There are two rotational friction factors for a general spheroid, one for a rotation about the axial semiaxis (denoted ) and other for a rotation about one of the equatorial semiaxes (denoted ). 
Perrin showed that
for both prolate and oblate spheroids.  For spheres, , as may be seen by taking the limit .
These formulae may be numerically unstable when , since the numerator and denominator both go to zero into the  limit.  In such cases, it may be better to expand in a series, e.g.,
for oblate spheroids.