Converting measurements of ice-sheet surface elevation change to mass change requires measurements of accumulation and knowledge of the evolution of the density profile in the firn. Most firn-densification models are tuned using measured depth–density profiles, a method which is based on an assumption that the density profile in the firn is invariant through time. Here we present continuous measurements of firn-compaction rates in 12 boreholes near the South Pole over a 2 year period. To our knowledge, these are the first continuous measurements of firn compaction on the Antarctic plateau. We use the data to derive a new firn-densification algorithm framed as a constitutive relationship. We also compare our measurements to compaction rates predicted by several existing firn-densification models. Results indicate that an activation energy of 60 kJ mol−1, a value within the range used by current models, best predicts the seasonal cycle in compaction rates on the Antarctic plateau. Our results suggest models can predict firn-compaction rates with at best 7% uncertainty and cumulative firn compaction on a 2 year timescale with at best 8% uncertainty.