Geez, you guys are making this "degrees of rotation" too complicated. It should be easy enough to approximate the degree of rotation by just eyeballing it. If that isn't good enough, get something made like this tool for Morgan dollars. It is calibrated into 2.4 degree increments. Chris
This is probably true for the 90, 180 and even 45 degree ones, but if you're trying to pick out ones that are say 15-25 degrees off to know whether to keep them or not you may need to measure. Or if you just want to know the exact rotation since some are random. I usually just put them in a flip so the obverse is as straight as possible and then hold the reverse up to the photo of the 360* protractor right on the pc, and then use a ruler if I need to down the center of the reverse.