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.

Distance between Sets


DISTANCE functions expressing the degree of dissimilarity of sets have found use in physical anthropology1, psychology2, numerical taxonomy3, ecology3 and elsewhere. During an ecological study by one of us, it was noticed that the similarity coefficient of Jaccard6, used in ecology, gives rise to a metric function satisfying the triangle inequality. For two non-empty finite sets X, Y, the Jaccard coefficient is the number of elements in the intersection XY of X and Y. This coefficient (we use absolute value signs to indicate number of elements) has a heuristic interpretation. It measures the probability that an element of at least one of two sets is an element of both, and thus is a reasonable measure of similarity or “overlap” between the two. The one-complement may then be considered a measure of the dissimilarity of the two sets.

This is a preview of subscription content

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. Mahanolobis, P. C., Proc. Nat. Inst. Sci. India, 2, 49 (1936).

    Google Scholar 

  2. McGill, W. J., Psychometrika, 19, 97 (1954).

    Article  Google Scholar 

  3. Sokal, R. R., and Sneath, P. H., Principles of Numerical Taxonomy (W. H. Freeman, 1963).

    MATH  Google Scholar 

  4. Orloci, L., J. Ecol., 54, 193 (1966).

    Article  Google Scholar 

  5. Levandowsky, M., thesis, Columbia University, New York, 1970.

  6. Jaccard, P., Bull. Soc. Vaud. Sci. Nat., 38, 69 (1902).

    Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and Permissions

About this article

Cite this article

LEVANDOWSKY, M., WINTER, D. Distance between Sets. Nature 234, 34–35 (1971).

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI:

Further reading


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