Midpoint: worked example
| Point 1: x | 2 |
|---|---|
| Point 1: y | 3 |
| Point 2: x | 8 |
| Point 2: y | 11 |
| Midpoint x | 5 |
| Midpoint y | 7 |
| Distance between the points | 10 |
Midpoint: formula
Enter the x and y coordinates of the two points. The midpoint is the average of the x values and the average of the y values, and the calculator also gives the distance between them. Coordinates can be negative or decimals.
For points in 3D, add the third coordinate the same way, though this tool covers the plane. Check that each pair is entered as x then y.
Midpoint: changing Point 1: x
| Point 1: x | Midpoint x | Midpoint y | Distance between the points |
|---|---|---|---|
| 0 | 4 | 7 | 11.3 |
| 1 | 4.5 | 7 | 10.6 |
| 2 (example) | 5 | 7 | 10 |
| 3 | 5.5 | 7 | 9.4 |
| 4 | 6 | 7 | 8.9 |
Midpoint: compare input ranges
| Input | Tested from | To | Midpoint x: low input | Midpoint x: high input | Swing |
|---|---|---|---|---|---|
| Point 1: x | 1 | 3 | 4.5 | 5.5 | 1 (20%) |
| Point 2: x | 7 | 9 | 4.5 | 5.5 | 1 (20%) |
| Point 1: y | 2 | 4 | 5 | 5 | 0 |
| Point 2: y | 10 | 12 | 5 | 5 | 0 |
Midpoint: individual input comparisons
| Input | Value | Midpoint x | Midpoint y | Distance between the points |
|---|---|---|---|---|
| Point 1: x | 0 | 4 | 7 | 11.3 |
| 1 | 4.5 | 7 | 10.6 | |
| 2 | 5 | 7 | 10 | |
| 3 | 5.5 | 7 | 9.4 | |
| 4 | 6 | 7 | 8.9 | |
| Point 1: y | 1 | 5 | 6 | 11.7 |
| 2 | 5 | 6.5 | 10.8 | |
| 3 | 5 | 7 | 10 | |
| 4 | 5 | 7.5 | 9.2 | |
| 5 | 5 | 8 | 8.5 | |
| Point 2: x | 6 | 4 | 7 | 8.9 |
| 7 | 4.5 | 7 | 9.4 | |
| 8 | 5 | 7 | 10 | |
| 9 | 5.5 | 7 | 10.6 | |
| 10 | 6 | 7 | 11.3 | |
| Point 2: y | 9 | 5 | 6 | 8.5 |
| 10 | 5 | 6.5 | 9.2 | |
| 11 | 5 | 7 | 10 | |
| 12 | 5 | 7.5 | 10.8 | |
| 13 | 5 | 8 | 11.7 |
Midpoint: combined input changes
| Point 1: x / Point 2: x | 6 | 8 | 10 |
|---|---|---|---|
| 0 | 3 | 4 | 5 |
| 1 | 3.5 | 4.5 | 5.5 |
| 2 | 4 | 5 | 6 |
| 3 | 4.5 | 5.5 | 6.5 |
| 4 | 5 | 6 | 7 |
Midpoint: which assumptions move the result?
Midpoint: values and definitions
| Quantity and definition | Value used |
|---|---|
| Point 1: x | 2 |
| Point 1: y | 3 |
| Point 2: x | 8 |
| Point 2: y | 11 |
| Midpoint x | 5 |
| Midpoint y | 7 |
| Distance between the points | 10 |
Midpoint: half and double Point 1: x
| Point 1: x | Midpoint x |
|---|---|
| 1 | 4.5 |
| 2 | 5 |
| 4 | 6 |
Common error: Averaging the distances instead of the coordinates. The midpoint comes from the coordinates, and the distance between the endpoints is a separate result.
On a map, coordinates such as latitude and longitude are on a sphere, so the plane midpoint is only an approximation over long distances. The midpoint of a segment is not the center of an irregular shape. Unequal scales on the axes distort distance.
Rounding matters when coordinates are large.
Geometry calculators: Rectangle Area & Perimeter Calculator, Circle Area & Circumference Calculator, Triangle Area (Heron's Formula) Calculator, Sphere Volume & Surface Area Calculator, Cylinder Volume & Surface Area Calculator, Cone Volume & Surface Area Calculator.
The midpoint of a segment is the average of its endpoints, taken one axis at a time. Points (2, 3) and (8, 11) share a midpoint of (5, 7), and the distance between them is 10, since the run is 6 and the rise is 8. The same idea finds the center of a wall between two corners, the halfway stop between two towns on a map, or the center of a circle from the ends of a diameter.
Enter the points in the same coordinate system. Mixing map coordinates with local ones places the midpoint somewhere neither point is near.
See the distance and slope calculator for lines, the Pythagorean theorem page for distances, and the right triangle calculator for angles. The ellipse and circle calculators cover curves, and the dot product page handles vectors. The arc length calculator gives curved distances.
How is the distance related to the midpoint?
The midpoint is at half of the distance along the segment, so each half is half the total length.
Does this work for points on a globe?
Only approximately over short distances. Long distances on a globe need spherical geometry, since the shortest path between two places curves along the surface.
How do I find the midpoint of two points?
Average the x coordinates and average the y coordinates. The midpoint of 2, 3 and 8, 11 is 5, 7.