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Birla Institute of Technology & Science (BITS), Hyderabad
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Distance between two points in 3D space Solution

STEP 0: Pre-Calculation Summary
Formula Used
distance_between_two_points = sqrt((X2 coordinate of second point-X1 coordinate of first point)^2+(Y2 coordinate of second point-Y1 coordinate of first point)^2+(Z2 coordinate of first point-Z1 coordinate of first point)^2)
d = sqrt((x2-x1)^2+(y2-y1)^2+(z2-z1)^2)
This formula uses 1 Functions, 6 Variables
Functions Used
sqrt - Squre root function, sqrt(Number)
Variables Used
X2 coordinate of second point- X2 coordinate of second point is the x-coordinate/ abscissa of the second point.
X1 coordinate of first point- X1 coordinate of first point is the x-coordinate/abscissa of the first point.
Y2 coordinate of second point- Y2 coordinate of second point is the y-coordinate/ordinate of the second point.
Y1 coordinate of first point- Y1 coordinate of first point is the y-coordinate/ ordinate of the first point.
Z2 coordinate of first point- Z2 coordinate of first point is the z-coordinate/ applicate of the second point.
Z1 coordinate of first point- Z1 coordinate of first point is the z-coordinate/ applicate of the first point.
STEP 1: Convert Input(s) to Base Unit
X2 coordinate of second point: 1 --> No Conversion Required
X1 coordinate of first point: 0 --> No Conversion Required
Y2 coordinate of second point: 1 --> No Conversion Required
Y1 coordinate of first point: 0 --> No Conversion Required
Z2 coordinate of first point: 1 --> No Conversion Required
Z1 coordinate of first point: 0 --> No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
d = sqrt((x2-x1)^2+(y2-y1)^2+(z2-z1)^2) --> sqrt((1-(0))^2+(1-(0))^2+(1-(0))^2)
Evaluating ... ...
d = 1.73205080756888
STEP 3: Convert Result to Output's Unit
1.73205080756888 --> No Conversion Required
FINAL ANSWER
1.73205080756888 <-- Distance between 2 points
(Calculation completed in 00.000 seconds)

7 Distance in 3D space Calculators

Distance between two points in 3D space
distance_between_two_points = sqrt((X2 coordinate of second point-X1 coordinate of first point)^2+(Y2 coordinate of second point-Y1 coordinate of first point)^2+(Z2 coordinate of first point-Z1 coordinate of first point)^2) Go
Distance between plane in normal formal and point
length = modulus((Direction Ratio 1*X Coordinate in 3D Space)+(Direction Ratio 2*Y Coordinate in 3D Space)+(Direction Ratio 3*Z Coordinate in 3D Space)-(Constant Coefficient of Plane1)) Go
Distance between 2 parallel planes
length = (Constant Coefficient of Plane2-Constant Coefficient of Plane1)/((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2) Go
Distance of point from origin
distance_1 = sqrt((X1 Coordinate in 3D Space)^2+ (Y1 Coordinate in 3D Space)^2+ (Z1 Coordinate in 3D Space)^2) Go
Length of line given direction ratio and projection of line with x axis
length = (Projection of line)/(Direction Ratio 1) Go
Length of line given direction ratio and projection of line with y axis
length = (Projection of line)/(Direction Ratio 2) Go
Length of line given direction ratio and projection of line with z axis
length = (Projection of line)/(Direction Ratio 3) Go

Distance between two points in 3D space Formula

distance_between_two_points = sqrt((X2 coordinate of second point-X1 coordinate of first point)^2+(Y2 coordinate of second point-Y1 coordinate of first point)^2+(Z2 coordinate of first point-Z1 coordinate of first point)^2)
d = sqrt((x2-x1)^2+(y2-y1)^2+(z2-z1)^2)

What is a 3D coordinate system ?

A three-dimensional Cartesian coordinate system is formed by a point called the origin (denoted by O - (0, 0, 0)) and a basis consisting of three mutually perpendicular vectors. These vectors define the three coordinate axes: the x-axis, y-axis and z-axis. They are also known as the abscissa, ordinate and applicate axis, respectively. The coordinates of any point in space are determined by three real numbers: (x, y, z)

How to Calculate Distance between two points in 3D space?

