Decode a Rotation Matrix

Decode Rotation Matrix

Decode Rotation Matrix

Enter the elements of the 2×2 rotation matrix:


Decode a Rotation Matrix tool allows you to input the elements of a 2×2 rotation matrix and deciphers the angle of rotation it represents.

Matrix Input:

  • You can input the elements of the rotation matrix in the provided table. The default values represent the identity matrix, which indicates no rotation.
  • Each cell in the table corresponds to an element of the rotation matrix.

Decode Rotation Matrix:

  • Clicking the “Decode Rotation Matrix” button calculates the angle of rotation based on the provided matrix elements.
  • The calculated angle of rotation is displayed below the button.

Benefits of Using This Tool:

  1. Quick Deciphering: Easily determine the angle of rotation encoded in a given 2×2 rotation matrix.
  2. Accuracy: Precisely calculates the angle of rotation using the matrix elements.
  3. Educational: Helps understand the relationship between rotation matrices and angles of rotation.


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

Q: How does the tool calculate the angle of rotation? A: The tool uses the elements of the rotation matrix to calculate the angle of rotation using trigonometric functions.

Q: What does the identity matrix represent in terms of rotation? A: The identity matrix represents no rotation. The default values in the input table correspond to the identity matrix.