Temperature scaling studies suggest that hourly rainfall magnitudes might increase beyond thermodynamic expectations with global warming1-3; that is, above the Clausius-Clapeyron (CC) rate of 6.5% °C-1. However, there is limited evidence of such increases in long-term observations. Here, we calculate continental-average changes in the magnitude and frequency of extreme hourly and daily rainfall observations from Australia over the years 1990-2013 and 1966-1989. Observed changes are compared with the uncertainty from natural variability and expected changes from CC scaling as a result of global mean surface temperature change. We show that increases in daily rainfall extremes are consistent with CC scaling, but are within the range of natural variability. In contrast, changes in the magnitude of hourly rainfall extremes are close to or exceed double the expected CC scaling, and are above the range of natural variability, exceeding CC × 3 in the tropical region (north of 23° S). These continental-scale changes in extreme rainfall are not explained by changes in the El Niño-Southern Oscillation or changes in the seasonality of extremes. Our results indicate that CC scaling on temperature provides a severe underestimate of observed changes in hourly rainfall extremes in Australia, with implications for assessing the impacts of extreme rainfall.