Unit Vector Calculator
Enter a nonzero 2D or 3D vector to calculate its magnitude and the unit vector pointing in the same direction.
Written and checked by TheToolNet Editorial Team · Last reviewed: September 20, 2026 · Editorial method
Calculate a unit vector
Unit vector formula
û = u ÷ |u|
For ⟨3,4⟩, the magnitude is √(3²+4²)=5, so the unit vector is ⟨0.6,0.8⟩. Its magnitude is 1 while its direction matches the original.
Why the zero vector cannot be normalized
Normalization divides by magnitude. The zero vector's magnitude is zero and it has no defined direction, so no unit vector exists. OpenStax reviews vector magnitude and components in its vectors chapter.