Meeting point calculator

Worked example: four Midwest state capitals

The tool opens with four people: one each in Columbus, Ohio; Indianapolis, Indiana; Lansing, Michigan; and Frankfort, Kentucky. It computes two candidate meeting points and measures every person's straight-line trip to each.

The least-travel point at 39.8650° N, 84.7619° W brings the group's combined travel to 482.6 miles. The geographic midpoint at 40.1683° N, 84.6508° W costs 487.6 miles in total, but its longest single trip is 177.3 miles against 198.5 for the least-travel point. Lansing is the outlier to the north: the midpoint leans toward it, while the least-travel point stays closer to the three cities that sit near each other. Which one is fairer depends on whether you care about the group's total miles or about the person with the longest drive.

How to use it

1. Type a town, ZIP code, address, or coordinates in each Person box and pick a match. Person 1 also has Use GPS.
2. Press Add person for more boxes, up to 20, or click the map to add someone at that spot. The X next to a box removes it, down to two people.
3. Choose Meet at: Least total travel or Geographic midpoint. The map draws a line from each person to the chosen point, and the readout names the nearest town.
4. Read each person's trip in the table under the map, with total and longest trip rows, and press Download CSV to save it. Copy the page link to share the same group.

Two answers to where to meet

The geographic midpoint is the center of mass of the group. Each location is turned into a vector from the center of the Earth, the vectors are averaged, and the average is pushed back out to the surface. It is the natural extension of the halfway point between two places, and for two people it gives exactly that halfway point. Because it is an average, one person far from the rest pulls it toward them.

The least total travel point is the geometric median: the spot where the sum of everyone's straight-line distance is as small as it can be. It resists outliers. If most of the group lives in one city, it sits in that city, even when one person lives far away. For three people whose triangle has no angle of 120 degrees or more, it is the point where the three routes meet at equal 120 degree angles. For two people every point on the line between them has the same total, so the tool reports the midpoint.

How the least-travel point is computed

There is no closed formula for the geometric median, so the tool finds it by iteration. It starts at the geographic midpoint and applies Weiszfeld's method: each step moves toward a weighted average of the people, where closer people get more weight. On the sphere the step is taken in the flat tangent plane at the current estimate and then wrapped back onto the globe. If the estimate lands exactly on someone's location, a correction published by Vardi and Zhang decides whether to stay or move on. If it lands exactly opposite someone on the globe, where that person has no single direction, it steps off that spot first. The loop stops when a step is shorter than a millimeter.

When everyone is within about 3,000 miles of some common center, the total has a single lowest point and the result is that point. For groups spread around the globe the total can dip in more than one place, so the tool also restarts from the three people with the lowest totals, compares every result with each person's own location and the geographic midpoint, and keeps the lowest total it finds. For those groups it is the best answer found, not a proven minimum.

Distances use the haversine formula on a sphere of radius 6,371.0088 km. The nearest town is the closest US Census place of 1,000 or more people (Vintage 2024) to whichever point you choose with Meet at.

Limits

Every distance is a straight line, so neither point knows about roads, rivers, or ferries. A least-travel point on the wrong side of a lake can be a poor place to meet. Treat both points as a search area, then check the drive for each person with the crow flies calculator and its driving comparison.

Neither point minimizes the longest single trip. If fairness to the person with the farthest drive matters most, compare the Longest trip row under each column and try nearby towns by hand. Towns come from incorporated places only, so unincorporated communities are not suggested, and outside the US the nearest town row still points to a US place.