The following is an example of the algorithm for determining the axis/angle representation of misorientation between two texture components given as Euler angles:
:Copper [90,35,45]
:S3 [59,37,63]
The first step is converting the Euler angle representation,  to an orientation matrix  by:
where  and  represent  and  of the respective Euler component.  This yields the following orientation matrices:
The misorientation is then:
The axis/angle description (with the axis as a unit vector) is related to the misorientation matrix by:
(There are errors in the similar formulae for the components of r given in the book by Randle and Engler (see refs.), which will be corrected in the next edition of their book. The above are the correct versions, note a different form for these equations has to be used if Θ = 180 degrees.)
For the copper—S misorientation given by , the axis/angle description is 19.5° about [0.689,0.623,0.369], which is only 2.3° from <221>.  This result is only one of the 1152 symmetrically related possibilities but does specify the misorientation.  This can be verified by considering all possible combinations of orientation symmetry (including switching symmetry).