Using a comparative evaporation kinetics approach, we describe a new and accurate method for determining the equilibrium hygroscopic growth of aerosol droplets. The time-evolving size of an aqueous droplet, as it evaporates to a steady size and composition that is in equilibrium with the gas phase relative humidity, is used to determine the time-dependent mass flux of water, yielding information on the vapor pressure of water above the droplet surface at every instant in time. Accurate characterization of the gas phase relative humidity is provided from a control measurement of the evaporation profile of a droplet of know equilibrium properties, either a pure water droplet or a sodium chloride droplet. In combination, and by comparison with simulations that account 0 10 20 30 for both the heat and mass transport governing the droplet evaporation kinetics, these measurements allow accurate retrieval of the equilibrium properties of the solution droplet (i.e., the variations with water activity in the mass fraction of solute, diameter growth factor, osmotic coefficient or number of water molecules per solute molecule). Hygroscopicity measurements can be made over a wide range in water activity (from >0.99 to, in principle, <0.05) on time scales of <10 s for droplets containing involatile or volatile solutes. The approach is benchmarked for binary and ternary inorganic solution aerosols with typical uncertainties in water activity of <+/- 0.2% at water activities >0.9 and similar to +/- 1% below 80% RH, and maximum uncertainties in diameter growth factor of +/- 0.7%. For all of the inorganic systems examined, the time-dependent data are consistent with large values of the mass accommodation (or evaporation) coefficient (>0.1).