The functionality of a monomer molecule is the number of functional groups which participate in the polymerization. Monomers with functionality greater than two will introduce branching into a polymer, and the degree of polymerization will depend on the average functionality f per monomer unit. For a system containing N molecules initially and equivalent numbers of two functional groups A and B, the total number of functional groups is Nf. 
And the modified Carothers equation is
: , where p equals to