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Great-Circle Distance (Haversine)

Shortest-path distance and initial bearing between two lat/lon positions on the spherical earth.

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Formula, assumptions, and limits

d=2Rarcsinsin2Δφ2+cosφ1cosφ2sin2Δλ2d = 2R \arcsin\sqrt{\sin^2 \tfrac{\Delta\varphi}{2} + \cos\varphi_1 \cos\varphi_2 \sin^2 \tfrac{\Delta\lambda}{2}}
SymbolMeaningUnit
φ1,φ2\varphi_1, \varphi_2Latitudes°
λ1,λ2\lambda_1, \lambda_2Longitudes°
RREarth mean radius (nm)nm
ddDistancenm

Source: Bowditch - American Practical Navigator Ch.4; Admiralty Manual of Navigation (BR45)

In short

Shortest-path distance and initial bearing between two lat/lon positions on the spherical earth.

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