Angle of Repose

Pronunciation: /ˈæŋ.gəl ʌv ˌriˈpoʊz/ Explain

A pile of soil showing the angle of repose.
Figure 1 - Angle of repose.

An angle of repose is the maximum angle from the horizontal that a pile of granular material can have and still be stable. Stable means that the material does not keep sliding down unless something changes. This can apply to a granular material, such as sand, poured on a level surface. The sand will form a cone. The angle of repose is the angle of the side of the cone of sand from the base.

The angle of repose for any particular material is related to the density, surface area and shapes of the particles, and the coefficient of friction of the material. A material with a larger angel of repose will form a steeper pile.

Angle of repose is used to:

  • design machinery used to hold and transport granular material such as conveyor belts;
  • calculate the danger of avalanche;
  • determine if a slope is likely to collapse;


  1. McAdams, David E.. All Math Words Dictionary, angle of repose. 2nd Classroom edition 20150108-4799968. pg 16. Life is a Story Problem LLC. January 8, 2015. Buy the book

More Information

  • Angle of Repose. Science Direct. 6/19/2018.

Cite this article as:

McAdams, David E. Angle of Repose. 1/10/2019. All Math Words Encyclopedia. Life is a Story Problem LLC.

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Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/14/2018: Removed broken links, updated license, implemented new markup. (McAdams, David E.)
5/5/2011: Initial version. (McAdams, David E.)

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