Abstract The probability of a finite or dangling chain on an ideal polymer network has been derived by a simple recursive scheme. In contrast to the method of Dobson and Gordon, probability generating function formalism is not required. The general result, Equations (21), and its specific solutions, Equations (23), (24), and (30), give the finite chain probability as a function of reactant type and extent of polymerization. They cover most of the important types of network forming polymerizations. From the finite chain probability, useful property relations such as sol fraction, crosslink density, and the number of elastically effective network chains are developed. Because of their simplicity, we expect these relations to be further developed and applied to network polymer property measurements.