Abstract Star formation rate (SFR) distributions of galaxies are often assumed to be bimodal with modes corresponding to star-forming and quiescent galaxies, respectively. Both classes of galaxies are typically studied separately, and SFR distributions of star-forming galaxies are commonly modelled as lognormals. Using both observational data and results from numerical simulations, I argue that this division into star-forming and quiescent galaxies is unnecessary from a theoretical point of view and that the SFR distributions of the whole population can be well fitted by zero-inflated negative binomial distributions. This family of distributions has three parameters that determine the average SFR of the galaxies in the sample, the scatter relative to the star-forming sequence and the fraction of galaxies with zero SFRs, respectively. The proposed distributions naturally account for (i) the discrete nature of star formation, (ii) the presence of ‘dead’ galaxies with zero SFRs and (iii) asymmetric scatter. Excluding ‘dead’ galaxies, the distribution of log SFR is unimodal with a peak at the star-forming sequence and an extended tail towards low SFRs. However, uncertainties and biases in the SFR measurements can create the appearance of a bimodal distribution.