In this paper we present parameterized equations for calculation of sulfuric acid--water critical nucleus compositions, critical cluster radii and homogeneous nucleation rates for tropospheric and stratospheric conditions. The parameterizations are based on a classical nucleation model. We used an improved model for the hydrate formation relying on ab initio calculations of small sulfuric acid clusters and on experimental data for vapor pressures and equilibrium constants for hydrate formation. The most rigorous nucleation kinetics and the thermodynamically consistent version of the classical binary homogeneous nucleation theory were used. The parameterized nucleation rates are compared with experimental ones, and at room temperature and relative humidities above 30% they are within experimental error. At lower temperatures and lower humidities the agreement is somewhat poorer. Overall, the values of nucleation rates are increased compared to a previous parameterization and are within an order of magnitude compared with theoretical values for all conditions studied. The parameterized equations will reduce the computing time by a factor 1/500 compared to nonparameterized nucleation rate calculations and therefore are in particular useful for large-scale models. The parameterized formulas are valid at temperatures between 230.15 K and 305.15 K, relative humidities between 0.01% and 100%, and sulfuric acid concentrations from 104 to 1011 cm-3. They can be used to extrapolate the classical results down to 190 K. The parametrization is limited to cases where nucleation rates are between 10-7 and 1010 cm-3s-1, and the critical cluster contains at least four molecules.