3D Rotation Matrix Calculator (Z-axis)
Easily generate a 3x3 rotation matrix around the Z-axis for 3D transformations. Input angle in degrees or radians for instant matrix calculation and visualization.
Rotation Matrix (Z-axis):
$$ R_z(\theta) = \begin{pmatrix} \cos(\theta) & -\sin(\theta) & 0 \\ \sin(\theta) & \cos(\theta) & 0 \\ 0 & 0 & 1 \end{pmatrix} $$
Understanding 3D Rotation Matrices (Z-axis)
In 3D space, a rotation matrix is used to perform rotations about an axis. For a Z-axis rotation, imagine spinning an object around the Z-axis. The Z-axis rotation matrix \( R_z(\theta) \) by an angle \( \theta \) is given by:
$$ R_z(\theta) = \begin{pmatrix} \cos(\theta) & -\sin(\theta) & 0 \\ \sin(\theta) & \cos(\theta) & 0 \\ 0 & 0 & 1 \end{pmatrix} $$
This matrix transforms a 3D vector by rotating it counter-clockwise around the Z-axis by the angle \( \theta \). Angles are typically provided in degrees or radians. This tool helps you generate this matrix by simply inputting the rotation angle. Use it in computer graphics, robotics, and any field requiring 3D spatial transformations.
Learn more about rotation matrices on Wikipedia.