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Carothers Equation Calculator

Enter the monomer conversion p to find the degree of polymerization.

How to use

  1. Enter your values in the fields above.
  2. Press Calculate to see your result instantly.
  3. Use the Share button to copy a link to your result.

About this calculator

In step-growth (condensation) polymerization — the process behind nylon, polyester and many other engineering plastics — monomers react two at a time, building chains gradually as the reaction proceeds. The Carothers equation, Xn = 1/(1 − p), relates the number-average degree of polymerization Xn to p, the fraction of functional groups that have reacted.

The relationship is famously unforgiving: to reach a useful chain length, conversion has to be pushed very close to 100% — at p = 0.99, Xn is only 100, while getting to Xn = 1000 requires p = 0.999. This calculator applies the equation directly, and it’s a standard reference for polymer chemists and materials scientists designing and controlling reactions to hit a target molecular weight.

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