Midpoint calculator
The true halfway point between two places, or the geographic centre of a whole group, measured over the curved Earth.
35.6850°, 139.7514° · Asia/Tokyo
34.1140°, -118.4068° · America/Los Angeles
168° 39′ 10.5″ W
Midpoint of two points on a graph (x, y)
Doing geometry rather than geography? On a flat coordinate plane the midpoint formula is M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2).
y = (3 + 7) / 2 = 5
This flat formula is only right for latitude/longitude over short distances; for places on Earth use the calculator above.
Why averaging coordinates fails
Tokyo sits at 139.75° E and Los Angeles at 118.41° W (−118.41). Their numerical average longitude is about 10.7° E, which is in the Mediterranean, on the opposite side of the planet from the Pacific the flight actually crosses. Tick the box above to see the naive point on the globe.
The fix is to stop treating latitude and longitude as flat x and y. Each place becomes a point in 3D: x = cos φ cos λ, y = cos φ sin λ, z = sin φ. Average those (weighted if you like), then convert back with φ = atan2(z, √(x²+y²)) and λ = atan2(y, x). The result lies on the great circle between two places, exactly halfway along it.
Try London and New York: the naive answer still lands in the Atlantic, but about 760 km south of the real midpoint, because the true route bends toward the pole.
Frequently asked questions
How do you find the halfway point between two places?
Convert each place’s latitude and longitude into a 3D point on a unit sphere, average the x, y and z values, and convert the result back to latitude and longitude. For two places this gives the exact midpoint of the great-circle route; for more places it gives their geographic centre.
Why not just average the latitudes and longitudes?
Because longitude lines converge toward the poles and wrap at ±180°. Averaging Tokyo and Los Angeles numerically lands in the Atlantic side of the world, not the Pacific. The toggle on this page shows how far off the naive average can be.
Can I find a midpoint between three or more locations?
Yes. Add as many places as you like. With weights, you can pull the centre toward places where more people are travelling from, for example the home cities of team members.
What is the difference between the centre of gravity and the point of least total distance?
The centre of gravity is the average position of all places on the globe, the balance point if each place had a weight. The point of least total distance (also called the geometric median) minimises the sum of everyone’s straight-line travel. With three or more places they differ, and the least-distance point is pulled toward clusters and ignores far-off outliers more.
What is the midpoint formula?
On a flat x–y plane, M = ((x₁ + x₂)/2, (y₁ + y₂)/2): average the x values and average the y values. On the Earth that only works for short distances; the calculator converts places to 3D vectors instead.
Is the midpoint the fairest place to meet?
It is equal in straight-line distance, not travel time. Once you have the point, look for the nearest well-connected city or airport around it.