Drainage density reflects the signature of climate on the topography and dictates the boundary conditions for surface hydrology. Hence defining the relationship between drainage density and climate is important in assessing the sensitivity of water resources and hydrology to climate change. Here we analyze the equilibrium relationship between drainage density and climate and estimate the relative sensitivity of drainage density to climate change. We conclude that the sign of the resulting change in drainage density depends not only on the direction of the change in climate but also on the prevailing climatic regime.