3D Distance Calculator
Calculate the straight-line distance between two points in 3D space using their x, y, and z coordinates.
Extending the distance formula to three dimensions
The familiar 2D distance formula extends naturally to three dimensions by adding a third term for the z-axis difference: distance equals the square root of (Δx)² + (Δy)² + (Δz)². It's the same Pythagorean-theorem logic as the 2D case, just applied across one additional dimension.
This generalizes further to any number of dimensions in higher mathematics, following the same pattern — though 3D distance is by far the most common practical application outside of pure math contexts.
Where 3D distance calculations are used
This formula is fundamental to 3D graphics and game development (calculating distances between objects in a scene), physics simulations, robotics and spatial navigation, GPS and satellite positioning systems, and molecular modeling in chemistry, where atomic distances in 3D space are routinely calculated.
Any application involving objects positioned in three-dimensional space — whether physical or virtual — relies on this same underlying distance formula, making it one of the more broadly applicable calculations in applied mathematics.
Frequently asked questions
How is this different from the standard 2D distance formula?
It's the same underlying principle, extended with one additional term for the z-axis (depth) difference — the 2D formula is simply this one with the z-component removed.
What units does the result use?
The result is in whatever unit your coordinates are in — if your x, y, z values are in meters, the distance will be in meters; the calculator doesn't assume or convert units.