Great Circle / Haversine Distance Calculator

How to use this tool

1. Enter the latitude and longitude of the two points in decimal degrees.
2. The calculator returns distance in km and miles, the initial bearing, and the midpoint.

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