Assessing the impacts of anthropogenic degradation and climate change on global carbon cycling is hindered by a lack of clear, flexible, and easy-to-use productivity models along with scarce trait and productivity data for parameterizing and testing those models. We provide a simple solution: a mechanistic framework (RS-CFM) that combines remotely-sensed foliar-trait and canopy-structural data with trait-based metabolic theory to efficiently map productivity at large spatial scales. We test this framework by quantifying net primary productivity (NPP) at high-resolution (0.01-ha) in hyper-diverse Peruvian tropical forests (30,040 hectares) along a 3,322-m elevation gradient. Our analysis captures hotspots and elevational shifts in productivity more accurately and in greater detail than alternative empirical- and process-based models that use plant functional types. This result exposes how high-resolution, location-specific variation in traits and light competition drive variability in productivity, opening up possibilities to fully harness remote sensing data and reliably scale up from traits to map global productivity in a more direct, efficient, and cost-effective manner.