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Spatially averaged erosion rates of small catchments can be accurately inferred from the concentrations of cosmogenic nuclides in stream sediment. Here we test this technique at two catchments by comparing erosion rates inferred from cosmogenic nuclides with rates of alluvial fan deposition over the past 16,000 years. These two independent estimates agree within one standard error, demonstrating that cosmogenic nuclide signatures of stream sediment can be used to measure spatially averaged long-term erosion rates. Using this technique, we show that long-term erosion rates are an exponential function of average hillslope gradient at these sites.