 The first point
X1
Y1
Z1
The second point
X2
Y2
Z2
The distance
Distance (d)

# Three-Dimensional Distance Calculator

By Bogna Haponiuk

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]`

1. Calculate the result:

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

Bogna Haponiuk