = lat2 - lat1

a = (sin(dlat/2))^2 + cos(lat1) * cos(lat2) * (sin(dlon/2))^2

c = 2 * arcsin(min(1,sqrt(a)))

d = R * c