2D Rotation Matrix Generator

Easily generate and visualize 2D rotation matrices. Enter an angle and see the matrix and its interactive graphical representation.

Enter Angle

degrees

Select Units

Rotation Matrix:

Visualization:

Understanding 2D Rotation Matrices

In linear algebra, a 2D rotation matrix is used to perform rotations in a two-dimensional plane. It's defined by an angle θ and can rotate a vector either clockwise or counterclockwise around the origin of the coordinate system. The standard form for a counterclockwise rotation by an angle θ is given by:

$$\begin{pmatrix} \cos(\theta) & -\sin(\theta) \\ \sin(\theta) & \cos(\theta) \end{pmatrix}$$

Here, cos(θ) and sin(θ) are the cosine and sine of the rotation angle θ, respectively. Angles are typically measured in degrees or radians. Radians are the standard unit in mathematics, where 180 degrees equals π radians. This tool allows you to input an angle in either degrees or radians and instantly generates the corresponding 2D rotation matrix, along with a visual representation of how a standard vector is rotated by this matrix. Use this to understand transformations in geometry, computer graphics, and physics.

Learn more about rotation matrices on Wikipedia.