Calculators > Geometry > Solid > Distance Calculator 3D

Distance Calculator 3D

Enter Points:
(X1, Y1, Z1) =
(X2, Y2, Z2) =
 
 
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About this Calculator

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, decimals and fractions.
(6 and/or 6.5 and/or 6 1/2)

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:

3 dimensional distance equation

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:

3d distance equation step 1

combining terms inside parentheses we get:

3d distance equation step 2

squaring terms we get,

3d distance equation step 3

adding the 3 results,

3d distance equation step 4

finally,

d = 19.849433