Three-Dimensional Distance Calculator

Created by Bogna Szyk
Reviewed by Jack Bowater
Last updated: Dec 06, 2021

Our three-dimensional distance calculator is a tool that finds the distance between two points, provided you give their coordinates in space. If you want to determine the distance between two points on a plane (two-dimensional distance), use our distance calculator. You can also check our rate of change calculator to determine the relation between two coordinates.

The distance formula

To find the distance between two points in a three-dimensional coordinate system, you need to apply the following formula:

D = √[(x₂ - x₁)² + (y₂ - y₁)² +(z₂ - z₁)²]

where:

  • D is the distance between two points,
  • (x₁, y₁, z₁) are the coordinates of the first point,
  • (x₂, y₂, z₂) are the coordinates of the second point.

Notice that the value obtained when using this formula is always positive. This is because we consider a scalar value of distance - that is, it is impossible to have a negative value for distance.

How to calculate the 3D distance

  1. Choose the coordinates of the first point - for example (1,1,1).
  2. Choose the coordinates of the second point - for example, (3,6,9).
  3. Input these values to the formula:

D = √[(x₂ - x₁)² + (y₂ - y₁)² +(z₂ - z₁)²] = √[(3-1)² + (6-1)² +(9-1)²]
4. Calculate the result:

D = √[2² + 5² +8²] = √[4 + 25 +64] = √93 = 9.643

Bogna Szyk
3D scatter plot with two points connected with a line representing the distance between them
The first point
X1
Y1
Z1
The second point
X2
Y2
Z2
The distance
Distance (d)
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