Midpoint Calculator
Find the geographic center point between two or more GPS coordinates. Calculate the centroid for meeting points, search areas, or puzzle solutions.
Geographic midpoint: The center of gravity for all input coordinates, calculated as if each point had equal mass on a sphere. For 2 points, this is the exact center; for 3+ points, it's the centroid.
What is a Geographic Midpoint?
A geographic midpoint (also called centroid or center of gravity) is the central location among two or more GPS coordinates. For two points, it's the exact halfway point. For three or more points, it's the point that minimizes the total distance to all input coordinates.
Unlike simply averaging latitudes and longitudes, this tool calculates the true geographic center accounting for the Earth's spherical shape.
How Midpoint Calculation Works
For accurate results on Earth's surface, we use 3D Cartesian coordinates:
- Convert each coordinate to 3D (X, Y, Z) on a unit sphere
- Average all X, Y, and Z values
- Convert the average point back to latitude/longitude
This method works correctly even when points are spread across large distances or near the poles.
Midpoint Calculator in Geocaching
Geocachers use midpoint calculations in several ways:
Common Uses
- Puzzle solutions: Some puzzles require finding the center of given points
- Meeting spots: Find a fair meeting point between cachers
- Multi-cache planning: Estimate the central area of all stages
- Search area center: Define the center of a search zone
Puzzle Cache Patterns
Midpoint calculations appear in various puzzle types:
- "The cache is at the center of these three waypoints"
- "Find the midpoint between Stage 1 and Stage 3"
- "Calculate the centroid of the polygon formed by these coordinates"
Two Points vs Multiple Points
Two Points (Simple Midpoint)
For exactly two coordinates, the midpoint is the exact center of the line connecting them. This is the most common case in geocaching multi-caches.
Three or More Points (Centroid)
For three or more points, the result is the centroid—the geometric center that balances all points equally. Think of it as the balance point if you placed equal weights at each location.
Simple Averaging vs Geographic Midpoint
Simply averaging latitudes and longitudes gives incorrect results because:
- Longitude lines converge at the poles (1° longitude = 111km at equator, 0km at poles)
- Earth is spherical, not flat
- Points near ±180° longitude cause wrapping issues
Our calculator handles these correctly using spherical geometry.
Tips for Using the Midpoint Calculator
- Enter one coordinate per line: The tool parses each line separately
- Mix formats freely: You can combine DD, DDM, and DMS formats
- Check parsed points: Review the "Parsed Points" section to verify your coordinates were understood correctly
- Verify on maps: Use the Google Maps link to visualize the result
Practical Applications
Meeting Point
Enter each person's starting location to find a fair meeting spot that minimizes everyone's travel distance.
Search Area Center
When searching an area, enter the boundary coordinates to find the center point for systematic searching.
Cache Placement
Cache owners can use midpoints to position caches equidistant from landmarks or existing stages.
Related Navigation Tools
- Distance Calculator: Measure distances from the midpoint to each original coordinate.
- Coordinate Converter: Convert the midpoint between DD, DDM, and DMS.
- Waypoint Projection: Project new waypoints from the midpoint.
- Bearing Calculator: Find bearings from the midpoint to other locations.