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Interactions between biomolecules control the processes of life in health and their malfunction in disease, making their characterization and quantification essential. Immobilization- and label-free analytical techniques are desirable because of their simplicity and minimal invasiveness, but they struggle with quantifying tight interactions. Here, we show that mass photometry can accurately count, distinguish by molecular mass, and thereby reveal the relative abundances of different unlabelled biomolecules and their complexes in mixtures at the single-molecule level. These measurements determine binding affinities over four orders of magnitude at equilibrium for both simple and complex stoichiometries within minutes, as well as the associated kinetics. These results introduce mass photometry as a rapid, simple and label-free method for studying sub-micromolar binding affinities, with potential for extension towards a universal approach for characterizing complex biomolecular interactions., (© 2020 The Authors. Published by Wiley-VCH Verlag GmbH & Co. KGaA.)