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# 3D Distance Calculator

Insert the given values and click on calculate button to get the distance between the given points.

Table of Contents:

The length of the line segment between any two locations serves as their distance. The distance between two locations in coordinate geometry can be measured by measuring the length of the line segment connecting them.

## Formula of 3D distance

**d = √ (x _{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} + (z_{2} - z_{1} )^{2}**

**Example 1:**

Determine the distance between these points

d =? x_{1} = 3, y_{1} = 4, z_{1} = 5, x_{2} = 7, y_{2} = 8, z_{2} = 2

**Solution**

Formula:

d = √ (x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} + (z_{2} - z_{1} )^{2}

Replace them with their given values

d = √ (7 - 3 )^{2} + (8 - 4 )^{2} + (2 - 5 )^{2}

d = √ (4 )^{2} + (4 )^{2} + ( -3 )^{2}

d = √ (16) + (16) + (9)

d = √ 41

Now taking the square root to evaluate the distance

d = 6.4031

**Example 2:**

**Determine the distance between these points**

d =? x_{1} = 2, y_{1} = 6, z_{1} = 2, x_{2} = 4, y_{2} = 8, z_{2} = 4

**Ans:**

Formula:

d = √ (x_{2} - x_{1} )^{2} + (y_{2} - y_{1} )^{2} + (z_{2} - z_{1} )^{2}

Replace them with their given values

d = √ (4 - 2 )^{2} + (8 - 6 )^{2} + (4 - 2 )^{2}

d = √ (2)^{2} + (2)^{2} + (2)^{2}

d = √ 4+4+4

d = √ 12

Now taking the square root to evaluate the distance

d = 3.4641