Geographic Midpoint Calculator
The geographic midpoint of two locations is the point on the great-circle path lying exactly halfway between them on the surface of the Earth. Because the Earth is curved and longitude wraps at the date line, you cannot simply average the coordinates. This calculator converts each latitude and longitude to a 3D unit vector, averages and normalizes them, then converts back to a latitude and longitude. Enter the two points in decimal degrees with north and east positive, and it returns the true halfway point along the shortest path.
Geographic midpoint formula
Convert to radians; for each point
x = cos(lat) * cos(lon), y = cos(lat) * sin(lon), z = sin(lat)
Sum and average the vectors: X, Y, Z
mid lon = atan2(Y, X)
mid lat = atan2(Z, sqrt(X*X + Y*Y))
The averaged vector points toward the midpoint direction; its latitude and longitude are recovered with atan2, which resolves the correct quadrant and handles the date line.
Midpoint context
- The vector method gives the great-circle midpoint, the halfway point on the shortest surface path.
- Averaging raw coordinates fails near the date line and at high latitudes.
- North and east are positive; south and west are negative decimal degrees.
- The result assumes a spherical Earth; ellipsoidal differences are small for typical uses.
- For two antipodal points the midpoint is undefined because infinitely many great circles connect them.
Geographic midpoint: frequently asked questions
What is the geographic midpoint of two points?
It is the point on the great-circle path that lies exactly halfway between two locations on the surface of the Earth. Because the Earth is curved, this is not the same as averaging the latitudes and longitudes; the correct midpoint is found by converting to Cartesian coordinates, averaging the unit vectors, and converting back.
Why can't I just average the coordinates?
Averaging latitude and longitude fails because longitude wraps around at 180 degrees and lines of longitude converge at the poles. The vector method handles the curvature and the date line correctly, so it gives the true halfway point along the shortest path.
How is the midpoint computed?
Each point is converted to a 3D unit vector. The two vectors are summed and the result is normalized back to the unit sphere. The latitude and longitude of that resulting direction is the midpoint. This is the standard spherical midpoint used in navigation.
Does this assume a perfect sphere?
Yes. The Earth is slightly flattened (an ellipsoid), so the spherical midpoint can differ from the ellipsoidal midpoint by a small amount, typically meters to a few hundred meters over long distances. For most mapping and planning uses the spherical result is more than adequate.
What sign convention do I use for coordinates?
Use decimal degrees with north and east positive, south and west negative. For example New York is about 40.71, -74.01. Longitudes range from -180 to 180 and latitudes from -90 to 90.
Official sources
- NOAA National Geodetic Survey: National Geodetic Survey.
- U.S. Geological Survey: U.S. Geological Survey.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.