Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Feret‘s Statistical Diameter as a Measure of Particle Size


VARIOUS measures of the size of irregularly shaped particles as seen in profile under the microscope have been used, chosen according to their theoretical significance or practical ease of measurement. These include, using Heywood‘s notation1,2 : (i) the diameter of the circle of equal area, d ; (ii) the diameter of the circle of equal perimeter, D ; (iii) the length of line bisecting the profile area (Martin‘s statistical diameter3), M ; and (iv) the perpendicular distance between parallel tangents touching opposite sides of the profile (Feret‘s statistical diameter4), F. M and F are determined for randomly oriented particles, thus giving an average value over all possible orientations. d is usually regarded as the ideal measure of particles seen in profile, but is somewhat difficult to determine experimentally with precision. It is, however, common practice when sizing very small particles to estimate d visually by comparing them with standard reference circles on a Patterson and Cawood or similar type of eyepiece graticule5,6. M and F are convenient to measure in practice with aid of an eyepiece scale or filar micrometer, and have been extensively used by various Workers. D, or rather the ratio D/d, termed by Heywood1 the ‘contour ratio', and its reciprocal called the ‘degree of circularity' by Wadell7, have been used in discussing the shape and hydrodynamical properties of particles. For these purposes D has usually been determined by direct perimeter measurement of the projected images of particles. It does not appear to have been adopted intentionally in any work known to me as a direct single measure of particle size.

This is a preview of subscription content, access via your institution

Relevant articles

Open Access articles citing this article.

Access options

Rent or buy this article

Get just this article for as long as you need it


Prices may be subject to local taxes which are calculated during checkout


  1. Heywood, H., Proc. Inst. Mech. Eng., 125, 383 (1933).

    Article  CAS  Google Scholar 

  2. Heywood, H., Bull. Inst. Min. and Met., No. 477 (March 1946).

  3. Martin, G., Blyth, C. E., and Tongue, H., Trans. Brit. Ceramic Soc., 23, 61 (1923–24).

    Google Scholar 

  4. Feret, L. R., Assoc. Internat. pour l‘Essai des Mat., Zurich, 1931, 2, Group D.

  5. Patterson, H. S., and Cawood, W., Trans. Farad. Soc., 32, 1084 (1936).

    Article  CAS  Google Scholar 

  6. Fairs, G. L., Chem. Ind., 62, 1374 (1943).

    Google Scholar 

  7. Wadell, H., J. Frank. Inst., 217, 459 (1934).

    Article  Google Scholar 

  8. Rose, H. E., and Lloyd, H. B., J. Soc. Chem. Ind., 65, 52 (1946).

    Article  CAS  Google Scholar 

  9. Cauchy, A., C.R. Acad. Sci., Paris, 13, 1060 (1841).

    Google Scholar 

  10. Vouk, V. (see following communication).

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and Permissions

About this article

Cite this article

WALTON, W. Feret‘s Statistical Diameter as a Measure of Particle Size. Nature 162, 329–330 (1948).

Download citation

  • Issue Date:

  • DOI:

This article is cited by


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing