Antibodies play crucial roles in health and disease and are invaluable tools for diagnostics, research, and therapy. Although antibodies bind bivalently, we lack methods to analyse bivalent binding. Here, we introduce a particle-based model and use it to analyse bivalent binding of SARS-CoV-2 RBD-specific antibodies in surface plasmon resonance assays. The method reproduces the monovalent on/off-rates and enables measurements of new parameters, including the molecular reach, which is the maximum antigen separation that supports bivalent binding. We show that the molecular reach (22-46 nm) exceeds the physical size of an antibody (15 nm) and that the variation in reach across 45 patient-isolated antibodies is the best correlate of viral neutralisation. Using the complete set of fitted parameters, the model predicts an emergent antibody binding potency that equals the neutralisation potency. This novel analytical method should improve our understanding and exploitation of antibodies and other bivalent molecules.