Midpoint Coordinates Calculator
The midpoint between two places on the Earth is the point halfway along the shortest (great-circle) path that joins them. Because the Earth is curved, you cannot simply average the two latitudes and longitudes; doing so gives a noticeably wrong answer over long distances. This tool computes the true great-circle midpoint using the standard spherical formula, returning the midpoint's latitude and longitude in decimal degrees. Enter both points in decimal degrees, with negative values for south latitude and west longitude. It is handy for choosing a meeting place between two locations or finding the centre of a route.
Great-circle midpoint formula
Bx = cos(lat2) * cos(dLon)
By = cos(lat2) * sin(dLon)
lat_m = atan2(sin(lat1) + sin(lat2), sqrt((cos(lat1) + Bx)^2 + By^2))
lon_m = lon1 + atan2(By, cos(lat1) + Bx)
where dLon = lon2 - lon1
The two points are treated as unit vectors on a sphere. The formula effectively averages those vectors and projects the result back onto the surface, giving the point that lies on the great circle exactly halfway between the originals. The longitude is normalised to the range minus 180 to 180 degrees. This is the correct geographic midpoint, which a simple numeric average of the coordinates does not reproduce over long or high-latitude spans.
Worked example
The midpoint between New York (40.7128, -74.0060) and London (51.5074, -0.1278) works out to about latitude 52.37 degrees and longitude -41.29 degrees, a point in the North Atlantic well north of the straight-line average of the latitudes (46.1) and longitudes (-37.1). The difference shows why the great-circle formula is needed: the shortest path arcs north, so its midpoint sits at a higher latitude than a naive average suggests.
Frequently asked questions
Why not just average the two coordinates?
Averaging latitudes and longitudes treats the Earth as flat. Over short distances the error is tiny, but over long or high-latitude spans the great-circle path curves toward the pole, so its true midpoint can be far from the numeric average. The spherical formula used here gives the point genuinely halfway along the shortest route.
Is the great-circle midpoint the shortest-route midpoint?
Yes. The great circle is the shortest path between two points on a sphere, and this midpoint lies exactly halfway along it by arc length. If you instead followed a constant-bearing rhumb line, its midpoint would be slightly different, because the rhumb line is a longer, curved-on-the-map route.
What coordinate signs should I use?
Enter latitudes as positive for north and negative for south, and longitudes as positive for east and negative for west. So a New York longitude is -74.0060. The midpoint longitude is returned in the range minus 180 to 180 degrees with the same sign convention.
Does this work across the date line?
Yes. The formula uses the longitude difference and trigonometric functions, and the result is normalised to the minus 180 to 180 range, so it handles pairs of points that straddle the 180-degree meridian correctly, returning a midpoint with the proper sign rather than an averaged value on the wrong side of the globe.
Official sources
- NOAA National Geodetic Survey: geodetic computations.
- U.S. Geological Survey: coordinate systems and mapping.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.