Hopper Volume Calculator
Volume, working capacity and mass for conical, square, flat-bottom and asymmetrical hoppers, with loose/packed density and angle-of-repose limits.
Volume, working capacity and mass for conical, square, flat-bottom and asymmetrical hoppers, with loose/packed density and angle-of-repose limits.
Material poured into the center forms a cone at its angle of repose (α). The hopper is at working capacity when that surge just reaches the top edge: material can't be filled higher without spilling at the walls. The small voids between the sloped surface and the rim are not usable, so working capacity is below the struck (brim-full) volume. The surge is capped at the straight-wall height.
Optional. Enter loose and/or packed bulk density, and the angle of repose for a working-capacity estimate.
Calculates volume, working capacity and material mass for conical, square, flat-bottom and asymmetrical hoppers, with an angle-of-repose limit on working fill. It assumes ideal geometry, level filling and uniform bulk density, and approximates an asymmetrical cone as an equivalent symmetric frustum. It is a capacity estimator, not a flow or structural design tool: mass-flow versus funnel-flow behavior requires measured material properties.