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Great-Circle Distance (Haversine)

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

Formula

$$ d = 2R \arcsin\sqrt{\sin^2 \tfrac{\Delta\varphi}{2} + \cos\varphi_1 \cos\varphi_2 \sin^2 \tfrac{\Delta\lambda}{2}} $$

Symbol legend

SymbolMeaningUnitSource
$\varphi_1, \varphi_2$Latitudes°chart / GPS
$\lambda_1, \lambda_2$Longitudes°chart / GPS
$R$Earth mean radius (nm)nm3440.065
$d$Distancenmresult

Sources

  • Bowditch - American Practical Navigator Ch.4.
  • Admiralty Manual of Navigation (BR45).