📍 Midpoint Calculator
The midpoint is the point that splits a line segment into two equal halves — the average of the two endpoints, coordinate by coordinate. It is one of the most-used formulas in coordinate geometry: it locates centres, bisects segments and anchors constructions from triangles to circles.
Enter any two points and this calculator returns the exact midpoint (as fractions when the answer is a clean fraction), plus the segment length and slope, with the segment and its midpoint drawn on a graph.
How to use this calculator
The midpoint formula averages the x-coordinates and the y-coordinates separately: M = ((x₁ + x₂)/2, (y₁ + y₂)/2).
- Type the x and y of the first point.
- Type the x and y of the second point.
- Press Calculate — the midpoint is the hero result.
- Check the graph: the red point M sits exactly halfway along the segment.
Midpoint Worked Example
Find the midpoint of A(1, 2) and B(5, 6). Average the x values: (1 + 5)/2 = 3. Average the y values: (2 + 6)/2 = 4. The midpoint is M(3, 4) — and indeed the distance from M to A equals the distance from M to B (both are √8 ≈ 2.83), which is exactly what "halfway" means. Those are the default values in the calculator above.
Frequently asked questions
What is the midpoint formula?
M = ((x₁ + x₂)/2, (y₁ + y₂)/2). You average the two x-coordinates to get the midpoint’s x, and average the two y-coordinates to get its y. It works because the midpoint is the centre of the segment in both directions at once.
Can a midpoint have fractions or decimals?
Yes — whenever a coordinate sum is odd, the midpoint lands on a half (or another fraction). For example the midpoint of (0, 0) and (3, 5) is (1.5, 2.5). This calculator shows clean fractions like 3/2 when the value is exact.
What is the difference between a midpoint and a bisector?
A midpoint is a point — the single centre point of a segment. A bisector is a line (or segment) that passes through the midpoint and cuts the segment in half; the perpendicular bisector does so at a right angle. Every segment has one midpoint but infinitely many bisectors through it.
How do I find an endpoint if I know the midpoint and the other endpoint?
Double the midpoint and subtract the known endpoint: x₂ = 2·Mx − x₁ and y₂ = 2·My − y₁. For midpoint (3, 4) and endpoint (1, 2), the missing endpoint is (2·3 − 1, 2·4 − 2) = (5, 6).