Potential evapotranspiration (PET) represents the evaporative demand in the atmosphere for the removal of water from the land and is an essential variable for understanding and modelling land–atmosphere interactions. Weather generators are often used to generate stochastic rainfall time series; however, no such model exists for the generation of a stochastically plausible PET time series. Here we develop a stochastic PET generator, stoPET, by leveraging a recently published global dataset of hourly PET at 0.1∘ resolution (hPET). stoPET is designed to simulate realistic time series of PET that capture the diurnal and seasonal variability in hPET and to support the simulation of various scenarios of climate change. The parsimonious model is based on a sine function fitted to the monthly average diurnal cycle of hPET, producing parameters that are then used to generate any number of synthetic series of randomised hourly PET for a specific climate scenario at any point of the global land surface between 55∘ N and 55∘ S. In addition to supporting a stochastic analysis of historical PET, stoPET also incorporates three methods to account for potential future changes in atmospheric evaporative demand to rising global temperature. These include (1) a user-defined percentage increase in annual PET, (2) a step change in PET based on a unit increase in temperature, and (3) the extrapolation of the historical trend in hPET into the future. We evaluated stoPET at a regional scale and at 12 locations spanning arid and humid climatic regions around the globe. stoPET generates PET distributions that are statistically similar to hPET and an independent PET dataset from CRU, thereby capturing their diurnal/seasonal dynamics, indicating that stoPET produces physically plausible diurnal and seasonal PET variability. We provide examples of how stoPET can generate large ensembles of PET for future climate scenario analysis in sectors like agriculture and water resources with minimal computational demand.