Distance Calculator | Three Dimensional Space
Calculator Use
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,
\[ d = 19.849433 \]