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Geographic Midpoint Calculator

Find the geographic midpoint between two locations.

How it is calculated

The tool finds the midpoint along the great-circle (shortest) path on a spherical Earth. With latitudes φ and longitude difference Δλ in radians: Bx = cos φ2 · cos Δλ, By = cos φ2 · sin Δλ, φm = atan2(sin φ1 + sin φ2, √((cos φ1 + Bx)² + By²)) and λm = λ1 + atan2(By, cos φ1 + Bx).

Inputs are decimal degrees: north and east positive, south and west negative. The result is given with five decimals and the longitude is normalised to between −180 and +180. This is not the average of the two latitudes and longitudes, which would give a wrong point over long distances. The Earth is treated as a sphere, so ellipsoid errors of a few tenths of a percent are possible.

Worked example

Point 1: 40.7128, −74.0060 (New York). Point 2: 51.5074, −0.1278 (London). The longitude difference is 73.8782°. Putting these into the formulas gives φm ≈ 52.368° and λm ≈ −41.290°. The tool shows latitude 52.36844 and longitude −41.29031, a point in the North Atlantic that is further north than either city because the shortest route curves toward the pole.

Try this example →

Common mistakes

  • Entering west longitudes or southern latitudes without the minus sign.
  • Typing degrees-minutes-seconds such as 40°42′46″ in a decimal-degree field.
  • Averaging the coordinates by hand and expecting the same answer; for long distances the great-circle midpoint is noticeably different.
  • Swapping latitude and longitude between the fields.

Sources

About this calculator

This calculator finds the geographic midpoint between two latitude/longitude coordinates along the great-circle path — the shortest route over the Earth's curved surface — by converting each point to 3D Cartesian coordinates, averaging them, and converting back to latitude/longitude. This is different from (and more accurate than) simply averaging the two latitudes and longitudes directly, which distorts distance, especially over long ranges or near the poles.

It's used to find a fair meeting point between two people or offices in different cities, plan refueling or layover stops on long routes, and in logistics and event planning where a truly equidistant central location matters.

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Comments (1)

  • Editorial team

    The result is the great-circle midpoint, the halfway point along the shortest path over the globe, so it is not the average of the two latitudes and longitudes. For far-apart cities the two give clearly different places. Enter coordinates as decimal degrees, with south and west as negative numbers. For two points on opposite sides of the Earth, the midpoint is not unique. Which pair of places are you trying to meet between?

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