The midpoint formula
M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2)
For (−2, 3) and (6, −1): x = (−2 + 6) ÷ 2 = 2 and y = (3 + (−1)) ÷ 2 = 1, so the midpoint is (2, 1).
Finding a missing endpoint
x₂ = 2·mx − x₁ · y₂ = 2·my − y₁
If the midpoint is (2, 1) and one end is (−2, 3), the other end is (2·2 − (−2), 2·1 − 3) = (6, −1).
Distance between the points
d = √((x₂ − x₁)² + (y₂ − y₁)²)
This is the Pythagorean theorem applied to the horizontal and vertical gaps. For the example: √(8² + 4²) = √80 ≈ 8.944.
Uses outside the classroom
Midpoints help you center a picture on a wall, find a fair meeting spot on a map grid, or place a support halfway along a beam. In design software, the midpoint of a selection is how objects get aligned to each other.
Need the equation of the line too? Use the slope calculator.
Last reviewed October 2026.
Frequently asked questions
What is the midpoint formula?
The midpoint of two points (x₁, y₁) and (x₂, y₂) is ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). You average the x-coordinates and average the y-coordinates.
How do I find an endpoint if I know the midpoint?
Choose "Find an endpoint" and enter the midpoint and the known endpoint. The missing endpoint is (2·mx − x₁, 2·my − y₁), because the midpoint sits exactly halfway between the two ends.
Does the calculator give the distance too?
Yes. It shows the length of the segment using the distance formula √((x₂ − x₁)² + (y₂ − y₁)²), along with the slope of the line through both points.
Can I use decimals and negative numbers?
Yes. Coordinates can be any real numbers, including negatives and decimals.
What is the perpendicular bisector?
It is the line that passes through the midpoint at a right angle to the segment. Its slope is the negative reciprocal of the segment's slope. The calculator gives its equation.