ISO 9276-2:2014

Overview - ISO 9276-2:2014 (particle size analysis, moments & mean sizes)

ISO 9276-2:2014 specifies the equations, nomenclature and procedures for calculating moments, mean particle sizes (diameters) and standard deviations from a given particle size distribution (PSD). The standard describes two commonly used notation systems - the moment-notation (method of moments) and the moment-ratio-notation - and covers calculation from either histogram (discrete size classes) or analytical PSDs. The document treats particle size as the equivalent diameter (shape factors are not included) and includes numerical examples and guidance on accuracy.

Key topics and technical requirements

• Moment definitions and notation: complete and central moments for different quantity types (number, length, surface, volume/mass).
• Two notation systems:
  • Moment-notation (physics/engineering weighting principles)
  • Moment-ratio-notation (number statistics and frequency approach)
  • Relationship between the two notations is given (Clause 6).
• Mean particle sizes: arithmetic and weighted means (number-, area-, volume-weighted), including special means such as the Sauter mean diameter and volume specific surface area.
• Variance and standard deviation: formulas for spread of PSDs in both notation systems.
• Calculation methods: procedures for computing moments and means from histograms or lognormal/analytical distributions; numerical examples in annexes demonstrate step-by-step calculations.
• Reporting and accuracy: the standard requires reporting the measurement technique (because sizing depends on method), notes that equivalent diameter is assumed, and warns that incomplete distributions or very few size classes reduce accuracy.

Practical applications

ISO 9276-2 is used to derive consistent, comparable PSD parameters that link particle size to product and process properties. Typical applications include:

• Powder and bulk material characterization (flowability, packing)
• Pharmaceutical and chemical formulations (dissolution rate, suspension stability)
• Emulsions, aerosols and colloids where mean sizes influence performance
• Quality control, R&D and instrument data reporting for laser diffraction, sieving, microscopy and other sizing methods
• Process engineering decisions where specific weighted means (e.g., volume-weighted or Sauter mean) are causally related to performance

Who should use this standard

• Analytical laboratories and QA/QC teams performing particle size analysis
• Instrument manufacturers and software developers implementing PSD calculations
• Process and product engineers in pharmaceuticals, materials, mining, cosmetics and chemical industries
• Researchers and metrologists standardizing PSD reporting

Related standards

• ISO 9276-1: Graphical representation of PSD results
• ISO 9276-5: Calculation methods for lognormal distributions
• Other parts of ISO 9276 address model adjustment, classification processes and particle shape (Parts 3–6)

Keywords: ISO 9276-2, particle size analysis, particle size distribution, moments, mean particle size, Sauter mean diameter, histogram, lognormal, standard deviation.