The midpoint is the average of the endpoints. It is used to bisect segments, find centres of circles from a diameter, and locate meeting points halfway between two places on a grid.
How to use the Midpoint Calculator
- First point – x
- First point – y
- Second point – x
- Second point – y
Results update as you type, and everything is calculated in your browser.
How it works
Each coordinate of the midpoint is the mean of the corresponding coordinates of the endpoints.
Inputs explained
| Field | What to enter |
|---|---|
| First point – x | A number |
| First point – y | A number |
| Second point – x | A number |
| Second point – y | A number |
What each result means
- x midpoint = ([First point – x] + [Second point – x])÷2
- y midpoint = ([First point – y] + [Second point – y])÷2
- Segment length = sqrt(([Second point – x] – [First point – x])^2 + ([Second point – y] – [First point – y])^2)
- Distance from each end to the midpoint = sqrt(([Second point – x] – [First point – x])^2 + ([Second point – y] – [First point – y])^2)÷2
Example values
How the main result changes when First point – x changes and everything else stays at the example values above:
| First point – x | x midpoint |
|---|---|
| -1 | 2.5 |
| -1.5 | 2.25 |
| -2 | 2 |
| -2.5 | 1.75 |
| -3 | 1.5 |
| -4 | 1 |
Formula
M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Worked example
Inputs — First point – x: -2; First point – y: 3; Second point – x: 6; Second point – y: 9.
Results — x midpoint = 2; y midpoint = 6; Segment length = 10; Distance from each end to the midpoint = 5.
Key terms
- Midpoint
- The point dividing a segment into two equal parts.
Frequently asked questions
What is the midpoint of (−2, 3) and (6, 9)?
(2, 6).
Does the midpoint formula work in 3D?
Yes – average the z-coordinates too.
How do I find an endpoint from the midpoint?
Use the endpoint calculator: x₂ = 2x_M − x₁.
Is the midpoint on the perpendicular bisector?
Yes, by definition.