Midpoint Formula Calculator

Math Geometry • Coordinate Geometry

Written by STEM Calculators Team Published January 23, 2026 Updated February 24, 2026

Find the midpoint \(M\) of a line segment between points \(A\) and \(B\) in 2D or 3D: \(M=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2},\frac{z_1+z_2}{2}\right)\)

Inputs accept 1e-3, pi, e, sqrt(2), sin(), cos(), tan(), ln(), log(), abs(). Use * for multiplication.

Enter two points and click Calculate.

Segment diagram (pan/zoom enabled)

The midpoint \(M\) is marked on the segment \(\\overline{AB}\).

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Midpoint Formula Calculator – Find Midpoint of Line Segment (2D/3D)

Calculate the midpoint between two points in 2D or 3D using the midpoint formula, with step-by-step work and an interactive segment diagram.

What is the midpoint?

The midpoint of a segment \(\overline{AB}\) is the point exactly halfway between endpoints \(A\) and \(B\). Coordinate-wise, that means each midpoint coordinate is the average of the two endpoint coordinates.

Midpoint formula

2D (x–y plane)

If \(A(x_1,y_1)\) and \(B(x_2,y_2)\), then the midpoint is: \(M\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)\).

3D (x–y–z space)

If \(A(x_1,y_1,z_1)\) and \(B(x_2,y_2,z_2)\), then: \(M\left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2},\dfrac{z_1+z_2}{2}\right)\).

Why does it work?

A point halfway from \(A\) to \(B\) splits the segment in a \(1:1\) ratio. Along each axis, “halfway” means taking the average: \[ x_M = \frac{x_1+x_2}{2},\quad y_M = \frac{y_1+y_2}{2}\quad (\text{and } z_M=\frac{z_1+z_2}{2}\text{ in 3D}). \]

Worked example (2D)

Points \(A(1,2)\) and \(B(4,6)\):

\(x_M=\dfrac{1+4}{2}=\dfrac{5}{2}=2.5\)
\(y_M=\dfrac{2+6}{2}=\dfrac{8}{2}=4\)

So \(M(2.5,4)\).

Common mistakes

Forgetting parentheses: \(\dfrac{x_1+x_2}{2}\) is not the same as \(x_1+\dfrac{x_2}{2}\).
Mixing coordinates: average \(x\)’s with \(x\)’s, \(y\)’s with \(y\)’s (and \(z\)’s with \(z\)’s).
Sign errors: if a coordinate is negative, include the sign in the sum.

Visualization tip

The interactive diagram shows \(\overline{AB}\) with the midpoint \(M\) highlighted. In 3D mode, rotate the view to see separation along \(z\).

Frequently Asked Questions

What is the midpoint of a line segment in coordinate geometry?

The midpoint is the point exactly halfway between endpoints A and B. Each midpoint coordinate is the average of the corresponding endpoint coordinates.

What is the midpoint formula in 2D and 3D?

In 2D, M = ((x1 + x2)/2, (y1 + y2)/2). In 3D, add the z-coordinate: M = ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2).

Why do parentheses matter in the midpoint formula?

You must add the two coordinates first and then divide by 2. Writing x1 + x2/2 is not the same as (x1 + x2)/2.

Can the midpoint have negative or decimal coordinates?

Yes. If an endpoint coordinate is negative or fractional, it is included in the average normally, and the midpoint can be negative or fractional as well.

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Frequently Asked Questions

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