Three-Dimensional Distance Calculator

By Bogna Szyk
Last updated: May 21, 2020

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.

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
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