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3D Distance Calculator: Straight Line Distance Between Points

Written by:
PK

This is a 3D distance formula calculator, which will calculate the straight line or euclidean distance between two points in three dimensions

Alternatively, see the other Euclidean distance calculators:

3D Distance Calculator

Formula for 3D Euclidean Distance

The formula for three-dimension distance is:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}

Where:

  • d: the distance between the two points (the hypotenuse)
  • x1, y1, z1: the x, y, and z coordinates of point 1
  • x2, y2, z2: the x, y, and z coordinates of point 2

Example Distance Calculation

Let's say you have 2 points, (x, y, z):

  • (4, 9, 3)
  • (0, 6, 14)

Here's how you do the math:

d=\sqrt{(0-4)^2+(6-9)^2+(14-3)^2}=\\\sqrt{(-4)^2+(-3)^2+(11)^2}=\\=\sqrt{16+9+121}=\\\sqrt{146}\approx12.083046

Approximately 12.083 units separate the two points.

Using the 3D Distance Formula Calculator

To start, leave the Dimensions setting at 3.

Next, enter the x, y, and z coordinates of the two points. The top table holds the X, Y, & Z for the first point, the lower holds the X, Y, & Z for the second.

Finally, hit the Compute Distance button and we'll show you the distance between points.

Afterwards, visit our other calculators and tools.

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