Midpoint Calculator
The point halfway between two points in 2D or 3D, or the missing endpoint when you know one end and the midpoint.
Result
Point: (2.5, 4)
Exact arithmetic on the coordinates entered. Nothing is estimated.
- x
- 2.5
- y
- 4
- Length of the whole segment
- 5
https://calcgallery.com/geometry/midpoint-calculator/
Results follow the mathematical operation and values shown. Check that you selected the intended operation, convention and dataset type before relying on the result. Read the full disclaimer
How to use the Midpoint Calculator
- Choose whether you want the midpoint or the other endpoint, in two or three dimensions.
- Enter the known endpoint, then either the second endpoint or the midpoint.
- Read the point, with each coordinate and the length of the whole segment below it.
The midpoint formula
M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)Each coordinate of the midpoint is the average of the two endpoints’ coordinates, calculated one axis at a time. Halfway between 1 and 4 is 2.5, and halfway between 2 and 6 is 4, so the midpoint of (1, 2) and (4, 6) is (2.5, 4).
Three dimensions
Add the z coordinates and halve them in the same way:
M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2, (z₁ + z₂) ÷ 2)Working backwards to an endpoint
If you know one end and the midpoint, the other end is as far beyond the midpoint as the known end is before it:
x₂ = 2 × Mx − x₁y₂ = 2 × My − y₁The page finds the midpoint and the far endpoint in exactly opposite ways. Going forward and then back returns the point you started with.
Also reported
The length of the whole segment, from one endpoint to the other, uses the distance formula. The midpoint splits it into two equal halves. The distance calculator also gives the slope and the change along each axis.
Coordinates are plain numbers, so the page has no unit switch. Whatever unit the coordinates are in, the answer is in the same unit.
With your numbers
- Mx = (1 + 4) ÷ 2 = 2.5
- My = (2 + 6) ÷ 2 = 4
- Midpoint = (2.5, 4)
Quick reference
Exact arithmetic on the coordinates entered. Nothing is estimated.
| Example | Point |
|---|---|
| (1, 2) and (4, 6) | (2.5, 4) |
| (0, 0) and (3, 4) | (1.5, 2) |
| (−3, −4) and (3, 4) | (0, 0) |
| (1, 2, 3) and (4, 6, 15) | (2.5, 4, 9) |
| End (1, 2), midpoint (2.5, 4) | (4, 6) |
| End (0, 0), midpoint (5, −3) | (10, -6) |
| End (1, 2, 3), midpoint (2.5, 4, 9) | (4, 6, 15) |
Common questions about the Midpoint Calculator
- Is the midpoint always between the two points?
- Yes. It lies on the straight line joining them, exactly halfway, so it is the same distance from each. That is true in any number of dimensions and for negative coordinates too.
- What if the two points are the same?
- Then the midpoint is that point, and the segment has a length of zero. The page gives both rather than refusing.
- How do I find the point one third of the way along?
- Use the section formula. The point a fraction t of the way from P₁ to P₂ is P₁ + t × (P₂ − P₁), taken for each coordinate. For a third, t = 1/3; the midpoint is the case t = ½. This page covers the midpoint only.
- How do I find the other end of a line from its midpoint?
- Choose "The other endpoint". Each coordinate of the far end is twice the midpoint minus the known end: x₂ = 2 × Mx − x₁. With one end at (1, 2) and the midpoint at (2.5, 4), the other end is (4, 6).