Angle of Repose Calculator
Calculate angle of repose from pile height and base radius or diameter, then see tan(θ), slope percent, and a practical material-flow interpretation.
What is angle of repose?
The angle of repose is the steepest stable angle a loose granular material forms against a horizontal surface. It is used as a practical indicator for powders, soil, sand, gravel, grain, and other bulk solids.
What formula is used?
μ ≈ tan(θ)
For a simple cone-pile test, the tangent of the angle is height divided by radius. Educational physics references often connect the limiting angle with friction using μ = tan(θ), which is why the calculator also displays an approximate friction coefficient.
When is this useful?
It helps compare how materials flow, how steep a stockpile may stand, and how powders behave during handling. The result is also useful for early hopper, chute, and stockpile discussions, although industrial flow design normally needs more testing.
What mistakes should I avoid?
Do not assume one sample angle applies everywhere. Moisture, particle size distribution, compaction, vibration, particle shape, and segregation can all change the measured angle.
Frequently asked questions
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Use whichever measurement you have. If you enter diameter, the calculator divides it by two to get radius.
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They are related but not always identical. Angle of repose is a simple pile observation, while internal friction angle is usually determined through soil or material testing.
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Yes. Moisture can make particles stick together, often increasing the angle of repose.
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A higher angle usually means the material forms a steeper pile, often because particles are rough, angular, cohesive, or moist.
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No. Hopper design usually needs wall friction, flow function testing, arching behavior, and discharge requirements.