Midpoint Calculator

The midpoint of a line segment is the point exactly halfway between its two ends. To find it, average the x-coordinates and average the y-coordinates. This midpoint calculator does that with exact fractions, plots the segment, and checks that the midpoint is the same distance from both ends.

How to use the midpoint calculator

Enter the first point (x₁, y₁).
Enter the second point (x₂, y₂).
Press Calculate to see the midpoint and the graph.

Formula

M = \left(\frac{x_1 + x_2}{2},\; \frac{y_1 + y_2}{2}\right)

Worked example: (−2, 3) and (6, −1)

x₁: -2
y₁: 3
x₂: 6
y₂: -1

✓ Answer checked

M = \left(2,\; 1\right)

The midpoint sits exactly halfway along the segment.

Step-by-step working (2 steps)

Average the x-coordinates Midpoint formula
Add the x-values and halve.
$\frac{x_1 + x_2}{2} = \frac{-2 + 6}{2} = 2$
Average the y-coordinates
Add the y-values and halve.
$\frac{y_1 + y_2}{2} = \frac{3 + -1}{2} = 1$

Formulas used

M = \left(\frac{x_1 + x_2}{2},\; \frac{y_1 + y_2}{2}\right)

How this was checked

✓ M is the same distance from both endpoints, and that distance is exactly half the segment.

Frequently asked questions

What is the midpoint of (−2, 3) and (6, −1)?

(2, 1). Average the x-values: (−2 + 6) ÷ 2 = 2. Average the y-values: (3 + (−1)) ÷ 2 = 1.

How do I find a missing endpoint?

Double the midpoint and subtract the known endpoint: x₂ = 2Mₓ − x₁ and y₂ = 2Mᵧ − y₁.

Can the midpoint have fractions?

Yes. For example, the midpoint of (1, 2) and (4, 4) is (5/2, 3).

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