An online calculator to calculate the distance between two points on Earth, given their
latitudes and longitudes,
is presented. The distance in question is the shortest distance, the great-circle distance (arc of a circle), along the surface of the Earth.
You may first need to know how to find the latitude and longitude of a position on Earth.
Enter coordinates in decimal degrees. Use negative for South latitudes and West longitudes.
Let \( \theta_1 \) and \( \phi_1 \) be the latitude and longitude of an initial point (origin) on Earth and \( \theta_2 \) and \( \phi_2 \) be the latitude and longitude of a final point (destination) on Earth.
Let \( \Delta \theta = \theta_2 - \theta_1 \) and \( \Delta \phi = \phi_2 - \phi_1 \) (in radians).
The central angle \( c \) between the two points on the surface of the Earth is given by:
\[ c = 2 \arctan2 \left( \sqrt{a}, \sqrt{1-a} \right) \]
where
\[ a = \sin^2\left(\frac{\Delta \theta}{2}\right) + \cos(\theta_1) \cos(\theta_2) \sin^2\left(\frac{\Delta \phi}{2}\right) \]
The distance \( D \) between the two points is given by the Haversine formula:
\[ D = R \cdot c \]
where \( R \) is the radius of the Earth and is approximated by \( R \approx 6378 \) km.
| From | To | Distance (km) |
|---|---|---|
| North Pole \( (90^\circ N, 0^\circ) \) | Equator \( (0^\circ, 0^\circ) \) | ~10,018 km |
| North Pole \( (90^\circ N, 0^\circ) \) | South Pole \( (90^\circ S, 0^\circ) \) | ~20,036 km |
| New York \( (40.71^\circ N, 74.01^\circ W) \) | London \( (51.51^\circ N, 0.13^\circ W) \) | ~5,570 km |