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:

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.

PK

PK started DQYDJ in 2009 to research and discuss finance and investing and help answer financial questions. He's expanded DQYDJ to build visualizations, calculators, and interactive tools.

PK lives in New Hampshire with his wife, kids, and dog.