Angle of Repose Calculator

What Is Angle of Repose?

The angle of repose is the steepest angle at which a pile of granular material remains stable without sliding. When material is poured onto a flat surface, it naturally forms a conical pile whose slope angle depends on the material properties including particle size, shape, moisture content, and surface roughness.

This angle is crucial in civil engineering (slope stability, embankment design), mining (stockpile design), agriculture (grain storage), pharmaceutical manufacturing (powder flow), and geology (scree slope analysis). Materials with higher angles of repose are more cohesive and resist flowing.

Angle of Repose Formula

Where theta is the angle of repose in radians, h is the height of the conical pile, and r is the base radius. The volume formula gives the total material in the conical stockpile.

Angle of Repose for Common Materials

FAQ

Why does moisture change the angle?

Water between particles creates capillary forces that increase cohesion, allowing steeper piles. This is why wet sand can be shaped into castles while dry sand collapses into flat piles. However, saturated material behaves like a liquid and flows easily with near-zero angle of repose.

How is this used in engineering?

Engineers use the angle of repose to design stable embankments, mine tailings dams, grain silos, and stockpile areas. Retaining walls and slopes must be designed with angles below the repose angle or reinforced with geotextiles or vegetation to prevent failure.

Is angle of repose the same as friction angle?

They are related but not identical. The angle of repose applies to loose, poured material. The internal friction angle is a soil mechanics parameter measured under controlled conditions. For dry, cohesionless granular materials, they are approximately equal, but for cohesive soils, the friction angle may differ significantly.