Midpoint Calculator
Average the coordinates of two points to find the point exactly halfway between them.
How to use the Midpoint Calculator
- Choose the find.
- Enter the point a: x.
- Enter the point a: y.
- Enter the point b: x.
- Enter the point b: y.
- Enter the midpoint m: x.
- Enter the midpoint m: y.
- Press Calculate. The result updates automatically as you type.
About the Midpoint Calculator
The midpoint of a line segment is the point that splits it into two equal halves. Its coordinates are simply the averages of the endpoints' coordinates, so (2, 3) and (8, 11) meet in the middle at (5, 7). The same idea works in three dimensions by averaging the z values as well.
Midpoints appear in geometry proofs (medians of triangles, perpendicular bisectors, the center of a circle from the ends of a diameter), in graphics and CAD work, and in everyday layout tasks such as centering a shelf between two studs on a measured wall. The reverse mode is handy for homework problems that give one endpoint and the midpoint and ask for the other end.
Formula
M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
To find a missing endpoint, reverse it: x₂ = 2·Mₓ − x₁ and y₂ = 2·M_y − y₁.
Example calculation
Using the default values:
- Find = Midpoint of A and B
- Point A: x = 2
- Point A: y = 3
- Point B: x = 8
- Point B: y = 11
the calculator returns:
- Midpoint M: (5, 7)
- Length of AB: 10
- Distance from A to M: 5
Frequently asked questions
What is the midpoint formula?
Add the x-coordinates and divide by 2, then do the same with the y-coordinates.
How do I find an endpoint from the midpoint?
Double the midpoint coordinate and subtract the known endpoint. With A = (2, 3) and M = (5, 7): B = (10 − 2, 14 − 3) = (8, 11).
Can the midpoint have fractional coordinates?
Yes. Between (1, 2) and (4, 7) the midpoint is (2.5, 4.5).
Last updated: · Category: Math calculators