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Great Circle Distance

Shortest distance between two points on the Earth for long-range navigation.

Formula

d=Rarccos⁡(sin⁡ϕ1sin⁡ϕ2+cos⁡ϕ1cos⁡ϕ2cos⁡Δλ)d = R\arccos(\sin\phi_1\sin\phi_2 + \cos\phi_1\cos\phi_2\cos\Delta\lambda)

Variables

dDistance
REarth radius
\phiLatitudes
\Delta\lambdaLongitude difference

Example

The shortest air route from New York to Tokyo curves near the Arctic — a great-circle path.

Did You Know?

The shortest route between two cities curves toward the pole — why flights to Asia arc over the Arctic.

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