Degree of Polymerization Calculator
The degree of polymerization (DP) is the number of monomer repeat units in an average polymer chain and is one of the most fundamental characterization parameters for polymers. A high DP generally means stronger mechanical properties and higher melt viscosity. The number-average degree of polymerization is calculated as DP = Mn / M0, where Mn is the number-average molecular weight (from GPC or osmometry) and M0 is the molar mass of the monomer repeat unit. For a copolymer, M0 should be the weighted average molar mass of the repeat unit composition. This calculator also shows the weight-average degree of polymerization from Mw.
Degree of polymerization formula
DP(n) = Mn / M0
Where Mn is the number-average molecular weight and M0 is the molar mass of the monomer repeat unit, both in g/mol. The result is dimensionless and represents the average chain length. For the weight-average DP: DP(w) = Mw / M0. The PDI = DP(w) / DP(n) = Mw / Mn.
Monomer repeat unit masses of common polymers
- Polyethylene (-CH2CH2-): M0 = 28.05 g/mol.
- Polypropylene (-CH2CHCH3-): M0 = 42.08 g/mol.
- Polystyrene (-CH2CHPh-): M0 = 104.15 g/mol.
- Poly(methyl methacrylate) PMMA: M0 = 100.12 g/mol.
- Nylon-6 (-NH(CH2)5CO-): M0 = 113.16 g/mol.
Degree of polymerization: frequently asked questions
What is the degree of polymerization?
The degree of polymerization (DP) is the number of monomer repeat units in an average polymer chain. It is calculated as DP = Mn / M0, where Mn is the number-average molecular weight and M0 is the molar mass of one repeat unit (monomer).
What is the difference between Mn and Mw?
Mn (number-average molecular weight) weights each chain equally by count. Mw (weight-average molecular weight) gives more weight to larger chains. The ratio Mw/Mn is the polydispersity index (PDI), which equals 1.0 for a perfectly monodisperse polymer and is greater than 1 for all real polymers.
What is a typical degree of polymerization for common polymers?
Polyethylene (commercial grade): DP typically 1,000 to 10,000. Cellulose (cotton): DP approximately 10,000 to 15,000. Nylon-6,6: DP approximately 50 to 150 for typical grades. Polystyrene (general purpose): DP approximately 1,000 to 5,000.
How does DP relate to physical properties?
Higher DP means longer chains, which generally increases tensile strength, melt viscosity, and glass transition temperature up to a plateau. Below a critical DP (entanglement molecular weight), polymer chains do not entangle and the material is brittle with poor mechanical properties.
How is Mn measured experimentally?
Common methods include gel permeation chromatography (GPC), end-group analysis by NMR or titration, membrane osmometry, and vapor pressure osmometry. GPC is the most widely used technique and reports Mn, Mw, and PDI simultaneously using calibration standards.
Official sources
- IUPAC: Glossary of Basic Terms in Polymer Science (IUPAC Recommendations).
- NIST: NIST Polymer Science Division.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.