14294 IUPAC Gold Book - z-average particle diameter 10.1351/goldbook.14294 14294 current 1 Calculated using the following equation: \[\left\langle d_{\rm{z}} \right\rangle = \bar d_{\rm{z}} = \frac{\Sigma N_{i} d_{i}^{5}}{\Sigma N_{i}d_{i}^{4}}\] In the formulae, \(N_{i}\) denotes the number of particles of diameter \(d_{i}\). Averages may be denoted by \(\left\langle ~ \right\rangle\) or by \(\bar{~}\). In principle, any method suitable for measuring the diameters of single particles (e.g., electron microscopy) could be used for the determination of all the averages given in the table. However, some experimental methods allow determination only of particular diameter averages. Average diameters are defined and calculated by using relations or ratios between the main momentums of a representative statistical distribution that is the particle diameter distribution (e.g., \(z\mbox{-}\rm{average}\) diameter is the fifth momentum over the fourth one). The definition of the \(z\mbox{-}\rm{average}\) diameter is meaningful only for latexes where the particles all have the same density and refractive index PAC, 2011, 83, 2229. 'Terminology of polymers and polymerization processes in dispersed systems (IUPAC Recommendations 2011)' on page 2233 (https://doi.org/10.1351/PAC-REC-10-06-03) https://goldbook.iupac.org/terms/view/14294/html https://goldbook.iupac.org/terms/view/14294/json https://goldbook.iupac.org/terms/view/14294/plain Citation: 'z-average particle diameter' 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.14294 The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms. If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org . The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using. 2026-05-09T18:16:12+00:00