Number Average Molecular Weight Calculator

Mn is measured by colligative property methods including membrane osmometry, vapor pressure osmometry, cryoscopy (freezing point depression), and ebulliometry (boiling point elevation). End-group analysis by NMR or titration also yields Mn. MALDI-TOF mass spectrometry provides direct molecular weight distributions from which Mn is computed.

Because Mn weights each molecule equally regardless of size, a large number of small molecules can significantly lower the average. In contrast, Mw weights molecules by their mass, so large molecules dominate. This difference makes Mn particularly useful for detecting oligomeric impurities or incomplete reactions.

Mn counts each molecule equally (number-weighted average), while Mw weights each molecule by its mass (weight-weighted average). Mw is always greater than or equal to Mn. The ratio Mw/Mn defines the polydispersity index (PDI), which measures the breadth of the molecular weight distribution.

Commercial polymers typically have Mn values from 10,000 to 500,000 g/mol. Polyethylene used in packaging may have Mn around 20,000–50,000 g/mol, while engineering plastics like polycarbonate range from 15,000–40,000 g/mol. Ultra-high molecular weight polyethylene can exceed 1,000,000 g/mol.

The degree of polymerization (DP) equals Mn divided by the molar mass of the repeating unit (M₀): DP = Mn / M₀. For example, if Mn is 100,000 g/mol and the monomer unit weighs 100 g/mol, the average chain contains 1,000 repeat units.

This calculator supports three fractions. For more complex distributions, set unused fractions to zero (N=0) or use the same formula iteratively. In practice, GPC software computes Mn from hundreds or thousands of data points along the chromatographic elution curve.

A polydisperse sample has a broader molecular weight distribution, meaning Mn is further from Mw. For a perfectly monodisperse sample, Mn equals Mw and PDI equals 1. Living polymerization techniques can achieve PDI values of 1.01–1.10, while free radical polymerization typically gives PDI of 1.5–2.5.

Mn influences melt viscosity, glass transition temperature, mechanical strength, and crystallization behavior. Polymers below a critical Mn value are too brittle for structural applications. Above a certain Mn threshold, entanglement density becomes sufficient to provide toughness and ductility essential for film, fiber, and molded part performance.

Mn is expressed in grams per mole (g/mol) or equivalently daltons (Da). In older literature you may see atomic mass units (amu). For very large polymers, kDa (kiloDaltons) is commonly used, where 1 kDa = 1,000 g/mol.