Enter any vector into the normalize vector calculator. The calculator will normalize this vector and display the unit vector.

## Normalizing a Vector Formula

The following formula is used to normalize a vector.

u = U / |U|

|U| = Sqaure Root ( X^2 + Y^2+Z^2)

- Where U is the original vector
- |U| is the magnitude of the vector
- u is the unit vector

How to normalize a vector

**First, calculate the magnitude of the original vector**Using the formula above, calculate the magnitude of the original vector.

**Next, divide each component of the vector by the magnitude.**For example, for a vector x,y,z, divide x by the magnitude, y by the magnitude, and z by the magnitude. The results of those divisions are your unit vector values.

## FAQ

**What is normalizing a vector?**

Normalizing a vector is the process of turning a vector into its unit vector. This process involves dividing a vector by its magnitude. The results is a vector with the same direction, but with a magnitude of 1.

**Why would you normalize a vector?**

Normalizing a vector can simply problems. For example, if you want to multiply two vectors A and B, you can actually multiply their unit vectors to get the direction, then multiply that answer by the magnitudes to get the resulting vector of A * B.