Midpoint Calculator
Find the point exactly halfway between two coordinates — or work backwards from a midpoint and one endpoint to the missing endpoint.
- x = (2 + 8) ÷ 2 = 5
- y = (3 + 11) ÷ 2 = 7
- Segment length
- 10
- Each half
- 5
- Perpendicular bisector
- y = -0.75x + 10.75
How the midpoint formula works
The midpoint's x-coordinate is the average of the two x-values, and its y-coordinate is the average of the two y-values. For (2, 3) and (8, 11): M = ((2 + 8)/2, (3 + 11)/2) = (5, 7).
To find a missing endpoint, reverse it: B = 2M − A. If M = (5, 7) and A = (2, 3), then B = (10 − 2, 14 − 3) = (8, 11).
The perpendicular bisector passes through the midpoint at right angles to the segment. Every point on it is the same distance from both endpoints, which is how you find the center of a circle through three points.
Questions people ask
What is the midpoint formula?
M = ((x₁ + x₂)/2, (y₁ + y₂)/2) — the average of the x-coordinates and the average of the y-coordinates.
How do I find an endpoint from the midpoint?
Double the midpoint and subtract the known endpoint: x₂ = 2xₘ − x₁ and y₂ = 2yₘ − y₁.
Does the midpoint formula work in 3D?
Yes. Average the z-coordinates too: ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2).