# Quaternion Calculation

Calculator to convert a quaternion into conjugate, inverse and normal

## Quaternion Calculator

On this page you will find a calculator for quaternion conversions to conjugate, inverse and normal.

To perform the calculation select the math function that are to be calculated and enter the quaternion values. Then click the Calculate button.

Empty fields are counted as 0.

Quaternion Calculator

 Input Quaternion Result X Vector = Y Vector Z Vector W Rotation
 Operator Conjugate Inverse Normalize Negate Decimal places 0 1 2 3 4 6 8 10

## Description

The quaternion represents a vector used to encode three-dimensional physical rotations. It is used to efficiently rotate an object about the (x,y,z) vector by angle theta, where:

w = cos(theta/2)

### Array

W - The rotation component of the quaternion.
X - The X value of the vector component of the quaternion.
Y - The Y value of the vector component of the quaternion.
Z - The Z value of the vector component of the quaternion.

## Description of the functions

### Conjugatet

Returns the conjugate of a specified quaternion.

### Inverse

Returns the inverse of a quaternion.

### Normalize

Divides each component of a specified quaternion by its length.
This gives a new quaternion with length 1.

### Negate

Reverses the sign of each component of the vector.