Create a Rotation Matrix

Rotation Matrix

Rotation Matrix Generator

Enter the angle of rotation (in degrees):


Create a Rotation Matrix tool allows you to input an angle of rotation and generates the corresponding 2×2 rotation matrix.

Angle Input:

  • You can input the angle of rotation in degrees using the provided input field. The default value is 45 degrees.

Generate Rotation Matrix:

  • Clicking the “Generate Rotation Matrix” button calculates the rotation matrix based on the input angle.
  • The rotation matrix is displayed below the button, showing the values of each element.

Benefits of Using This Tool:

  1. Ease of Use: Simple interface requiring only the angle of rotation input.
  2. Accuracy: Ensures accurate generation of the rotation matrix based on the input angle.
  3. Educational: Helps understand the concept of rotation matrices and their relationship to angles.


Q: What is a rotation matrix? A: A rotation matrix is a 2×2 matrix used to perform rotations in the plane. It represents a transformation that rotates points in the plane around the origin by a specified angle.

Q: How does the tool calculate the rotation matrix? A: The tool converts the input angle from degrees to radians, then calculates the sine and cosine of the angle. These values are used to construct the rotation matrix.

Q: Can I use this tool for angles other than 45 degrees? A: Yes, you can input any angle in degrees, and the tool will generate the corresponding rotation matrix for that angle.