Distance Calculator 3D: Find Distance Between Two 3D Points

Distance Calculator 3D

This is a worked example. Change the values, then press Calculate.

DISTANCE —

Δx —

Δy —

Δz —

Solution

Adding a third dimension to the distance formula extends the same Pythagorean logic used in 2D, this calculator finds the straight-line distance between two points in 3D space.

How to use this calculator

Enter the coordinates of Point 1 (x1, y1, z1) and Point 2 (x2, y2, z2).
Read the calculated Distance, plus Δx, Δy, and Δz, and the step-by-step solution.

What this calculator does

The distance between two points in three-dimensional space extends the 2D distance formula by adding a third coordinate difference, squared and summed alongside the other two before taking the square root.

Distance = √[(x2 − x1)² + (y2 − y1)² + (z2 − z1)²]

Why adding a dimension is just adding a term

The 3D distance formula isn’t a fundamentally different concept from the 2D version, it’s the same Pythagorean relationship extended by simply adding one more squared difference term under the square root. This pattern continues into any number of dimensions in more advanced mathematics, each additional dimension just adds another squared coordinate difference to the sum.

Frequently asked questions

How is the 3D distance formula different from the 2D version?

It adds one more term, the squared difference in the z-coordinate, alongside the x and y differences already used in 2D, following the same underlying Pythagorean pattern extended into a third dimension.

Does this formula work for any two points in 3D space, including negative coordinates?

Yes, since each coordinate difference is squared before summing, negative coordinates and negative differences are handled correctly without any special adjustment needed.