Title: number-average molar mass
Long Title: IUPAC Gold Book - number-average molar mass
DOI: 10.1351/goldbook.12216
Status: current

Definition
The equation for number-average molar mass is \[M_{\rm{n}} = \frac{1}{\sum\limits_{M} (w_{M}/M)}\]
The equation for number-average molecular weight  is \[M_{\rm{r,n}} = \frac{1}{\sum\limits_{M_{\rm{r}}}(w_{M_{\rm{r}}}/M_{\rm{r}})}\]

Notes
1) For definition of the symbols, see molar-mass average.
2) Quantities number-average molecular weight, number-average relative molar mass, and number-average relative molecular mass (\(M_{\rm{r,n}}\)) are synonyms. These quantities are dimensionless (pure numbers) and are not associated with any units.

Related Term
- molar-mass average: https://goldbook.iupac.org//terms/view/12215

Source
- PAC, 2015, 87, 71. 'Definitions of terms relating to individual macromolecules, macromolecular assemblies, polymer solutions, and amorphous bulk polymers (IUPAC Recommendations 2014)' on page 83 (https://doi.org/10.1515/pac-2013-0201)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/12216/html
- json: https://goldbook.iupac.org/terms/view/12216/json
- xml: https://goldbook.iupac.org/terms/view/12216/xml

Citation: Citation: 'number-average molar mass' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.12216
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Accessed: 2026-04-18T06:44:57+00:00