A new parameterization is proposed to link the droplet number concentration to the size distribution and chemical composition of aerosol and updraft velocity. Except for an empirical assumption of droplet growth, the parameterization is formulated almost entirely on first principles to allow for satisfactory performance under a variety of conditions. For a series of updraft velocity ranging from 0.03 to 10.0 m s-1, the droplet number concentrations predicted with the parameterization are in good agreement with the detailed parcel model simulations with an average error of -4 c 26% (one standard deviation). The accuracy is comparable to or better than some existing parameterizations. The parameterization is able to account for the effects of droplet surface tension and mass accommodation coefficient on activation without adjusting the empirical parameter. These desirable attributes make the parameterization suitable for being used in the prognostic determination of the cloud droplet number concentration in general circulation models (GCMs).