Exact and approximate general expressions for the growth and decay probabilities of a cluster in one-component nucleation are given. A method is proposed for a model-independent determination of the nucleus size with the help of data for the dependence of the cluster growth probability on the cluster size. Monte Carlo simulation data for the cluster growth probability are obtained for homogeneous one-component nucleation of droplets in Lennard-Jones vapors. From these data, the size of the nucleus droplet and the Zeldovich factor are determined by the newly proposed method. (C) 2003 American Institute of Physics.