An elegant, simple, and exact analytical solution (AS) was obtained for a large range of elementary steps with practical importance in free radical polymerization. The AS matches excellently with the numerical solution for the four cases of monomer polymer systems studied ranging from the slowest to the fastest. It works equally well for different initiators, different initiator and monomer concentrations, presence or absence of solvent, various solvent volume fractions, and different temperatures. It also matches quite well with experimental data reported in the literature. This AS is not only in line with previous published solutions but also extends their applicability in a natural way. Overall, the conceptual correctness as well as predictive capabilities of the derived AS are established beyond doubt. This AS has the potential to be used in various practical applications such as model based process control, CFD simulations, and so forth.