Phosphorus (P) is an essential element for plant growth. Low P availability in soils is likely to limit crop yields in many parts of the world, but this effect has never been quantified at the global scale by process-based models. Here we attempt to estimate P limitation in three major cereals worldwide for the year 2000 by combining information on soil P distribution in croplands and a generic crop model, while accounting for the nature of soil-plant P transport. As a global average, the diffusion-limited soil P supply meets the crop's P demand corresponding to the climatic yield potential, due to the legacy soil P in highly fertilized areas. However, when focusing on the spatial distribution of P supply versus demand, we found strong limitation in regions like North and South America, Africa, and Eastern Europe. Averaged over grid cells where P supply is lower than demand, the global yield gap due to soil P is estimated at 22, 55, and 26% in winter wheat, maize, and rice. Assuming that a fraction (20%) of the annual P applied in fertilizers is directly available to the plant, the global P yield gap lowers by only 5-10%, underlying the importance of the existing soil P supply in sustaining crop yields. The study offers a base for exploring P limitation in crops worldwide but with certain limitations remaining. These could be better accounted for by describing the agricultural P cycle with a fully coupled and mechanistic soil-crop model.Read less <