Vector Magnitude Calculator

About this calculator

This calculator finds the magnitude (length) of a 3D vector from its x, y, and z components using the Euclidean norm, √(x² + y² + z²) — the direct generalization of the Pythagorean theorem into three dimensions. Leaving z at zero reduces it to the familiar 2D case.

Physics and engineering students use it to find the resultant size of a force, velocity, or displacement vector, while game developers and 3D graphics programmers use the same formula constantly to normalize direction vectors and measure distances between points in a scene.