About the Midpoint Formula Calculator
What is the Midpoint Formula Calculator?
The midpoint of a line segment is the point exactly halfway between its two endpoints. Its coordinates are simply the averages of the endpoints' x-coordinates and y-coordinates. Midpoints are used in coordinate geometry proofs, to find the centre of a circle from a diameter and to bisect lines.
Enter the coordinates of the two endpoints. The calculator gives the midpoint, its x and y coordinates separately and the distance between the two points (the length of the segment).
How to use the Midpoint Formula Calculator
- x₁ (sample: -2)
- y₁ (sample: 5)
- x₂ (sample: 6)
- y₂ (sample: -1)
- Press Find Midpoint (results also refresh as you type). The result card shows the Midpoint, along with Midpoint x, Midpoint y and Distance between the points.
Formula used
M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
- (x₁, y₁), (x₂, y₂) = the endpoints of the segment
To find a missing endpoint when you know one endpoint and the midpoint, reverse the formula: x₂ = 2Mₓ − x₁ and y₂ = 2M_y − y₁.
Worked example
These are the sample values already filled in the calculator above, and the result it returns for them:
| Input | Sample value |
|---|---|
| x₁ | -2 |
| y₁ | 5 |
| x₂ | 6 |
| y₂ | -1 |
| Result | Value |
|---|---|
| Midpoint | (2, 2) |
| Midpoint x | 2 |
| Midpoint y | 2 |
| Distance between the points | 10 |
Tips for using the Midpoint Formula Calculator
- If the segment is a diameter of a circle, its midpoint is the centre and half its length is the radius.
- The midpoint always lies on the segment, so its coordinates fall between the endpoints' coordinates.