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
| Symbol | Meaning | Unit | Source |
|---|---|---|---|
| $\varphi_1, \varphi_2$ | Latitudes | ° | chart / GPS |
| $\lambda_1, \lambda_2$ | Longitudes | ° | chart / GPS |
| $R$ | Earth mean radius (nm) | nm | 3440.065 |
| $d$ | Distance | nm | result |
Sources
- Bowditch - American Practical Navigator Ch.4.
- Admiralty Manual of Navigation (BR45).