# Distance Calculator | Three Dimensional Space

## Calculator Use

Enter 2 sets of coordinates in the 3 dimensional Cartesian coordinate system, (X_{1}, Y_{1}, Z_{1}) and (X_{2}, Y_{2}, Z_{2}), to get the distance formula calculation for the 2 points and calculate distance between the 2 points.

Accepts positive or negative integers and decimals.

## Distance Formula:

The distance between two points is the length of the path connecting them. The shortest path distance is a straight line. In a 3 dimensional plane, the distance between points (X_{1}, Y_{1}, Z_{1}) and (X_{2}, Y_{2}, Z_{2}) is given by:

## How to Calculate Distance between 2 points

To calculate the distance between 2 points, (X_{1}, Y_{1}, Z_{1}) and (X_{2}, Y_{2}, Z_{2}), for example, (5,6,2) and (-7,11,-13), we plug our values into the distance formula:

combining terms inside parentheses we get:

\[ d = \sqrt {(-12)^2 + (5)^2 + (-15)^2} \]squaring terms we get,

\[ d = \sqrt {144 + 25 + 225} \]adding the 3 results,

\[ d = \sqrt {394} \]finally,

\[ d = 19.849433 \]