Unit Vector Calculator

This unit vector calculator will very much help you transform any vector into a vector of length 1 without changing its course of direction. If you want to know how to calculate a unit vector’s components, then you do not need to look for any other tool or method.

You can now obtain the result simply by dividing the components of any arbitrary vector by its magnitude. 

A unit vector is defined as a vector of length which is equal to 1. When the unit vector is used to describe any spatial direction, it can be called a direction vector accordingly.

In a Cartesian coordinate system of Mathematics, the three-unit vectors that form the basis of the 3D space are:

  • (1, 0, 0) – that describes the x-direction
  • (0, 1, 0) – that describes the y-direction
  • (0, 0, 1) – that describes the z-direction

Here, every vector in a 3-dimensional space is equal to a sum of unit vectors. So, if you are given an arbitrary vector, it is highly possible to calculate what is the unit vector along the same direction.

In order to do that, you have to apply the following formula:

û = u / |u| where:

  • û is the unit vector,
  • u is an arbitrary vector in the form (x, y, z), and

|u| is the magnitude of the vector u.