Methods, systems, and apparatus, including computer programs encoded on a computer storage medium, for shaping compute load using virtual capacity. In one aspect, a method includes obtaining a load forecast that indicates forecasted future compute load for a cell, obtaining a power model that models a relationship between power usage and computational usage for the cell, obtaining a carbon intensity forecast that indicates a forecast of carbon intensity for a geographic area where the cell is located, determining a virtual capacity for the cell based on the load forecast, the power model, and the carbon intensity forecast, and providing the virtual capacity for the cell to the cell.