Receptor internalization by endocytosis regulates diverse cellular processes from the rate of nutrient uptake to the timescale of essential signaling events. The established view is that internalization is tightly controlled by specific protein binding interactions. However, recent work suggests that biophysical factors influence the process in ways that cannot be explained by biochemistry alone. Specifically, work from several groups suggests that increasing the steric bulk of receptors may inhibit their uptake by multiple types of trafficking vesicles. How do biochemical and biophysical factors work together to control internalization? Here we show that receptor uptake is well-described by a thermodynamic tradeoff between receptor-vesicle binding energy and the entropic cost of confining receptors within endocytic vesicles. Specifically, using large ligands to acutely increase the size of engineered variants of the transferrin receptor, we demonstrate that an increase in the steric bulk of a receptor dramatically decreases its probability of uptake by clathrin-coated structures. In agreement with a simple thermodynamic model, all data follow a single trend relating occupancy of the endocytic structure to occupancy of the surrounding plasma membrane. This fundamental scaling law provides a simple tool for predicting the impact of biophysical factors on receptor uptake rate, including receptor size, affinity for endocytic structures, and expression level. In agreement with these predictions, our results demonstrate how receptors of varying size and affinity compete for limited space within crowded endocytic structures. Understanding this biophysical competition is important for predicting receptor uptake in settings where endocytosis is saturated by receptor overexpression, as is the case in many tumor cells. More broadly, this work demonstrates that bulky ligands can drive the accumulation of specific receptors at the plasma membrane surface, providing a biophysical tool for targeted modulation of signaling and metabolism from outside the cell.