Midpoint Calculator
The point exactly halfway between two points, and the perpendicular bisector through it.
The midpoint is the average of the coordinates: average the x values, average the y values.
How the midpoint calculator works
The midpoint is the average of the coordinates: average the x values, average the y values. That is all it is, and it generalises to any number of dimensions.
The perpendicular bisector is the line through the midpoint at right angles to the segment. Every point on it is equidistant from the two original points, which is why it is the construction behind circumcentres, Voronoi diagrams and locating something equally far from two places.
Formula: M = ((x₁+x₂)/2, (y₁+y₂)/2)
Worked examples
| Inputs | Midpoint | Note |
|---|---|---|
| Between (2, 3) and (8, 15) | (5, 9) | (5, 9) |
| Across the origin | (0, 0) | (0, 0) |
| A horizontal segment | (5, 5) | (5, 5) |
FAQFrequently asked questions
How do I find the midpoint?
Average the x coordinates and average the y coordinates.
What is a perpendicular bisector?
The line through the midpoint at right angles to the segment. Every point on it is the same distance from both ends.
Does the order of the points matter?
No. Averaging is symmetric, so either order gives the same midpoint.
Does this work in three dimensions?
Yes — average each coordinate. This page handles the two-dimensional case.
What are the quarter points?
The points a quarter and three quarters of the way along, which come up when dividing a segment into four.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- National curriculum in England — Mathematics — the terms and methods taught in UK schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.