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

Rotation angle for X
Rotation angle for Y
Rotation angle for Z
Unit of the angle
Rotation mode
Decimal places
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 is the counterclockwise rotation of the Z-axis. The rotation matrix looks like this


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


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.

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