How this calculator works
A great circle is the largest circle that can be drawn on a sphere, and its plane passes through the centre. The shortest path between two points on a sphere is always an arc of a great circle, which is why long-haul flights bend toward the poles on a flat map. This calculator uses the haversine form of the spherical distance formula because it stays accurate for very short distances, where the simpler law of cosines loses precision. The initial bearing is the compass direction you would follow at departure; it changes along the route because meridians converge at the poles.
Formula
a = sin²(Δφ/2) + cos φ₁ cos φ₂ sin²(Δλ/2); d = 2R arcsin(√a); θ = atan2(sin Δλ cos φ₂, cos φ₁ sin φ₂ - sin φ₁ cos φ₂ cos Δλ).
Worked example
From London (51.5074 N, 0.1278 W) to New York (40.7128 N, 74.0060 W), the great-circle distance on a 6371 km sphere is about 5570 km and the initial bearing is about 288°. Two points on the equator separated by 90° of longitude are a quarter of the way around the world, about 10008 km apart.
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Frequently asked questions
Is this the same as driving distance?
No. The great-circle distance is the shortest path over the surface of a smooth sphere. Roads follow terrain, coastlines and networks, so a driving route is always longer, sometimes much longer.
Why is the Earth radius adjustable?
The Earth is not a perfect sphere; its mean radius is about 6371 km, but a local radius or the radius of another planet or moon can be entered instead. Changing the radius scales the distance proportionally.
What does the bearing mean?
It is the angle clockwise from true north at the starting point, from 0° to 360°. A bearing of 90° means due east, and 288° points west-northwest. The bearing is not constant along a great circle.