Great Circle Distance Calculator

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.