Distance Calculator — Between Coordinates or Points

Distance between two places

On a map, the shortest path between two places is a curve: the Earth is round, and the straight line on a flat map is not the shortest way across its surface. The calculator measures the great-circle distance — the length of that shortest path, “as the crow flies”. Enter latitude and longitude in decimal degrees (40.7128, −74.0060) or in degrees, minutes and seconds (40°42′46″ N, 74°0′22″ W), and it returns the distance in miles, kilometers and nautical miles, the initial compass bearing and the midpoint.

The main figure uses Vincenty’s formula on the WGS 84 ellipsoid, the model of the Earth’s shape that GPS and most maps use; the U.S. National Geodetic Survey’s inverse calculator uses the same method. The on a sphere line uses the simpler haversine formula with a mean radius of 6,371 km. The two differ by up to about 0.5%: for New York to Los Angeles, 2,450.95 miles on the ellipsoid and 2,445.56 on the sphere.

Unit	Length
1 mile	1.609344 km
1 nautical mile	1.852 km (1.15078 miles)
1° of latitude	about 69 miles (111 km)
1° of longitude at the equator	about 69.2 miles (111.32 km), shrinking to 0 at the poles

Distance between two points on a plane

For points on a grid, graph or floor plan, the distance comes from the Pythagorean theorem: the horizontal and vertical differences are the two legs of a right triangle and the distance is its hypotenuse. From (1, 1) to (4, 5), Δx = 3 and Δy = 4, so d = √(3² + 4²) = 5. The calculator also gives the slope (Δy ÷ Δx = 1.333), the angle of the line (53.13°), its equation (y = 1.333x − 0.333) and the midpoint. For right triangles in general, use the Pythagorean theorem calculator.

Distance in three dimensions

In space, add the third difference under the square root: d = √(Δx² + Δy² + Δz²). From (1, 1, 1) to (2, 2, 2) the distance is √3 ≈ 1.732. This is the straight line through space, used for things like the diagonal of a box or the distance between points in a 3D model; the diagonal of a room 12 × 10 × 8 ft is √(144 + 100 + 64) ≈ 17.55 ft.

Miles, kilometers and nautical miles

The mile used in the U.S. is exactly 1,609.344 meters, and a nautical mile — used at sea and in aviation — is exactly 1,852 meters, close to one minute of latitude. To convert a distance you already have, use km to miles or miles to km; for the area enclosed by a shape, the area calculator.

Frequently asked questions

How do I find the distance between two coordinates?

Enter each place's latitude and longitude. The calculator measures the shortest path over the Earth's surface — the great-circle or 'as the crow flies' distance — in miles, kilometers and nautical miles.

Why is the driving distance longer?

Roads curve around terrain and follow the street grid, so a trip by road is always longer than the straight line. Use a map app for routes; this calculator gives the direct distance.

What is the distance formula for two points?

d = √((x₂ − x₁)² + (y₂ − y₁)²). From (1, 1) to (4, 5) that is √(3² + 4²) = 5. In three dimensions, add (z₂ − z₁)² under the root.

Why are there two Earth distances?

The Earth is slightly flattened at the poles. The main result follows the WGS 84 ellipsoid that GPS uses; the haversine figure treats the Earth as a perfect sphere and can differ by up to about half a percent.

How do I enter degrees, minutes and seconds?

Type them with symbols or spaces, such as 40°42′46″ N or 40 42 46 N. South latitudes and west longitudes are negative in decimal form, so 74°0′22″ W is −74.006.

What is the initial bearing?

The compass direction to set off in from point A along the shortest path. On long routes the bearing changes along the way, which is why flights from New York to Europe head northeast first.