Grounding lines are a key indicator of ice-sheet instability, because changes in their position reflect imbalance with the surrounding ocean and affect the flow of inland ice. Although the grounding lines of several Antarctic glaciers have retreated rapidly due to ocean-driven melting, records are too scarce to assess the scale of the imbalance. Here, we combine satellite altimeter observations of ice-elevation change and measurements of ice geometry to track grounding-line movement around the entire continent, tripling the coverage of previous surveys. Between 2010 and 2016, 22%, 3% and 10% of surveyed grounding lines in West Antarctica, East Antarctica and at the Antarctic Peninsula retreated at rates faster than 25 m yr^{−1} (the typical pace since the Last Glacial Maximum) and the continent has lost 1,463 km^2 +- 791 km^2 of grounded-ice area. Although by far the fastest rates of retreat occurred in the Amundsen Sea sector, we show that the Pine Island Glacier grounding line has stabilized, probably as a consequence of abated ocean forcing. On average, Antarctica’s fast-flowing ice streams retreat by 110 metres per metre of ice thinning.