From simulations with EPIC-IIASA, we derived gridded predictions of average annual changes in topsoil organic carbon storage (kg C m-2yr-1) for croplands and grassland under different types of management. Predictions were made for present-day (2015-2024) and for different future periods (2041-2060, 2061-2080, 2081-2100) following high mitigation (RCP-SSP 126) and low mitigation (RCP-SSP 585) scenarios. Further, we provide future projections based on two global circulation models: of the MPI in Germany and the IPSL in France. We further provide maps of present-day topsoil (0-15 cm) organic carbon stocks (kg C m-2) under current crop- and grassland management as reference, and simulations of climate change impacts under business as usual scenarios.