Accurate prediction of global sea-level rise requires that we understand the cause of recent, widespread and intensifying(1,2) glacier acceleration along Antarctic ice-sheet coastal margins(3). Atmospheric and oceanic forcing have the potential to reduce the thickness and extent of floating ice shelves, potentially limiting their ability to buttress the flow of grounded tributary glaciers(4). Indeed, recent ice-shelf collapse led to retreat and acceleration of several glaciers on the Antarctic Peninsula(5). But the extent and magnitude of ice-shelf thickness change, the underlying causes of such change, and its link to glacier flow rate are so poorly understood that its future impact on the ice sheets cannot yet be predicted(3). Here we use satellite laser altimetry and modelling of the surface firn layer to reveal the circum-Antarctic pattern of ice-shelf thinning through increased basal melt. We deduce that this increased melt is the primary control of Antarctic ice-sheet loss, through a reduction in buttressing of the adjacent ice sheet leading to accelerated glacier flow(2). The highest thinning rates occur where warm water at depth can access thick ice shelves via submarine troughs crossing the continental shelf. Wind forcing could explain the dominant patterns of both basal melting and the surface melting and collapse of Antarctic ice shelves, through ocean upwelling in the Amundsen(6) and Bellingshausen(7) seas, and atmospheric warming on the Antarctic Peninsula(8). This implies that climate forcing through changing winds influences Antarctic ice-sheet mass balance, and hence global sea level, on annual to decadal timescales.