# Unit Vector Calculator – Normalize a Vector

Enter a vector to find the unit vector in the same direction.

## Unit Vector:

### Magnitude

### Steps to Solve

#### Use the Unit Vector Formula

â = a / |a|

#### Step One: Solve the Magnitude

|a| = x² + y²

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

#### Step Two: Divide by the Magnitude

Divide each vector component by the magnitude.

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

### Magnitude

### Steps to Solve

#### Use the Unit Vector Formula

â = a / |a|

#### Step One: Solve the Magnitude

|a| = x² + y² + z²

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

#### Step Two: Divide by the Magnitude

Divide each vector component by the magnitude.

#### Substitute Values and Solve

Enter vector coordinates above to see the solution here

## On this page:

## How to Find a Unit Vector

A unit vector is a vector with a length, or magnitude, of 1. You can scale a vector to a unit vector by reducing its length to 1 without changing its direction.

This is often referred to as vector normalization.

### Unit Vector Formula

To normalize a vector to a unit vector, use the following formula:

û = u / |u|

Thus, the unit vector *û* of vector *u* is equal to each component of vector *u* divided by its magnitude *|u|*.

## How to Use the Unit Vector Formula

The first step to scale a vector to a unit vector is to find the vector’s magnitude. You can use the magnitude formula to find it.

|u|= x² + y² + z²

The magnitude *|u|* of vector *u* is equal to the square root of the sum of the square of each of the vector’s components *x*, *y*, and *z*.

Then, divide each component of vector *u* by the magnitude *|u|*. The resulting components form the unit vector.

**For example,** given a vector (3, 5, 8), let’s find the unit vector.

Start by solving the magnitude.

|u|= 3² + 5² + 8²

|u|= 9 + 25 + 64

|u|= 98

Then, divide each vector coordinate by the magnitude 98.

x_{û} = 3 / √98 = 0.303

y_{û} = 5 / √98 = 0.505

z_{û} = 8 / √98 = 0.808

So, the unit vector *û* is (0.303, 0.505, 0.808).

û = (0.303, 0.505, 0.808)