The ongoing debate about the nature of coupling between climate and tectonics in mountain ranges derives, in part, from an imperfect understanding of how topography, climate, erosion, and rock uplift are interrelated. Here, we demonstrate that erosion rate is nonlinearly related to fluvial relief with a proportionality set by mean annual rainfall. These relationships can be quantified for tectonically active landscapes, and calculations based on them enable estimation of erosion where observations are lacking. Tests of the predictive power of this relationship in the Himalaya, where erosion is well constrained, affirm the value of our approach. Our model allows estimation of erosion rates in fluvial landscapes using readily available datasets, and the underlying relationship between erosion and rainfall offers the promise of a deeper understanding of how climate and tectonic evolution affect erosion and topography in space and time and of the potential influence of climate on tectonics.