The sub-kilometre scale distribution of snow depth on Arctic sea ice impacts atmosphere-ice fluxes of energy and mass, and is of importance for satellite estimates of sea-ice thickness from both radar and lidar altimeters. While information about the mean of this distribution is increasingly available from modelling and remote sensing, the full distribution cannot yet be resolved. We analyse 33 539 snow depth measurements from 499 transects taken at Soviet drifting stations between 1955 and 1991 and derive a simple statistical distribution for snow depth over multi-year ice as a function of only the mean snow depth. We then evaluate this snow depth distribution against snow depth transects that span first-year ice to multiyear ice from the MOSAiC, SHEBA and AMSR-Ice field campaigns. Because the distribution can be generated using only the mean snow depth, it can be used in the downscaling of several existing snow depth products for use in flux modelling and altimetry studies.