The midpoint formula
The midpoint of a segment is simply the average of its endpoints' coordinates:
M = ( (x₁ + x₂) ÷ 2 , (y₁ + y₂) ÷ 2 )
For the points (2, 3) and (8, 7): the x-coordinate is (2 + 8) ÷ 2 = 5 and the y-coordinate is (3 + 7) ÷ 2 = 5, so the midpoint is (5, 5).
Distance and slope too
The calculator also reports the distance between the points using the Pythagorean theorem, and the slope of the line through them:
Distance = √((x₂ − x₁)² + (y₂ − y₁)²)
For (2, 3) and (8, 7) the distance is √(6² + 4²) = √52 ≈ 7.21, and the slope is 4 ÷ 6 ≈ 0.67. For more on lines, see the slope calculator.
Working backward to an endpoint
If you know the midpoint M and one endpoint A, the other endpoint is B = (2·Mₓ − Aₓ, 2·M_y − A_y) — double the midpoint and subtract the point you have.
Frequently asked questions
What is the midpoint formula?
The midpoint of a segment is the average of the endpoints' coordinates: M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). For (2, 3) and (8, 7), the midpoint is ((2 + 8) ÷ 2, (3 + 7) ÷ 2) = (5, 5).
How do you find the midpoint between two points?
Add the two x-values and divide by 2 for the midpoint's x-coordinate, then do the same with the y-values for its y-coordinate. The result is the point exactly halfway along the straight segment connecting them.
What is the difference between midpoint and distance?
The midpoint is the point halfway between two points, given as a coordinate pair. The distance is how far apart they are, given as a single length. The midpoint averages the coordinates; the distance uses the Pythagorean theorem on the differences.
Can I find an endpoint if I know the midpoint?
Yes. If M is the midpoint of A and B, then B = (2·Mₓ − Aₓ, 2·M_y − A_y). Double the midpoint's coordinates and subtract the known endpoint to get the other end.
Does the midpoint formula work in three dimensions?
Yes — just average the z-coordinates as well: M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2, (z₁ + z₂) ÷ 2). This calculator covers the common two-dimensional case.
Disclaimer: Results are rounded for display and provided for educational purposes.