Matrix YawPitchRoll rotation
Online calculator for calculating the rotation around the X, Y and Z axes of a 3x3 matrix
This function calculates the 3D rotation of a solid using the quaternion.
The unit of measurement for angles can be switched between degrees or radians
Active rotation (rotating object) or passive rotation (rotating coordinates) can be calculated
To perform the calculation, enter the rotation angles. Then click the button 'Calculate'

Matrix rotation with the quaternion
This function calculates the 3D rotation of a solid with the quaternion. The quaternion is an extension of the complex numbers. In contrast to rotation with Euler angles, this avoids the problem that arises when two axes of rotation are superimposed in a configuration.
The matrices of the two methods differ because the assignment of the axes and the order of the calculation is different.
Calculator of a rotation with Euler angles can be found here.
The calculator assumes a rollpitchyaw rotation order when creating a rotation matrix, ie an object is first rotated around the Z axis, then around the X axis and finally around the Y axis.
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 Xaxis
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 Xaxis
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 Zaxis. The rotation matrix looks like this
Pitch
Pitch is the counterclockwise rotation of the Yaxis. The next figure shows the rotation matrix for this
Roll
Roll is the counterclockwise rotation of the X axis. The rotation matrix for the Xaxis 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.
Matrix 3x3 Functions
Addition • Subtraction • Multiplication • Scalar Multiplication • Rotation X axis • Rotation Y axis • Rotation Z axis • Y, P, R Rotation quaternion • Y, P, R Rotation Euler angles • Invert • DeterminantMatrix 4x4 Functions
Addition • Subtraction • Multiplication • Scalar Multiplication • Rotation X axis • Rotation Y axis • Rotation Z axis • Y, P, R Rotation • Vector Rotation • Invert • Determinant • interpolation
