Glaciers are highly effective agents of erosion that have profoundly shaped Earth's surface, but there is uncertainty about how glacial erosion should be parameterised in landscape evolution models. Glacial erosion rate is usually modelled as a function of glacier sliding velocity, but the empirical basis for this relationship is weak. In turn, climate is assumed to control sliding velocity and hence erosion, but this too lacks empirical scrutiny. Here, we present statistically robust relationships between erosion rates, sliding velocities, and climate from a global compilation of 38 glaciers. We show that sliding is positively and significantly correlated with erosion, and derive a relationship for use in erosion models. Our dataset further demonstrates that the most rapid erosion is achieved at temperate glaciers with high mean annual precipitation, which serve to promote rapid sliding. Precipitation has received little attention in glacial erosion studies, but our data illustrate its importance.