Ten compactness properties of circles: Measuring shape in geography

Shlomo Angel, Jason Parent, Daniel L. Civco

Research output: Contribution to specialist publicationArticle


This essay sheds new light on the meaning and measurement of compactness-one of the most intriguing and least-understood properties of geographic shapes. We articulate a unified theoretical foundation for the study of shape compactness that rests on two simple observations: First, that the circle is the most compact of shapes. And second, that there are 10-and possibly more-distinct geometrical properties of the circle that make it the most compact of shapes. We introduce these 10 properties, illustrate them with real-world examples and define indices associated with these properties that can be calculated using a geographic information system.

Original languageEnglish (US)
Number of pages21
Specialist publicationCanadian Geographer
StatePublished - Dec 2010


  • circle
  • compactness
  • landscape metrics
  • morphology

ASJC Scopus subject areas

  • Geography, Planning and Development
  • Earth-Surface Processes


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