(beginner) calculating orientation change with eulers

[astull]

I'm capturing Euler angles before and after a user manipulation. The object is fixed in location and only changes in orientation. What I want to measure is the error between a target orientation and the user's response orientation for the object. I've calculated the difference for each of the 3 axis but, if I understand correctly, this doesn't give a measure of the orientation change in 3D space. What is the proper method/strategy to attack this question? I'd like one measure of orientation error but I'm not sure how to get it.