Iceberg calving has been assumed to be the dominant cause of mass loss for the Antarctic ice sheet, with previous estimates of the calving flux exceeding 2,000 gigatonnes per year. More recently, the importance of melting by the ocean has been demonstrated close to the grounding line and near the calving front. So far, however, no study has reliably quantified the calving flux and the basal mass balance (the balance between accretion and ablation at the ice-shelf base) for the whole of Antarctica. The distribution of fresh water in the Southern Ocean and its partitioning between the liquid and solid phases is therefore poorly constrained. Here we estimate the mass balance components for all ice shelves in Antarctica, using satellite measurements of calving flux and grounding-line flux, modelled ice-shelf snow accumulation rates and a regional scaling that accounts for unsurveyed areas. We obtain a total calving flux of 1,321 +/- 144 gigatonnes per year and a total basal mass balance of -1,454 +/- 174 gigatonnes per year. This means that about half of the ice-sheet surface mass gain is lost through oceanic erosion before reaching the ice front, and the calving flux is about 34 per cent less than previous estimates derived from iceberg tracking. In addition, the fraction of mass loss due to basal processes varies from about 10 to 90 per cent between ice shelves. We find a significant positive correlation between basal mass loss and surface elevation change for ice shelves experiencing surface lowering and enhanced discharge. We suggest that basal mass loss is a valuable metric for predicting future ice-shelf vulnerability to oceanic forcing.