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Great-Circle Distance Calculator

Calculate the straight-line (great-circle) distance and initial compass bearing between two latitude/longitude coordinates.

Distance
5,570.2 km
Distance (miles)
3,461.2 mi
Initial bearing
51.2°

How it works

This calculates the 'as the crow flies' distance between two points on Earth's surface using the haversine formula, the standard closed-form method for great-circle distance on a sphere: a = sin²(Δφ/2) + cos(φ1)·cos(φ2)·sin²(Δλ/2), then distance = 2 · R · asin(√a), where φ and λ are latitude and longitude in radians and R is Earth's mean radius, 6,371 km — verified against published geodesy references rather than relied on from memory.

Treating Earth as a perfect sphere introduces a small, well-documented error (up to about 0.5% versus the true, slightly flattened WGS84 ellipsoid), so results can differ from a GPS-grade distance by a few meters per kilometer — accurate enough for travel planning, not for surveying.

The initial bearing — the compass heading you'd start out on to follow the great-circle route from point 1 to point 2 — is reported alongside the distance. Because a great-circle route curves relative to a flat map (except along the equator or a meridian), this bearing is only the heading at the very start of the trip, not a constant compass direction for the whole route.

FAQ

Why does the bearing change along the route instead of staying constant?

A great-circle path is the shortest route on a sphere, and following a constant compass bearing (a 'rhumb line') is almost never the shortest route — the two only coincide along the equator or when traveling due north/south along a meridian. This calculator reports only the initial bearing, the heading you'd start on; a real flight or ship's course continuously adjusts bearing to stay on the great-circle path.

Why is there no metric/imperial toggle?

Latitude and longitude are angular coordinates in degrees worldwide, not a physical length that varies by unit system, so there's nothing to toggle on the inputs. The resulting distance is shown directly in both kilometers and miles instead.

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