Projections of changes in Antarctic Ice Sheet (AIS) surface mass balance indicate a negative contribution to sea level because of the expected increase in precipitation due to the higher moisture holding capacity of warmer air. Observations over the past decades, however, are unable to constrain the relation between temperature and accumulation changes because both are dominated by strong natural variability. Here we derive a consistent continental-scale increase in accumulation of approximately 5 ± 1% K-1, through the assessment of ice-core data (spanning the large temperature change during the last deglaciation, 21,000 to 10,000 years ago), in combination with palaeo-simulations, future projections by 35 general circulation models (GCMs), and one high-resolution future simulation. The ice-core data and modelling results for the last deglaciation agree, showing uniform local sensitivities of 46% K-1. The palaeo-simulation allows for a continental-scale aggregation of accumulation changes reaching 4.3% K-1. Despite the different timescales, these sensitivities agree with the multi-model mean of 6.1 ± 2.6% K-1 (GCM projections) and the continental-scale sensitivity of 4.9% K-1 (high-resolution future simulation). Because some of the mass gain of the AIS is offset by dynamical losses induced by accumulation, we provide a response function allowing projections of sea-level fall in terms of continental-scale accumulation changes that compete with surface melting and dynamical losses induced by other mechanisms.