angle of repose

The angle of repose is the slope of the cone a powder makes when you pour it onto a flat surface. Pour dry sand and it forms a low, spreading heap; pour damp flour and it stacks into a steep, lumpy mound. The steeper the pile, the more the particles cling to one another and the worse the powder flows.

Formally it is the angle, measured from the horizontal, between the surface of the free-standing heap and the base. It is read as the inverse tangent of pile height divided by base radius. A low angle, below about 30 degrees, signals free-flowing powder; angles above about 40 degrees indicate cohesive powder that flows poorly and may bridge or stick in a hopper.

The measurement is appealingly simple and needs only a funnel, but it is sensitive to how it is done. The funnel height, orifice size, and whether the cone is built on a fixed base or allowed to spread all shift the result, so a method must be fixed and stated for numbers to be comparable.

In formulation it serves as a quick, cheap screen for powder flow before committing to tableting or capsule filling. It is best treated as one indicator among several, used alongside the Carr index, Hausner ratio and direct flow-rate measurement rather than relied on alone.