Calculators

Geometry

Solid

Enter 2 sets of coordinates in the 3 dimensional Cartesian coordinate system, (X₁, Y₁, Z₁) and (X₂, Y₂, Z₂), 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 (X₁, Y₁, Z₁) and (X₂, Y₂, Z₂) is given by:

\[ d = \sqrt {(x_{2} - x_{1})^2 + (y_{2} - y_{1})^2 + (z_{2} - z_{1})^2} \]

How to Calculate Distance between 2 points

To calculate the distance between 2 points, (X₁, Y₁, Z₁) and (X₂, Y₂, Z₂), for example, (5,6,2) and (-7,11,-13), we plug our values into the distance formula:

\[ d = \sqrt {(-7 - 5)^2 + (11 - 6)^2 + (-13 - 2)^2} \]

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,

\[ d = 19.849433 \]