# Matrix YawPitchRoll rotation

Online computer calculates the rotation of a 4x4 matrix around the Y, X and Z axes

## Rotate matrix around 3 axes

The active die rotation (rotate object) or the passive die rotation (rotate coordinates) can be calculated

The unit of measurement for the angle can be switched between degrees or radians

XYZ axis rotation calculator

 Input Rotation angle for X Rotation angle for Y Rotation angle for Z Unit of the angle Degree Radians Rotation mode Active Passive
 Decimal places 0 1 2 3 4 6 Result M11 M12 M13 M14 M21 M22 M23 M24 M31 M32 M33 M34 M41 M42 M43 M44

## Description of the matrix X, Y and Z axes rotation

The matrix rotation distinguishes between active and passive rotation.

### Active Rotation

With active rotation, the vector or the object is rotated in the coordinate system. The active rotation is also called a geometric transformation. The rotation is counterclockwise.

Example of a 90 ° rotation of the X-axis  ### Passive rotation

With passive rotation, the coordinate system is rotated. The vector remains unchanged. The rotation is clockwise.

Example of a 90 ° rotation of the X-axis  ### Yaw, Pitch, Roll Rotation

A 3D body can be rotated around three axes. These rotations are called yaw pitch rolls.

### Yaw

Yaw is the counterclockwise rotation of the Z-axis. The rotation matrix looks like this ### Pitch

Pitch is the counterclockwise rotation of the Y-axis. The next figure shows the rotation matrix for this ### Roll

Roll is the counterclockwise rotation of the X axis. The rotation matrix for the X-axis is shown in the next figure ## Formulas of the Yaw, Pitch, Roll rotation

Each rotation matrix is a simple extension of the 2D rotation matrix. For example, the Yaw matrix essentially performs a 2D rotation with respect to the coordinates while the coordinate remains unchanged. So the third row and the third column look like part of the identity matrix, while the top right part looks like the 2D rotation matrix.

The yaw, pitch and roll rotations can be used to place a 3D body in any direction. A single rotation matrix can be formed by multiplying the matrices.  