After having seen how to calculate the rotation matrix given the Euler angles, today we will see the opposite operation, again with the aim of developing a cross platform solution in C# to calculate the Euler angles from a rotation matrix.

Rotation Matrix to Euler Angles

The code to be considered takes into account 3 input parameters:

  • the rotation matrix, expressed as a multidimensional array of doubles;
  • the rotation sequence of the axes with which we wish to carry out the transformation;
  • the units of the Euler angles we wish to calculate.
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Also in this version of the code, we use two enums to better organise the code, from line 1 to 5 to define the two types of angles supported (radians and degrees), from 7 to 12 for the various axis rotation sequences (ZYX, ZYZ, XYZ).

To finish, we do a simple test, starting with calculating the rotation matrix defined as [33, 67, 32], where each value describes the rotations with respect to the X, Y and Z axes respectively.

At this point, we conclude the development by calculating backwards (row 17) and printing the resulting Euler angles which are equal to the starting angles.

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If we run the program we have just written, we will see that the final result, as long as we use rotations of type XYZ and ZYZ, will be a vector of doubles containing the values [33, 67, 32].


As already seen in the previous article, the rotation matrix is a matrix operator that allows a vector to be rotated around a given axis in space. It is a very useful tool in various fields of application, such as in robotics when solving inverse kinematics problems or in reference system transformations.

In this article, we have therefore presented a solution in C# that allows the Euler angles to be obtained from a known rotation matrix.