Drying and crystallization of solution droplets is a problem of broad relevance, determining the microstructures of particles formed in spray-drying, the phase of particles delivered by, for example, aerosol formulations for inhalation therapies, and the impact of aerosols on radiative forcing and climate. The ephemeral nature of free droplets, particularly when considering the drying kinetics of droplets with highly volatile constituents, has often precluded the accurate measurement of transient properties such as droplet size and composition, preventing the robust assessment of predictive models of droplet-drying rates, nucleation, and crystallization. Here, we report novel measurements of the drying kinetics of individual aqueous sodium chloride solution droplets using an electrodynamic balance to isolate and trap single aerosol droplets (radius approximate to 25 mu m). The initial solution droplet size and composition are shown to be highly reproducible in terms of drying rate and crystallization time when examined over hundreds of identical evaporating droplets. We introduce a numerical model that determines the concentration gradient across the radial profile of the droplet as it dries, considering both the surface recession because of evaporation and the diffusion of components within the droplet. Drying-induced crystallization is shown to be fully determined for this system, with nucleation and instantaneous crystallization occurring once a critical supersaturation level of 2.04 +/- 0.02 is achieved at the surface of the evaporating droplet. This phenomenological model provides a consistent account of the timescale and surface concentration of free-droplet crystallization on drying for the different drying conditions studied, a necessary step in progress toward achieving control over rates of crystallization and the competitive formation of amorphous particles.