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Three Dimensional Distance Calculator

3D Distance Calculator
Answer:

d = 10.246951

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


Distance Equation Solution:

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

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

\( d = \sqrt{100 + 4 + 1} \)

\( d = \sqrt105 \)

\( d = 10.246951 \)

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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,

\[ d = 19.849433 \]


 

Cite this content, page or calculator as:

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

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