A fast graphics processing unit implementation of the finite-difference time-domain model was used to determine the computational effort required to accurately characterize the mean scattering functions of randomly orientated aspherical particles. The influence of the number of randomized rotational positions on the accuracy of the mean scattering phase function curve was appraised. In general, multiplying the number of orientations by 100 gives increased accuracy of factor 10. Dependent on particle shape, certain regions of the phase function were insensitive to particle orientation. In addition, an error in a key previous publication on scattering by aspherical particles was identified.