Midpoint Calculator
Free midpoint calculator: enter two coordinate points to get the exact midpoint with formula steps shown, plus the distance between the points.
About the Midpoint Calculator
The midpoint of a segment joining (x₁, y₁) and (x₂, y₂) is simply the average of the coordinates: M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). This free midpoint calculator computes it instantly and writes out the substitution steps so the working can go straight into homework. It also reports the distance between the two points as a bonus.
The midpoint formula appears throughout coordinate geometry — finding the centre of a circle from a diameter's endpoints, bisecting a segment, locating a parallelogram's centre — and it is a fixture of matric, FSc, O-level and engineering-entrance syllabi in Pakistan and India. Everything computes live in your browser with no signup and no NaN on incomplete input.
How to Use the Midpoint Calculator
- 1Enter x₁ and y₁ for the first point.
- 2Enter x₂ and y₂ for the second point.
- 3Read the midpoint, the substituted formula steps and the distance between the points.
Frequently Asked Questions
How do I find the midpoint with an example?
Average each coordinate. For (2, 3) and (8, 7): M = ((2 + 8) ÷ 2, (3 + 7) ÷ 2) = (5, 5). The calculator shows this substitution line by line for any inputs, including negatives and decimals.
Why does averaging the coordinates give the midpoint?
Moving from one endpoint to the other changes x by Δx and y by Δy; the midpoint sits exactly half of each change along: x₁ + Δx/2 = (x₁ + x₂)/2. It is the one point equidistant from both endpoints on the segment itself.
How do I find an endpoint if I know the midpoint?
Reverse the formula: x₂ = 2mx − x₁ and y₂ = 2my − y₁. If the midpoint is (5, 5) and one endpoint is (2, 3), the other is (2×5 − 2, 2×5 − 3) = (8, 7). Handy for circle problems where the centre is the midpoint of a diameter.
Does the midpoint formula work with negative coordinates?
Yes — the arithmetic is identical. For (−4, 6) and (10, −2): M = ((−4 + 10) ÷ 2, (6 + (−2)) ÷ 2) = (3, 2). Just keep the signs when adding, which the calculator handles automatically.