Aim To describe and explain geographical patterns of false absence and false presence prediction errors that occur when describing current plant species ranges with species distribution models. Location Europe. Methods We calibrated species distribution models (generalized linear models) using a set of climatic variables and gridded distribution data for 1065 vascular plant species from the Atlas Florae Europaeae. We used randomly selected subsets for each species with a constant prevalence of 0.5, modelled the distribution 1000 times, calculated weighted averages of the model parameters and used these to predict the current distribution in Europe. Using a threshold of 0.5, we derived presence/absence maps. Comparing observed and modelled species distribution, we calculated the false absence rates, i.e. species wrongly modelled as absent, and the false presence rates, i.e. species wrongly modelled as present, on a 50 × 50km grid. Subsequently, we related both error rates to species range properties, land use and topographic variability within grid cells by means of simultaneous autoregressive models to correct for spatial autocorrelation. Results Grid-cell-specific error rates were not evenly distributed across Europe. The mean false absence rate was 0.16 ± 0.12 (standard deviation) and the mean false presence rate was 0.22 ± 0.13. False absence rates were highest in central Spain, the Alps and parts of south-eastern Europe, while false presence rates were highest in northern Spain, France, Italy and south-eastern Europe. False absence rates were high when range edges of species accumulated within a grid cell and when the intensity of human land use was high. False presence rates were positively associated with relative occurrence area and accumulation of range edges. Main conclusions Predictions for various species are not only accompanied by species-specific but also by grid-cell-specific errors. The latter are associated with characteristics of the grid cells but also with range characteristics of occurring species. Uncertainties of predictive species distribution models are not equally distributed in space, and we would recommend accompanying maps of predicted distributions with a graphical representation of predictive performance.