Population density in plants and animals is thought to scale with size as a result of mass-related energy requirements. Variation in resources, however, naturally limits population density and may alter expected scaling patterns. We develop and test a general model for variation within and between species in population density across the order Carnivora. We find that 10,000 kilograms of prey supports about 90 kilograms of a given species of carnivore, irrespective of body mass, and that the ratio of carnivore number to prey biomass scales to the reciprocal of carnivore mass. Using mass-specific equations of prey productivity, we show that carnivore number per unit prey productivity scales to carnivore mass near -0.75, and that the scaling rule can predict population density across more than three orders of magnitude. The relationship provides a basis for identifying declining carnivore species that require conservation measures.