Abstract Much previous modeling work on the climate response to volcanic eruptions has focused on specific past events. Here, we explore the climate response over a whole range of amplitudes covering (and exceeding) all events of the last six millennia, by simulating eruptions with 5, 10, 20, 40, 80, and 160 Tg of stratospheric injected sulfur. Our simulations show a strongly non‐linear relationship between eruption magnitude and climate response, with temperature and precipitation responding differently. Global mean surface cooling saturates at 40 TgS, whereas precipitation decreases all the way to 160 TgS. We also find that the precipitation responds and recovers faster than the temperature, especially for the larger events. Our findings imply that a severe reduction in precipitation, rather than a dramatic surface cooling, might be the most important climatic impact associated with very large eruptions.