A systematic approach has been made to the prediction of the pulse height distribution at the anode of the photomultiplier in a scintillation counter arising from a distribution of electrons in the scintillator. Iterative procedures were developed for use with a digital computer to calculate the distribution exactly. A more convenient continuous algebraic function was derived and applied to extend the method to higher input energies. The derived function is simple and is significantly more accurate than the usual Gaussian representation, particularly for small numbers of electrons.These methods were developed to explain the pulse height distributions observed with low and higher energy beta emitters in a liquid scintillation counter. The method can, however, be applied to any scintillation counter where the electron distribution in the scintillator is known.