We report measurements of the equilibrium constants, K-p, for the water mediated clustering of two and three sulfuric acid molecules for atmospheric temperatures and relative humidities. Limits for Kp for the formation of the sulfuric acid tetramer and higher clusters as well as the kinetics of small sulfuric acid cluster growth are also presented. These results put strong constraints on the rate of nucleation in the atmosphere via the H2SO4/H2O neutral mechanism. We show that the neutral nucleation of H2SO4 and H2O is slower than ion-induced nucleation of H2SO4 and H2O for most conditions found in the middle and upper troposphere. These laboratory-based upper limits to the nucleation rates are also much lower than the predictions of the liquid drop model/classical nucleation theory.