1. Degree of Polymerization, Dp
The degree of polymerization, or DP, is usually defined as the number of monomeric units in polymer molecule.

2. CAROTHERS THEORY where: No  number of molecules present initially
Carothers developed a simple method of analysis for predicting the molar mass of polymer prepared by polycondensation
He recognized that the number average degree of polymerization with respect to monomer unit.
Equation 1
where:
No  number of molecules present initially
N  number of molecules remaining after a time (t) of polymerization

3. ASSUMPTION FOR CAROTHERS THEORY
There are equal numbers of functional groups,
Xn can be related to the extent of reaction P at time t.
Number of functional groups that have reacted
P = _________________________________________________________
Number of functional groups present initially
Probability of functional group present initially has reacted.

4. Therefore the total number of molecules decreases by one for each pair-wise reaction between functional groups.
Equation 2

5. Combining equation (1) and (2) gives the Carothers equation.
This equation is applicable to RA2 + RB2 , ARB and RA2 polymerization’s in which there is an exact stoiciometric balance in the number of mutually reactive functional groups.