Midpoint Calculator

Two points

This midpoint calculator for two points finds the point exactly halfway between them. Students, teachers and anyone working with coordinate geometry use it to check homework, plan designs or solve map problems. It also shows the straight-line distance between the two points, and can work backwards to find a missing endpoint from the midpoint and one known point.

How the midpoint is found

The midpoint is the average of each coordinate pair. For the points (x1, y1) and (x2, y2):

  1. Mx = (x1 + x2) / 2 – add the x-values, then divide by 2.
  2. My = (y1 + y2) / 2 – add the y-values, then divide by 2.
  3. The midpoint M is (Mx, My).

The distance between the points comes from the distance formula: d = square root of ((x2 – x1) squared + (y2 – y1) squared). The missing-endpoint mode runs the midpoint formula backwards: since M = (A + B) / 2, the unknown endpoint is B = 2M – A, so x2 = 2 times xm minus x1 and y2 = 2 times ym minus y1.

Worked example: midpoint of (6, 3) and (12, 7)

  1. Average the x-values: (6 + 12) / 2 = 18 / 2 = 9.
  2. Average the y-values: (3 + 7) / 2 = 10 / 2 = 5.
  3. The midpoint is (9, 5).
  4. The distance is the square root of ((12 – 6) squared + (7 – 3) squared) = square root of (36 + 16) = square root of 52, about 7.21.

How to use this calculator

  1. Keep the “Midpoint of two points” mode and type both points (x1, y1) and (x2, y2) into the labelled boxes.
  2. Press Calculate to see the midpoint, the distance, and each step of the working.
  3. To find a missing endpoint instead, switch to “Find the missing endpoint” and enter the known endpoint plus the midpoint.

Limits of this tool

  • It works with flat two-dimensional points (x, y) only, not 3D points.
  • The distance is the straight-line distance, not a distance along roads or paths.
  • Decimals are fine, but fractions must be typed as decimals (for example, type 0.5 instead of 1/2).
  • It does not draw a graph of the points.

Frequently asked questions

What is the midpoint of two points?

The midpoint is the point exactly halfway between two points. Average the x-values and the y-values separately: Mx = (x1 + x2) / 2 and My = (y1 + y2) / 2.

Can this midpoint calculator for two points also find the distance?

Yes. Alongside the midpoint, the tool shows the straight-line distance between your two points, with the full working using the distance formula.

How do I find a missing endpoint from the midpoint?

Switch to the “Find the missing endpoint” mode and enter the known endpoint and the midpoint. The tool works backwards with B = 2M – A: double each midpoint value and subtract the known endpoint’s value.

Is the midpoint the same as averaging two numbers?

It is the same idea, applied to both coordinates. The midpoint averages the x-values and the y-values separately, giving the point halfway between the two.

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