Midpoint calculator — the point halfway between two coordinates

How to use the midpoint calculator

1. Enter the first endpoint as x₁ and y₁.
2. Enter the second endpoint as x₂ and y₂.
3. Read the Midpoint as an (x, y) pair.
4. The Working box shows the formula, your numbers inside it and the result.

What it does and when to use it

The midpoint splits a segment into two equal halves. In class it comes up when you find the centre of a circle from the ends of a diameter, draw a perpendicular bisector, or prove that the diagonals of a parallelogram cut each other in half. Outside school it locates the centre of a room plan, a meeting point halfway between two grid positions, or the middle of a beam on a drawing.

To measure how long the segment is, use the distance calculator. For the gradient and equation of the line, try the slope calculator. The coordinate line properties tool shows midpoint, distance and slope together.

How it works

The tool applies the midpoint formula:

M = ((x₁ + x₂)/2, (y₁ + y₂)/2)

It adds the two x values and halves the sum, then does the same for the y values. Nothing else is involved, so the order of the points makes no difference.

Worked examples

Step by step. Endpoints (−4, 7) and (6, −1).

1. Add the x values: −4 + 6 = 2. Halve it: 2 ÷ 2 = 1.
2. Add the y values: 7 + (−1) = 6. Halve it: 6 ÷ 2 = 3.
3. Put them together as a point.

The tool shows Midpoint: (1, 3). As a check, (1, 3) is 5 across and 4 down from (−4, 7), and the same 5 across and 4 down again reaches (6, −1).

Decimal endpoints. Endpoints (1.5, 2) and (4, 9). The working reads ((1.5 + 4)/2, (2 + 9)/2) and the answer is (2.75, 5.5).

Finding the other end. Suppose a diameter starts at (2, 3) and the centre is (5, −1). Using the tip in the FAQ, the other end is (2 × 5 − 2, 2 × (−1) − 3) = (8, −5). Enter (2, 3) and (8, −5) in the tool and it returns (5, −1), which confirms the answer.

Limits and tips

• Only two dimensions. For points with a z value, the 3D distance calculator also shows the 3D midpoint.
• Coordinates have no units; use the same unit for both points.
• Results show up to 10 significant figures, so fractions like 1/3 appear as decimals.
• The calculation runs in your browser.