Angle of repose
The angle of repose is the steepest slope at which a pile of loose grains can stay in place without sliding. If you pour sand into a cone, the angle between the slope of the cone and the horizontal surface is the angle of repose. It tells us how easily the material will slump or flow.
This angle depends on the grains themselves. Rough, angular grains grip each other better and can form steeper piles than smooth, round grains. Water can also raise the angle by helping particles stick together a bit more. Materials with a low angle of repose form flatter piles; those with a high angle can hold steeper slopes. The angle is important for how dense or loose a pile is, how it behaves on slopes, and how it will respond to shaking or loading.
Why it matters: engineers use the angle of repose to design equipment like hoppers, silos, and conveyors, and to judge whether a slope or pile might fail. It also helps explain natural slopes and landslides, such as talus slopes at the base of cliffs. In nature, some animals exploit the angle of repose to trap prey, like certain insects that dig pits in sand so the walls stay near the critical angle.
How it’s measured: there are several methods, and results can vary by method. Common approaches include:
- Tilting a box containing fine, non-cohesive material until it starts to slide, then reading the angle.
- Forming a cone of material and measuring height and base width to calculate the angle.
- Placing material in a rotating drum and watching how it flows to find the dynamic angle of repose.
In short, the angle of repose combines friction, grain shape, and moisture to describe how steeply a granular pile can stand before it collapses.
This page was last edited on 3 February 2026, at 12:04 (CET).