Great Circle Distance Calculator
Calculate the shortest distance between any two points on Earth using latitude and longitude.
Uses the Haversine formula for accurate results.
The great circle distance is the shortest path between two points on the surface of a sphere — the route a straight-line tunnel would take if you could bore through the Earth. On a globe, this path curves when projected onto a flat map, which is why long-haul flights appear to arc over the poles rather than fly in a straight line.
The calculation uses the Haversine formula, named after the haversine trigonometric function:
a = sin²(Δlat/2) + cos(lat₁) × cos(lat₂) × sin²(Δlon/2) c = 2 × atan2(√a, √(1−a)) d = R × c
Where R is Earth’s mean radius (6,371 km / 3,959 miles), lat₁ and lat₂ are the latitudes of the two points in radians, and Δlat and Δlon are the differences in latitude and longitude.
This formula is accurate to within 0.3% for any distance on Earth. For extreme precision (geodetic surveying), the Vincenty formula accounts for Earth’s ellipsoidal shape, but the Haversine is more than sufficient for navigation, travel planning, and distance estimation.
Practical uses:
- Flight distance planning (great circle = shortest flight path)
- Ship routing (great circle routes cross fewer nautical miles)
- Hiking and wilderness navigation
- Satellite ground track calculations
- Estimating driving vs flying time comparisons
Example: London (51.5°N, 0°W) to New York (40.7°N, 74°W): d ≈ 5,570 km / 3,461 miles — the great circle route that flights actually take, curving north over the Atlantic.
Note: actual travel distance (roads, airways) is always longer than the great circle distance.
Earth isn’t actually a sphere. It’s an oblate spheroid — flattened at the poles by about 21 km out of 6,378 km equatorial radius — so any formula that treats Earth as a sphere carries up to about 0.5% error. For navigation, hiking, and travel planning this is invisible; you’d be off by 50 metres on a 10 km hike. For geodetic surveying, GPS precision work, or aircraft instrument approaches, the Vincenty formula on the WGS-84 ellipsoid (the geometric model GPS satellites are based on) gives accuracy to roughly 0.5 mm. The Haversine result on this page is the right tool for almost everything outside professional surveying.
Always work in radians. Both latitudes and longitudes have to be converted from degrees first (multiply by π/180). Forgetting that conversion is the most common bug in great-circle code — and it produces a nonsense answer without any obvious error signal, so the result looks plausible. This calculator handles the conversion for you.