Online Calculator Resource

# Three Dimensional Distance Calculator

3D Distance Calculator

d = 10.246951

For:
(X1, Y1, Z1) = (7, 4, 3)
(X2, Y2, Z2) = (17, 6, 2)

Distance Equation Solution:

$$d = \sqrt{(17 - 7)^2 + (6 - 4)^2 + (2 - 3)^2}$$

$$d = \sqrt{(10)^2 + (2)^2 + (-1)^2}$$

$$d = \sqrt{100 + 4 + 1}$$

$$d = \sqrt105$$

$$d = 10.246951$$

## 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,

$d = \sqrt {144 + 25 + 225}$

$d = \sqrt {394}$

finally,

$d = 19.849433$

Cite this content, page or calculator as:

Furey, Edward "3D Distance Calculator"; from http://www.calculatorsoup.com - Online Calculator Resource.