The proportion of time an animal spends actively foraging in a day determines its long-term fitness. Here, we derive a general mathematical model for the scaling of this activity time with body size in consumers. We show that this scaling can change from positive (increasing with size) to negative (decreasing with size) if the detectability and availability of preferred prey sizes is a limiting factor. These predictions are supported by a global dataset on 73 terrestrial carnivore species from 8 families spanning >3 orders of magnitude in size. Carnivores weighing ∼5 kg experience high foraging costs because their diets include significant proportions of relatively small (invertebrate) prey. As a result, they show an increase in activity time with size. This shifts to a negative scaling in larger carnivores as they shift to foraging on less costly vertebrate prey. Our model can be generalized to other classes of terrestrial and aquatic consumers and offers a general framework for mechanistically linking body size to population fitness and vulnerability in consumers.