In active mountainous landscapes dominated by detachment-limited fluvial incision and hillslope landslides, the scaling relations that characterize both river profiles and planimetric organization of the river network can be linked to provide an analytic solution to describe the mean elevation of a watershed. This new analytical approach directly links mountain elevation, precipitation, bedrock erodibility and uplift rate, and yields results that are consistent with those obtained through classic 2-D surface process model. When applied to a growing linear mountain range the approach provides an approximate, but much faster, solution for 2-D or 3-D numerical models of crustal deformation that explicitly include surface processes.