Calculators / Calculus 3 / 3D Midpoint Calculator

Midpoint Between Two 3D Points

Published on: January 18, 2026

This 3D Midpoint Calculator helps you find the point exactly halfway between two points in three-dimensional space. Enter the coordinates of both points, then use the 3D midpoint formula by averaging the x-coordinates, y-coordinates, and z-coordinates separately. The three averages combine to give the midpoint coordinates. It is a simple way to check answers, understand the formula clearly, and practise coordinate geometry step by step.

Step-by-step method

  1. Identify the two 3D points.
  2. Write the midpoint formula in 3D.
  3. Substitute values and simplify each coordinate.

Formula:

M = (
x1 + x2
2
, 
y1 + y2
2
, 
z1 + z2
2
)

Example 1: (1,2,3),(4,6,3)

Step 1 - Identify the two points.

In this problem: Label the two points in 3D space.

P1 = ( 1, 2, 3 ), P2 = ( 4, 6, 3 )

Step 2 - Write the formula.

In this problem: Use the 3D midpoint formula.

M = (
x1 + x2
2
, 
y1 + y2
2
, 
z1 + z2
2
)

Step 3 - Substitute the values.

In this problem: Replace x1,y1,z1,x2,y2,z2 in the formula.

M = (
1 + 4
2
, 
2 + 6
2
, 
3 + 3
2
)

Step 4 - Simplify each coordinate.

In this problem: Compute each average and simplify.

M = (
5
2
, 4, 3 )

Final answer: M = ( 5/2, 4, 3 )

Example 2: (0,0,0),(1,1,1)

Step 1 - Identify the two points.

In this problem: Label the two points in 3D space.

P1 = ( 0, 0, 0 ), P2 = ( 1, 1, 1 )

Step 2 - Write the formula.

In this problem: Use the 3D midpoint formula.

M = (
x1 + x2
2
, 
y1 + y2
2
, 
z1 + z2
2
)

Step 3 - Substitute the values.

In this problem: Replace x1,y1,z1,x2,y2,z2 in the formula.

M = (
0 + 1
2
, 
0 + 1
2
, 
0 + 1
2
)

Step 4 - Simplify each coordinate.

In this problem: Compute each average and simplify.

M = (
1
2
, 
1
2
, 
1
2
)

Final answer: M = ( 1/2, 1/2, 1/2 )