In step-growth polymerization, the Carothers equation (or Carothers' equation) gives the degree of polymerization, X_n, for a given fractional monomer conversion, p.

There are several versions of this equation, proposed by Wallace Carothers, who invented nylon in 1935.

The simplest case refers to the formation of a strictly linear polymer by the reaction (usually by condensation) of two monomers in equimolar quantities. An example is the synthesis of nylon-6,6 whose formula is [−NH−(CH₂)₆−NH−CO−(CH₂)₄−CO−]_n from one mole of hexamethylenediamine, H₂N(CH₂)₆NH₂, and one mole of adipic acid, HOOC−(CH₂)₄−COOH. For this case

In this equation

This equation shows that a high monomer conversion is required to achieve a high degree of polymerization. For example, a monomer conversion, p, of 98% is required for ⁠${\displaystyle {\bar {X}}_{n}}$⁠ = 50, and p = 99% is required for ⁠${\displaystyle {\bar {X}}_{n}}$⁠ = 100.

If one monomer is present in stoichiometric excess, then the equation becomes

The effect of the excess reactant is to reduce the degree of polymerization for a given value of p. In the limit of complete conversion of the limiting reagent monomer, p → 1 and

Thus for a 1% excess of one monomer, r = 0.99 and the limiting degree of polymerization is 199, compared to infinity for the equimolar case. An excess of one reactant can be used to control the degree of polymerization.