Vector Magnitude

The magnitude (or norm) of a vector is its length in Euclidean space, computed using the Pythagorean theorem generalised to any number of dimensions. The unit vector in the same direction is the vector divided by its magnitude

The calculator uses the standard published formula for vector magnitude. Results are accurate to the precision of the inputs you provide. For financial, medical, or legal decisions, always verify with a qualified professional.

This calculator works with inches. You can enter values in the units shown — the calculator handles all conversions internally.

The core formula is: |v| = √(v₁² + v₂² + v₃² + ... + vₙ²) — Euclidean norm. Each step in the calculation is shown so you can verify the result manually.