3D Distance Calculator

3D Distance
Enter Points:
(X1, Y1, Z1) =
(X2, Y2, Z2) =
Answer:

d = 26.004807


Solving the 3D distance equation:

\( d = \sqrt {(17 - (-7))^2 + (6 - (-4))^2 + (2.5 - (3))^2} \)

\( d = \sqrt {(24)^2 + (10)^2 + (-0.5)^2} \)

\( d = \sqrt {576 + 100 + 0.25} \)

\( d = \sqrt 676.25 \)

\( d = 26.004807 \)

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, 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:

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

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,

\[ d = 19.849433 \]
 

Cite this content, page or calculator as:

Furey, Edward "3D Distance Calculator" From http://www.CalculatorSoup.com - Online Calculator Resource.