Midpoint Calculator

The midpoint formula

The midpoint of a line segment is the point exactly halfway between its two ends. To find it, average each coordinate: M = ((x₁ + x₂) ÷ 2, (y₁ + y₂) ÷ 2). On a number line there is only one coordinate, so the midpoint of −4 and 10 is (−4 + 10) ÷ 2 = 3. In three dimensions you add a third average for z. This midpoint calculator works in all three and shows each averaging step.

Worked example

Find the midpoint of A(2, 3) and B(8, 11). Add the x-values: 2 + 8 = 10, half of that is 5. Add the y-values: 3 + 11 = 14, half is 7. The midpoint is (5, 7). Check it: from A the point moves 3 right and 4 up, and B is another 3 right and 4 up. The segment is 10 units long (a 6-8-10 triangle) and the midpoint sits 5 units from each end.

Finding a missing endpoint

Sometimes you know the midpoint and one end and need the other end. Because M is the average of A and B, B = 2M − A, one coordinate at a time. With M = (5, 7) and A = (2, 3): x = 2 × 5 − 2 = 8 and y = 2 × 7 − 3 = 11, so B = (8, 11). Switch the mode to Missing endpoint and the tool does this for you.

Common mistakes

• Subtracting instead of adding. The midpoint averages the coordinates; subtracting gives the difference, which is the length along that axis.
• Mixing up x and y. Pair the x-values with each other and the y-values with each other.
• Forgetting the sign. A negative coordinate matters: the midpoint of (−6, 2) and (4, 8) has x = (−6 + 4) ÷ 2 = −1, not 5.

Midpoint, average and balance point

The midpoint is the mean of two points, so the same formula finds the average of two numbers; for longer lists use the average calculator. The midpoint is also where you would balance a uniform rod or place a meeting spot equidistant from two places on a map, as long as the map is flat enough that straight lines are a fair model: over long distances on Earth the midpoint along the surface is not the average of the latitudes and longitudes.