Standard climate projections represent future volcanic eruptions by a constant forcing inferred from 1850-2014 volcanic forcing. Using the latest ice-core and satellite records to design stochastic eruption scenarios, we show that there is a 95% probability that explosive eruptions could emit more sulfur dioxide (SO₂) into the stratosphere over 2015-2100 than current standard climate projections (i.e., ScenarioMIP). Our simulations using the UK Earth System Model with interactive stratospheric aerosols show that for a median future eruption scenario, the 2015-2100 average global-mean stratospheric aerosol optical depth (SAOD) is double that used in ScenarioMIP, with small-magnitude eruptions (< 3 Tg of SO₂) contributing 50% to SAOD perturbations. We show that volcanic effects on large-scale climate indicators, including global surface temperature, sea level and sea ice extent, are underestimated in ScenarioMIP because current climate projections do not fully account for the recurrent frequency of volcanic eruptions of different magnitudes.