The matrix formula developed in the context of hetrochain theory, (M) over bar (w) = (M) over bar (wp) + WF(I - M)S-1, was applied to describe the molecular weight development during free-radical homopolymerization. All of the required probabilistic parameters are expressed in terms of the kinetic-rate constants and various concentrations. In free-radical polymerization, the primary chains are formed consecutively, and the number of heterochain types, N, is extrapolated to infinity. Practically, such extrapolation can be conducted on the basis of the calculated values for only three different N values with sufficient accuracy. This matrix formula is valid regardless of the chemical and reactor systems used, as long as the primary chain-connection statistics is considered Markovian. The gel point can be determined simply by solving an equation det(I - M) = 0. (C) 2004 Wiley Periodicals, Inc.