Midpoint Between Two 3D Points

Published on: January 18, 2026
Final Answer: Free • Full Steps: Pro

This Midpoint Between Two 3D Points Calculator finds the point exactly halfway between two points in space, and shows the working line by line. Each coordinate of the midpoint is the average of the matching coordinates, because halving the gap along one axis has no effect on the others. The result is always on the straight line joining the two points. Following the same pattern every time keeps each axis averaged on its own.

Step-by-step method

  1. Set up the problem.
  2. Write the midpoint formula in 3D.
  3. Substitute values and simplify each coordinate.
See Example 1 Hide Example 1

Problem

\(P_{1} = \left(1,\; 2,\; 3\right),\; P_{2} = \left(4,\; 6,\; 3\right)\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the midpoint formula in 3D.
  3. Substitute values and simplify each coordinate.

Step 1

Step 1 - Set up the problem.

In this problem: The points are \(P_{1} = \left(1,\; 2,\; 3\right)\) and \(P_{2} = \left(4,\; 6,\; 3\right)\).

\(P_{1} = \left(1,\; 2,\; 3\right),\; P_{2} = \left(4,\; 6,\; 3\right)\)

Step 2

Step 2 - Write the midpoint formula in 3D.

In this problem: Average each pair of coordinates.

\(M = \left(\frac{x_{1} + x_{2}}{2},\; \frac{y_{1} + y_{2}}{2},\; \frac{z_{1} + z_{2}}{2}\right)\)

Step 3

Step 3 - Substitute values and simplify each coordinate.

In this problem: The midpoint is \(\left(\frac{5}{2},\; 4,\; 3\right)\).

\(M = \left(\frac{1 + 4}{2},\; \frac{2 + 6}{2},\; \frac{3 + 3}{2}\right) = \left(\frac{5}{2},\; 4,\; 3\right)\)

Final Answer

\(M = \left(\frac{5}{2},\; 4,\; 3\right)\)
See Example 2 Hide Example 2

Problem

\(P_{1} = \left(0,\; 0,\; 0\right),\; P_{2} = \left(1,\; 1,\; 1\right)\)

Approach

Step-by-step method

  1. Set up the problem.
  2. Write the midpoint formula in 3D.
  3. Substitute values and simplify each coordinate.

Step 1

Step 1 - Set up the problem.

In this problem: The points are \(P_{1} = \left(0,\; 0,\; 0\right)\) and \(P_{2} = \left(1,\; 1,\; 1\right)\).

\(P_{1} = \left(0,\; 0,\; 0\right),\; P_{2} = \left(1,\; 1,\; 1\right)\)

Step 2

Step 2 - Write the midpoint formula in 3D.

In this problem: Average each pair of coordinates.

\(M = \left(\frac{x_{1} + x_{2}}{2},\; \frac{y_{1} + y_{2}}{2},\; \frac{z_{1} + z_{2}}{2}\right)\)

Step 3

Step 3 - Substitute values and simplify each coordinate.

In this problem: The midpoint is \(\left(\frac{1}{2},\; \frac{1}{2},\; \frac{1}{2}\right)\).

\(M = \left(\frac{0 + 1}{2},\; \frac{0 + 1}{2},\; \frac{0 + 1}{2}\right) = \left(\frac{1}{2},\; \frac{1}{2},\; \frac{1}{2}\right)\)

Final Answer

\(M = \left(\frac{1}{2},\; \frac{1}{2},\; \frac{1}{2}\right)\)

Example Problems

Click one to load it into the box and solve it.