Distance Between Coordinates Calculator

What this tool does

This is the distance a bird or an aircraft covers, not a road. The bearing is the direction to set off in, measured clockwise from north — and on a long flight it keeps changing, because a great circle crosses each meridian at a different angle. The defaults are Lisbon to Paris; the last result is the rough flight time at a cruising speed of 850 km/h.

Formula

a = sin²(Δφ÷2) + cosφ₁ cosφ₂ sin²(Δλ÷2) ; d = 2R·atan2(√a, √(1−a))

Variables

Symbol	Meaning	Unit
`y1`	Latitude of the first point	°
`x1`	Longitude of the first point	°
`y2`	Latitude of the second point	°
`x2`	Longitude of the second point	°
`KM`	Distance	km
`MI`	Distance	mi
`NM`	Distance	NM
`BR`	Initial bearing	°
`HR`	Hours	h

Worked example

Latitude of the first point38.7223 °
Longitude of the first point-9.1393 °
Latitude of the second point48.8566 °
Longitude of the second point2.3522 °

Distance1452.9359 km
Distance902.8125 mi
Distance784.5226 NM
Initial bearing35.4349 °
Hours1.709 h

Limitations

The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
The default values are typical reference figures, not measurements of your situation. Replace them with your own data whenever you have it.

Frequently asked questions

How accurate is this on a real planet?

The haversine formula assumes a perfect sphere, and the Earth is flattened at the poles by about a third of a percent. Using the mean radius of 6371.0088 km, errors stay within roughly 0.5 percent anywhere — about seven kilometres on a 1450 km leg. Where that matters, surveying and navigation use Vincenty's formulae on an ellipsoid instead, which are far more involved.