Unit Vector Calculator

About this calculator

A unit vector points in exactly the same direction as an original vector but has a magnitude of exactly 1, which makes it useful anywhere only direction matters and length would just get in the way of the math. It's found by dividing each component of the vector by its magnitude, computed as the square root of the sum of the squared components: û = v ÷ |v|, where |v| = √(x² + y² + z²) for a 3D vector.

This calculator takes a vector's x, y, and z components, computes the magnitude, and returns the normalized unit vector. Physics students working with force and velocity directions, game and graphics programmers computing surface normals and lighting angles, and engineers doing structural or mechanical analysis use it whenever a calculation needs a pure direction — such as a light ray's angle of incidence — decoupled from the original vector's length.