Flow velocities within coral reefs are greatly reduced relative to those at the water surface. The in-reef flow controls key processes that flush heat, cycle nutrients and transport sediment from the reef to adjacent beaches, all key considerations in assessments of reef resilience and restoration interventions. An analytical framework is proposed and tested with a suite of high-resolution numerical experiments. We demonstrate a single parameter that describes the total coral frontal area explains variation of horizontally averaged velocity within a reef canopy across morphologies, densities, and flow depths. With the integration of existing data of coral cover and geometry, this framework is a practical step towards the prediction of near-bed flows in diverse reef environments.