Forests are integral to global carbon cycling but are threatened by anthropogenic degradation and climate change. Assessing this global threat has been hindered by a lack of clear, flexible, and easy-to-use productivity models along with a lack of functional trait and productivity data for parameterizing and testing those models. Current productivity models are either extremely complex requiring up to hundreds of parameters, many sub-models, and considerable computational expense or rely on statistical trait-growth relationships that can be hard to extrapolate to new systems or climates. Here we provide a simple alternative: a remote sensing canopy functional model (RS-CFM) that uses remotely-sensed foliar traits and canopy structure data to efficiently map productivity at high-resolution and large spatial scales. We test this model by quantifying net primary productivity (NPP) at 0.01-ha resolution in 30,040 hectares of Peruvian tropical rainforest along a 3,322-m Amazon-to-Andes elevation gradient. Our model predicts local NPP and elevational shifts in NPP much more accurately and in greater detail than a prominent alternative method—NASA’s MODIS NPP product. Furthermore, we show how NPP estimates depend on light competition and identify the appropriate spatial resolution for remote productivity estimation. Our framework opens up possibilities to fully harness remote sensing data and reliably scale up from traits to map regional or global productivity in a more direct, efficient, and cost-effective manner.