The biochemical basis of microtubule growth has remained elusive for over 30 years despite being fundamental for both cell division and associated chemotherapy strategies. Here, we combine interferometric scattering microscopy with recombinant tubulin to monitor individual tubulins binding to and dissociating from growing microtubule tips. We make direct, single-molecule measurements of tubulin association and dissociation rates. We detect two populations of transient dwell times and determine via binding-interface mutants that they are distinguished by the formation of one interprotofilament bond. Applying a computational model, we find that slow association kinetics with strong interactions along protofilaments best recapitulate our data and, furthermore, predicts plus-end tapering. Overall, we provide the most direct and complete experimental quantification of how microtubules grow to date.