We present a simple and pedagogical method for quickly calculating optical pumping processes based
on linearised population rate equations. The method can easily be implemented on mathematical
software run on modest personal computers, and can be generalised to any number of concrete
situations. We also show that the method is still simple with realistic experimental complications
taken into account, such as high level degeneracy, impure light polarisation, and an added external
magnetic field. The method and the associated mathematical toolbox should be of value in advanced
physics teaching, and can also facilitate the preparation of research tasks.