Abstract An analytical distribution function characterising the grain sizes of polycrystalline microstructures is presented. Contrary to standard mathematical probability functions that are still often used for description of experimentally obtained size distributions, this one is based on a statistical mean-field theory of grain growth and is fully consistent with the fundamental physical conditions of total-volume conservation and the existence of a finite average grain volume. It is found that this distribution function describes the grain size distribution obtained by Monte Carlo Potts model simulations better than standard mathematical distributions. Additionally, two-dimensional plane sections from the simulated three-dimensional grain structures are considered and compared with experimental data, and the analytic size distribution function is also compared with an experimental grain size distribution for pure iron obtained by serial sectioning.