Abstract How can rapidly growing food demands be met with least adverse impact on nature? Two very different sorts of suggestions predominate in the literature: wildlife-friendly farming, whereby on-farm practices are made as benign to wildlife as possible (at the potential cost of decreasing yields); and land-sparing, in which farm yields are increased and pressure to convert land for agriculture thereby reduced (at the potential cost of decreasing wildlife populations on farmland). This paper is about one important aspect of the land-sparing idea – the sensitivity of future requirements for cropland to plausible variation in yield increases, relative to other variables. Focusing on the 23 most energetically important food crops, we use data from the Food and Agriculture Organisation (FAO) and the United Nations Population Division (UNPD) to project plausible values for 2050 for population size, diet, yield, and trade, and then look at their effect on the area needed to meet demand for the 23 crops, for the developing and developed worlds in turn. Our calculations suggest that across developing countries, the area under those crops will need to increase very considerably by 2050 (by 23% under intermediate projections), and that plausible variation in average yield has as much bearing on the extent of that expansion as does variation in population size or per capita consumption; future cropland area varies far less under foreseeable variation in the net import of food from the rest of the world. By contrast, cropland area in developed countries is likely to decrease slightly by 2050 (by 4% under intermediate projections for those 23 crops), and will be less sensitive to variation in population growth, diet, yield, or trade. Other contentious aspects of the land-sparing idea require further scrutiny, but these results confirm its potential significance and suggest that conservationists should be as concerned about future agricultural yields as they are about population growth and rising per capita consumption.