Latitude Longitude Midpoint Calculator
Instantly convert latitude longitude midpoint with our free converter. See conversion tables, formulas, and step-by-step explanations.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Latitude Longitude Midpoint Calculator
Calculator
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Formula: midLat = atan2(sin(lat1)+sin(lat2), sqrt((cos(lat1)+Bx)^2 + By^2))
Worked example — Midpoint: approximately 52.33 N, 36.84 W (over the Atlantic Ocean, south of Greenland)
Formula
midLat = atan2(sin(lat1)+sin(lat2), sqrt((cos(lat1)+Bx)^2 + By^2))
The spherical midpoint formula uses Bx = cos(lat2)*cos(dLon) and By = cos(lat2)*sin(dLon) as intermediate values. The midpoint latitude is found using atan2 for proper quadrant handling. The midpoint longitude is computed by adding atan2(By, cos(lat1)+Bx) to the first longitude. This method correctly handles all cases including crossing the antimeridian.
Worked Examples
Example 1: Midpoint Between New York and London
Problem:Find the geographic midpoint between New York (40.7128 N, 74.006 W) and London (51.5074 N, 0.1278 W).
Solution:Convert to radians, compute Bx = cos(lat2)*cos(dLon), By = cos(lat2)*sin(dLon). midLat = atan2(sin(lat1)+sin(lat2), sqrt((cos(lat1)+Bx)^2 + By^2)) midLon = lon1 + atan2(By, cos(lat1)+Bx)
Result:Midpoint: approximately 52.33 N, 36.84 W (over the Atlantic Ocean, south of Greenland)
Example 2: Midpoint Between Los Angeles and Tokyo
Problem:Calculate the midpoint between LA (33.9425, -118.4081) and Tokyo (35.6762, 139.6503).
Solution:Apply spherical midpoint formula. Total distance is approximately 8,815 km. Midpoint lies along the great circle route over the Pacific.
Result:Midpoint: approximately 49.02 N, 168.85 W (over the North Pacific)
Frequently Asked Questions
What is the geographic midpoint between two coordinates?
The geographic midpoint is the point on Earth's surface that lies exactly halfway along the great circle path between two locations. Unlike a simple arithmetic average of coordinates, the geographic midpoint accounts for the curvature of the Earth using spherical trigonometry. This means the midpoint of two locations on the same latitude will not necessarily have the same latitude, especially for points far apart. The calculation converts coordinates to 3D Cartesian vectors, averages them, and converts back to geographic coordinates.
Why is the midpoint not just the average of two coordinates?
Simply averaging latitude and longitude values produces incorrect results because the Earth is a sphere, not a flat surface. Longitude lines converge at the poles, so one degree of longitude represents a much shorter distance near the poles than at the equator. Additionally, when two points are on opposite sides of the 180-degree meridian, a simple average would place the midpoint on the wrong side of the globe. The spherical midpoint formula handles these edge cases correctly by working in 3D Cartesian space.
What are practical uses for finding the geographic midpoint?
The geographic midpoint has many practical applications. It is commonly used to find a fair meeting place between two people in different cities, to plan refueling stops for long-distance flights, and to determine the center point of a delivery service area. Scientists use midpoint calculations when studying migration patterns, tracking storms, and analyzing satellite coverage areas. In logistics, finding the midpoint helps optimize warehouse placement between suppliers and customers.
Does the midpoint calculation work for antipodal points?
Antipodal points are locations on exact opposite sides of the Earth, such as the North and South poles. For perfectly antipodal points, the midpoint is mathematically undefined because every great circle connecting them has the same length, so there are infinite midpoints forming a complete circle around the Earth. In practice, most real-world coordinate pairs are not perfectly antipodal, and the formula will return a valid midpoint. If your inputs are very close to antipodal, the result may be numerically unstable.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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