Find the Midpoint Between Two Locations

The midpoint between two locations is the exact center point of the line segment that connects them, calculated as the average of their coordinates. For a flat map in two dimensions: M = ((x1+x2)/2, (y1+y2)/2). But when the two points are cities, towns, or any place on Earth's curved surface, a plain average of latitude and longitude gives the wrong answer, sometimes by hundreds of kilometers. The correct method uses the Haversine formula to find the great-circle midpoint, which follows the curve of the sphere.

If you average two latitude values and two longitude values directly, you treat the Earth as a flat plane. That works only for short distances, under about 10 kilometers, where the curvature is negligible. For a trip from London to New York, a flat average places the midpoint at roughly 50°N, 30°W, in the middle of the Atlantic. The true great-circle midpoint is near 51°N, 37°W, about 400 kilometers west of the flat average. The error grows as the distance increases and as the two points lie on different meridians. The midpoint must account for the sphere's geometry.

The Haversine method, originally used for navigation, provides the great-circle midpoint between two latitude/longitude pairs. The Movable Type Scripts reference by Chris Veness gives the standard implementation. It computes the midpoint along the great-circle arc, not a straight line through the Earth.

Formula

lat_m = atan2(sin(lat1)+sin(lat2), sqrt((cos(lat1)+cos(lat2))^2 + (sin(lat1)-sin(lat2))^2))
lon_m = lon1 + atan2(sin(lon2-lon1)*cos(lat2), cos(lat1)+cos(lat1)*cos(lon2-lon1))

The angles are in radians. The result is the midpoint on the sphere's surface. For most Earth distances, the error from assuming a perfect sphere is under 0.5%. For high-precision surveying, a geoid model like WGS84 is required.

Find the geographic midpoint between New York (40.7128°N, 74.0060°W) and Los Angeles (34.0522°N, 118.2437°W).0625 rad.

Compute the components:
sin(lat1)+sin(lat2) = 0.6580 + 0.5604 = 1.2184
cos(lat1)+cos(lat2) = 0.7332 + 0.8343 = 1.5675
sin(lat1)-sin(lat2) = 0.6580 - 0.5604 = 0.0976
Then sqrt((1.5675)^2 + (0.0976)^2) = 1.5707
86°N
7705)) = -1.2920 + atan2(-0.5614, 1.0725) = -1.2920 + (-0.4807) = -1.7727 rad = -101.56°W

The geographic midpoint is 37.86°N, 101.56°W, near the town of Meade, Kansas. A plain average would give 37.38°N, 96.12°W, an error of about 480 kilometers.

The geographic midpoint is the halfway point on the map, not the halfway point by drive time or by road distance. A midpoint between two cities may fall on a mountain, a lake, or a reservation with no services. If you are meeting someone, the best meeting point is often not the geometric midpoint but the place that balances drive time, road quality, and available amenities. Use a travel-time calculator or a meeting-point tool that accounts for road networks, not just coordinates.

Several free tools compute the geographic midpoint between two addresses or coordinates. Most use the Haversine method and give the midpoint in decimal degrees. Input the latitude and longitude of each point, and the tool returns the midpoint. Some tools also show the midpoint on a map. For a meeting point by drive time, use a route-planning service that lets you compare travel times from each starting point. Do not trust a single tool for critical logistics: cross-check with a second source.