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Abstract Crustal magma chambers can grow to be hundreds to thousands of cubic kilometers, potentially feeding catastrophic caldera‐forming eruptions. Smaller volume chambers are expected to erupt frequently and freeze quickly; a major outstanding question is how magma chambers ever grow to the sizes required to sustain the largest eruptions on Earth. We use a thermo‐mechanical model to investigate the primary factors that govern the extrusive:intrusive ratio in a chamber, and how this relates to eruption frequency, eruption size, and long‐term chamber growth. The model consists of three fundamental timescales: the magma injection timescaleτ_in, the cooling timescaleτ_cool, and the timescale for viscous relaxation of the crustτ_relax. We estimate these timescales using geologic and geophysical data from four volcanoes (Laguna del Maule, Campi Flegrei, Santorini, and Aso) to compare them with the model. In each of these systems,τ_inis much shorter thanτ_cooland slightly shorter thanτ_relax, conditions that in the model are associated with efficient chamber growth and simultaneous eruption. In addition, the model suggests that the magma chambers underlying these volcanoes are growing at rates between ~10⁻⁴and 10⁻² km³/year, speeding up over time as the chamber volume increases. We find scaling relationships for eruption frequency and size that suggest that as chambers grow and volatiles exsolve, eruption frequency decreases but eruption size increases. These scaling relationships provide a good match to the eruptive history from the natural systems, suggesting that the relationships can be used to constrain chamber growth rates and volatile saturation state from the eruptive history alone.