To constrain global warming, we must strongly curtail greenhouse gas emissions and capture excess atmospheric carbon dioxide. Regrowing natural forests is a prominent strategy for capturing additional carbon, but accurate assessments of its potential are limited by uncertainty and variability in carbon accumulation rates. To assess why and where rates differ, here we compile georeferenced measurements of carbon accumulation. Climatic factors explain variation in rates better than land-use history, so we combine the field measurements with 66 environmental covariate layers to create a global, one-kilometre-resolution map of potential aboveground carbon accumulation rates for the first 30 years of natural forest regrowth. This map shows over 100-fold variation in rates across the globe, and indicates that default rates from the Intergovernmental Panel on Climate Change (IPCC) may underestimate aboveground carbon accumulation rates by 32 per cent on average and do not capture eight-fold variation within ecozones. Conversely, we conclude that maximum climate mitigation potential from natural forest regrowth is 11 per cent lower than previously reported owing to the use of overly high rates for the location of potential new forest. Although our data compilation includes more studies and sites than previous efforts, our results depend on data availability, which is concentrated in ten countries, and data quality, which varies across studies. However, the plots cover most of the environmental conditions across the areas for which we predicted carbon accumulation rates (except for northern Africa and northeast Asia). We therefore provide a robust and globally consistent tool for assessing natural forest regrowth as a climate mitigation strategy.