Great-Circle Distance (Haversine)

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

NavigationSailings

Lat 1 (°)°Lon 1 (°)°Lat 2 (°)°Lon 2 (°)°

Great-circle distance: 3,012.6nm

Initial bearing (°T): 288.4°

Changing the inputs requires JavaScript. The calculator above shows its default inputs and result. The formula, symbols, and regulatory sources are shown in the Formula section below.

Formula, assumptions, and limits

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

Symbol	Meaning	Unit
$\varphi_1, \varphi_2$	Latitudes	°
$\lambda_1, \lambda_2$	Longitudes	°
$R$	Earth mean radius (nm)	nm
$d$	Distance	nm

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.

Learn the theory Marine Voyage Planning and Routing