The largest volcanic eruptions in the geologic record have no analogue in the historical record. These eruptions had global impacts1, 2, but are known only through their eruptive products. They have left behind calderas that formed as the surface collapsed when eruption evacuated magma chambers at 5–15 km depths3, 4. It is generally assumed that calderas reflect the spatial dimensions of underlying magma reservoirs. Here we use a numerical model of conduit flow and dynamic magma-chamber drainage to show that caldera size can be affected by the material properties of crystal-rich silicic magma. We find that magma in the chamber can experience a rheological transition during eruption. This transition causes magma near the conduit to behave as a fluid, whereas magma farther away behaves elastically and remains locked. The intervening surface—the yield surface—expands through the chamber as eruption progresses. If a yielding transition occurs, calderas can form before complete mobilization of the entire reservoir. The resulting distribution of eruption volumes is then bimodal, as observed in the geologic record. We suggest that the presence or absence of a magma yield stress determines whether caldera size reflects the true spatial extent of magma storage.