Great Circle / Haversine Distance Calculator

What is the haversine formula?

The haversine formula calculates the great-circle distance between two points on a sphere given their latitude and longitude. The "great-circle" distance is the shortest path between two points on the surface of a sphere - the path a plane or ship takes.

a = sin²(Δlat/2) + cos(lat₁) × cos(lat₂) × sin²(Δlon/2)
c = 2 × atan2(√a, √(1-a))
d = R × c
where R = 6,371 km (Earth's mean radius)

Why not simple Pythagorean distance?

Earth is a sphere (technically an oblate spheroid). Treating latitude and longitude as flat x/y coordinates introduces significant error over long distances. For example, 1 degree of longitude near the poles represents a much shorter distance than 1 degree near the equator. The haversine formula accounts for this by working in spherical geometry.

Earth's radius note

This calculator uses Earth's mean radius of 6,371 km (WGS-84). Earth is actually an oblate spheroid - the equatorial radius is 6,378 km and the polar radius is 6,357 km, a difference of about 21 km. Using the mean radius introduces an error of up to ~0.5% in calculated distances. For surveying and navigation requiring higher precision, use the WGS-84 ellipsoid model (Vincenty formula).

Great-circle vs. straight-line distance

The haversine formula calculates the great-circle distance - the shortest path along Earth's surface. A straight-line (chord) distance through the Earth's interior would be shorter but is not a usable travel path. Aircraft follow great-circle routes (or near-great-circle routes adjusted for jet streams) because they represent the shortest surface path between two points.

Practical examples