Distance between two points in 3D space calculator uses distance_between_two_points = sqrt((X2 coordinate of second point-X1 coordinate of first point)^2+(Y2 coordinate of second point-Y1 coordinate of first point)^2+(Z2 coordinate of first point-Z1 coordinate of first point)^2) to calculate the Distance between 2 points, The Distance between two points in 3D space is given by is the length measured from one point to other point in given space. Distance between 2 points and is denoted by d symbol.

How to calculate Distance between two points in 3D space using this online calculator? To use this online calculator for Distance between two points in 3D space, enter X2 coordinate of second point (x2), X1 coordinate of first point (x1), Y2 coordinate of second point (y2), Y1 coordinate of first point (y1), Z2 coordinate of first point (z2) & Z1 coordinate of first point (z1) and hit the calculate button. Here is how the Distance between two points in 3D space calculation can be explained with given input values -> 1.732051 = sqrt((1-(0))^2+(1-(0))^2+(1-(0))^2).

FAQ

What is Distance between two points in 3D space?
The Distance between two points in 3D space is given by is the length measured from one point to other point in given space and is represented as d = sqrt((x2-x1)^2+(y2-y1)^2+(z2-z1)^2) or distance_between_two_points = sqrt((X2 coordinate of second point-X1 coordinate of first point)^2+(Y2 coordinate of second point-Y1 coordinate of first point)^2+(Z2 coordinate of first point-Z1 coordinate of first point)^2). X2 coordinate of second point is the x-coordinate/ abscissa of the second point, X1 coordinate of first point is the x-coordinate/abscissa of the first point, Y2 coordinate of second point is the y-coordinate/ordinate of the second point, Y1 coordinate of first point is the y-coordinate/ ordinate of the first point, Z2 coordinate of first point is the z-coordinate/ applicate of the second point & Z1 coordinate of first point is the z-coordinate/ applicate of the first point.
How to calculate Distance between two points in 3D space?
The Distance between two points in 3D space is given by is the length measured from one point to other point in given space is calculated using distance_between_two_points = sqrt((X2 coordinate of second point-X1 coordinate of first point)^2+(Y2 coordinate of second point-Y1 coordinate of first point)^2+(Z2 coordinate of first point-Z1 coordinate of first point)^2). To calculate Distance between two points in 3D space, you need X2 coordinate of second point (x2), X1 coordinate of first point (x1), Y2 coordinate of second point (y2), Y1 coordinate of first point (y1), Z2 coordinate of first point (z2) & Z1 coordinate of first point (z1). With our tool, you need to enter the respective value for X2 coordinate of second point, X1 coordinate of first point, Y2 coordinate of second point, Y1 coordinate of first point, Z2 coordinate of first point & Z1 coordinate of first point and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Distance between 2 points?
In this formula, Distance between 2 points uses X2 coordinate of second point, X1 coordinate of first point, Y2 coordinate of second point, Y1 coordinate of first point, Z2 coordinate of first point & Z1 coordinate of first point. We can use 7 other way(s) to calculate the same, which is/are as follows -
  • length = (Projection of line)/(Direction Ratio 1)
  • length = (Projection of line)/(Direction Ratio 2)
  • length = (Projection of line)/(Direction Ratio 3)
  • distance_1 = sqrt((X1 Coordinate in 3D Space)^2+ (Y1 Coordinate in 3D Space)^2+ (Z1 Coordinate in 3D Space)^2)
  • length = modulus((Direction Ratio 1*X Coordinate in 3D Space)+(Direction Ratio 2*Y Coordinate in 3D Space)+(Direction Ratio 3*Z Coordinate in 3D Space)-(Constant Coefficient of Plane1))
  • length = (Constant Coefficient of Plane2-Constant Coefficient of Plane1)/((Direction Ratio 1)^2+(Direction Ratio 2)^2+(Direction Ratio 3)^2)
  • distance_between_two_points = sqrt((X2 coordinate of second point-X1 coordinate of first point)^2+(Y2 coordinate of second point-Y1 coordinate of first point)^2+(Z2 coordinate of first point-Z1 coordinate of first point)^2)
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