GPS Distance Calculator

Distance on a curved surface

The shortest path between two points on the Earth is not a straight line on a flat map but an arc of a great circle on the globe, or more exactly a geodesic on the ellipsoid. For short distances the difference is negligible; across an ocean it is the reason a flight from London to New York heads north-west over Ireland and Newfoundland instead of due west. This calculator gives two answers. The haversine formula treats the Earth as a sphere with the mean radius of 6,371 km. Vincenty’s method solves the problem on the WGS84 ellipsoid, which is 21 km flatter at the poles than at the equator, and is accurate to well under a millimetre.

A worked example

From London Heathrow (51.4700, −0.4543) to New York JFK (40.6413, −73.7781), the ellipsoidal distance is 5,554.9 km, or 3,451.7 statute miles and 2,999.4 nautical miles. The spherical haversine distance is 5,540.0 km, 14.9 km shorter, an error of 0.27%. That is typical: the sphere can be wrong by up to about 0.5%, depending on direction and latitude. Along the equator, one degree of longitude is 111.32 km on the ellipsoid but 111.20 km on the mean sphere, because the equatorial radius of 6,378 km is larger than the mean. North-south distances near the poles go the other way.

What the number is and is not

The result is the length of the shortest path over the surface of the ellipsoid at sea level. It is not a driving or walking distance, which follows roads and trails and is commonly 20% to 40% longer than the straight line in a city and far more in mountains. It also ignores height: two points 1 km apart horizontally with a 300 m height difference are about 1.04 km apart in three dimensions. Airlines plan routes along great circles but deviate for winds, airspace and tracks, so actual flown distances are usually a few percent longer than the geodesic. A common misconception is that the shortest route looks shortest on a Mercator map; on that projection great circles appear as curves bending towards the pole.

When the formulas struggle

Vincenty’s iteration fails to converge for points that are almost exactly opposite each other on the globe, such as the equator at 0° and 179.7° E with a small latitude offset. In that rare case the calculator falls back to the spherical result and says so. The haversine formula itself is numerically stable at all distances, which is why it replaced the older spherical law of cosines for short distances, where that formula loses precision.

How to use it

1. Enter the latitude and longitude of point A in decimal degrees or DMS.
2. Enter point B the same way, remembering the minus sign or S and W.
3. Read the ellipsoidal distance in kilometres, miles and nautical miles.
4. Compare it with the spherical figure to see how much the Earth’s flattening matters for your route.