The geographic midpoint calculator finds the geographic center of 2 to 10 locations using the Cartesian vector averaging method. Results appear on an interactive Leaflet map with numbered markers for each input point and a highlighted midpoint marker.
Enter Locations
Midpoint Results
How to Use the Geographic Midpoint Calculator
The geographic midpoint calculator finds the equidistant center point between multiple locations on Earth's surface. Unlike a simple average of latitudes and longitudes, the Cartesian vector method gives a mathematically correct result for any arrangement of points, including near the poles or across the International Date Line.
Step 1: Enter Coordinates
Two location rows appear by default. Enter the latitude and longitude for each location in Decimal Degrees (DD) format. Latitude ranges from -90 (South Pole) to +90 (North Pole). Longitude ranges from -180 (West) to +180 (East). Example: New York City is 40.7128, -74.0060.
Step 2: Add More Locations (Optional)
Click "+ Add Location" to add more input rows. The calculator supports up to 10 locations. Each location gets an equal weight in the midpoint calculation — there's no weighted average option in this tool. Click the remove button (×) on any row to delete it.
Step 3: Click Find Midpoint
Click the Find Midpoint button. The Leaflet map appears with numbered markers for each input location and a special teal marker for the midpoint. Lines connect each input location to the midpoint. The results panel shows midpoint coordinates in both DD and DMS formats, plus the distance from the midpoint to each input point.
How the Cartesian Midpoint Algorithm Works
Each latitude/longitude pair is converted to a unit vector in 3D Cartesian space using: x = cos(lat) × cos(lng), y = cos(lat) × sin(lng), z = sin(lat). All vectors are summed and normalized, then converted back to latitude/longitude using lat = atan2(z, √(x²+y²)) and lng = atan2(y, x). This gives the true geographic center for any set of points.
Common Use Cases
Finding the fairest meeting point for friends traveling from different cities, locating a central warehouse for multiple store locations, determining the geographic center of a sales territory, or calculating where to hold a team event for a distributed remote team. The midpoint from London (51.51°N, -0.13°E) and Sydney (-33.87°N, 151.21°E) falls in South Asia near the Bay of Bengal — roughly equidistant from both cities by air.
FAQ
Is this midpoint calculator free?
Yes, completely free. No signup, no account, no limits. Add up to 10 locations and find the geographic center instantly.
Is my location data safe?
All calculations run locally in your browser using math formulas. No coordinates are sent to any server.
What is the geographic midpoint?
The geographic midpoint is the average center of a set of locations on Earth's surface. Unlike averaging latitude and longitude directly, the true midpoint converts to 3D Cartesian coordinates first, then averages the vectors and converts back. This gives a correct result near the poles and across the International Date Line.
How is the geographic midpoint different from a simple average?
Averaging lat/lng directly gives wrong results near the poles and across the antimeridian (180° line). The Cartesian method converts each point to x/y/z coordinates on a unit sphere, averages those vectors, then converts back to lat/lng. This is mathematically correct for any distribution of points on a sphere.
What is the midpoint calculator useful for?
Finding a fair meeting point between people in different cities, planning events for geographically dispersed attendees, calculating the geographic center of a sales territory, or finding where to locate a warehouse equidistant from multiple customers.
Can I find the midpoint between more than two locations?
Yes. The calculator supports up to 10 locations. Add as many as you need with the Add Location button, then click Calculate. The midpoint shown is the geographic center of all input points weighted equally.
What coordinate format should I use?
Enter coordinates in Decimal Degrees (DD) format: latitude as a number between -90 and 90, longitude between -180 and 180. Negative values indicate South (latitude) or West (longitude). For example, New York City: 40.7128, -74.0060.