3D Distance Formula — Extending Pythagoras to Three Dimensions

Use the Free Calculator

Try our Pythagorean Calculator — instant results, no sign-up.

Overview

The Pythagorean theorem extends naturally to three dimensions, enabling distance calculations in space, GPS positioning, computer graphics, and engineering.

The Formula

3D Distance = √(Δx² + Δy² + Δz²)

Standard formula used by professionals worldwide

Worked Example

Step-by-step

Point A (0,0,0) to B (3,4,5) → d = √(9+16+25) = √50 = 7.07 units

Key Points

Accuracy: Results are as accurate as the inputs you provide
Units: Always use consistent units throughout your calculation
Privacy: All calculations on CalcHub Pro run in your browser — nothing is sent to any server

Frequently Asked Questions

How does GPS use 3D Pythagoras?

Satellites measure distances in 3D space. Multiple measurements triangulate your exact position.

How is this used in game development?

Collision detection, pathfinding, and lighting calculations all use 3D distance formulas.

What is the n-dimensional version?

Euclidean distance extends to any number of dimensions: d = √(Σdᵢ²). Used in machine learning.

𝕏 Share 💬 WhatsApp

Ready to Calculate?

Free, instant, no sign-up required.

Open Pythagorean →