How do you calculate the midpoint between two coordinates?

Convert both to 3-D vectors on the sphere, average them, and convert the result back to latitude and longitude. Averaging the latitude and longitude numbers directly fails whenever the points straddle the antimeridian.

What is the difference between a midpoint and a halfway point?

With two points they are the same place. With three or more, the geographic midpoint is the centre of gravity of the whole set, whereas a halfway point only exists along a single route.

How do weights change the result?

Each point pulls on the midpoint in proportion to its weight, so giving one location a weight of 3 is the same as putting three people there. Use it to balance for group sizes or delivery volumes.

Can I use this to find a fair place to meet?

Yes, and the travel distances make it useful — look at the furthest trip and the spread rather than the midpoint alone. A point that is fair by distance can still be unfair by transport links, so check the routes.

Why does the midpoint of two far-apart cities sit further north than both?

Great circles bow toward the pole on long east-west legs, because that is genuinely the shorter path over a sphere. It is the same reason flights between Europe and North America track over Greenland.

Geographic Midpoint Calculator

Find the true centre of two or more coordinates on the sphere, with optional weights and the travel distance from every point.

The Geographic Midpoint Calculator runs entirely in your browser. The coordinates you paste are never uploaded.

Open the Latitude & Longitude Map

关于 Geographic Midpoint Calculator

Averaging latitudes and longitudes gives the wrong answer, and obviously so once a pair straddles the antimeridian: the mean of 179°E and 179°W is 0°, the far side of the planet. The correct method converts every point into a vector on the sphere, averages those, and projects the result back onto the surface. That also handles more than two points sensibly and lets each carry a weight, so three people in one city pull the meeting point their way. Paste a list of coordinates and this calculator returns the midpoint, how far each person has to travel to reach it, the spread between the shortest and longest trip, and a GeoJSON file you can drop straight onto a map.

功能特性

Vector averaging, which survives the antimeridian and the poles
Any number of points, not just two
Optional per-point weights for group sizes
Travel distance from every point, in kilometres or miles
Furthest, average and spread figures for judging fairness
Great-circle halfway point when exactly two points are given
GeoJSON output with inputs and midpoint marked
Everything computes on your device

如何使用 Geographic Midpoint Calculator

Paste one coordinate pair per line as latitude, longitude
Add a weight and a label after the pair if you want them
Read the midpoint and the distance each point has to travel
Copy the GeoJSON to plot the result on a map

示例

输入

51.5074, -0.1278, 1, London
48.8566, 2.3522, 1, Paris
52.5200, 13.4050, 1, Berlin

输出

Midpoint 51.02385, 5.24559 — furthest trip 570 km, average 528 km

Three points have a midpoint but no halfway point; the two are only the same for a pair.

常见错误与故障排除

The midpoint landed in the sea or on a mountain. — It is mathematically correct and practically useless. Treat the result as a search area, then pick the nearest town that everyone can actually reach — the midpoint minimises straight-line distance, not travel time.
No midpoint could be calculated. — The points cancel out on the sphere, which happens with antipodes or a perfectly symmetrical ring. Add another point or a weight and a unique answer appears.
The midpoint of two points does not look halfway on a flat map. — Web maps use a Mercator projection, which stretches distances toward the poles. The great-circle halfway point is correct on the globe even when it looks displaced on the map.

常见问题

How do you calculate the midpoint between two coordinates?: Convert both to 3-D vectors on the sphere, average them, and convert the result back to latitude and longitude. Averaging the latitude and longitude numbers directly fails whenever the points straddle the antimeridian.
What is the difference between a midpoint and a halfway point?: With two points they are the same place. With three or more, the geographic midpoint is the centre of gravity of the whole set, whereas a halfway point only exists along a single route.
How do weights change the result?: Each point pulls on the midpoint in proportion to its weight, so giving one location a weight of 3 is the same as putting three people there. Use it to balance for group sizes or delivery volumes.
Can I use this to find a fair place to meet?: Yes, and the travel distances make it useful — look at the furthest trip and the spread rather than the midpoint alone. A point that is fair by distance can still be unfair by transport links, so check the routes.
Why does the midpoint of two far-apart cities sit further north than both?: Great circles bow toward the pole on long east-west legs, because that is genuinely the shorter path over a sphere. It is the same reason flights between Europe and North America track over Greenland.