Distance Between Coordinates

How it is calculated

The haversine formula gives the great-circle (shortest path over the surface) distance between two points on a sphere. With latitudes φ and longitudes λ in degrees, it computes a = sin²(Δφ/2) + cos φ1 × cos φ2 × sin²(Δλ/2) and then d = 2R × asin(√a), where R = 6371 km is the mean Earth radius. The result is in kilometres.

Enter coordinates as decimal degrees: north and east are positive, south and west are negative. Treating the Earth as a perfect sphere introduces an error of up to roughly half a percent compared with ellipsoidal methods. The result is the straight path over the surface, not the road, rail or flight route, and it ignores altitude.

Common mistakes

• Swapping latitude and longitude. Latitude comes first and ranges from −90 to 90.
• Entering degrees, minutes and seconds (41°00′29″) instead of decimal degrees.
• Forgetting the minus sign for south latitudes and west longitudes, which puts the point on the wrong side of the globe.
• Expecting driving distance. The road distance is usually longer than this straight-line figure.