# Number average molecular weight

The **number average molecular weight** is a way of determining the molecular weight of a polymer. Polymer molecules, even ones of the same type, come in different sizes (chain lengths, for linear polymers), so the average molecular weight will depend on the method of averaging. The *number average* molecular weight is the common, mean, average of the molecular weights of the individual polymers. It is determined by measuring the molecular weight of *n* polymer molecules, summing the weights, and dividing by *n*.

The number average molecular weight of a polymer can be determined by gel permeation chromatography, viscometry, light scattering, analytical ultracentrifugation, vapor pressure osmometry, end-group titration, and colligative properties.

An alternative measure of the molecular weight of a polymer is the weight average molecular weight. The ratio of the *weight average* to the *number average* is called the polydispersity index.

*High Number-Average Molecular Weight Polymers* may be obtained only with a high *fractional monomer conversion* in the case of step-growth polymerization, as per the Carothers' equation.