How this calculator works
For an approximately conical heap, measure its vertical height and horizontal radius from the centre to the foot of the slope. Their ratio gives the surface slope. The friction mode is the ideal block-on-incline estimate tan(theta) = mu_s. Real granular repose also depends on particle shape, cohesion, moisture and how the pile was formed; its measured angle need not equal a single sliding friction angle.
Formula
theta = atan(h/r); h = r tan(theta); ideal mu_s = tan(theta).
Worked example
A heap 1 m high with a 1 m radius has a 45 degree slope. An ideal static friction coefficient of 0.5 corresponds to 26.565 degrees.
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Frequently asked questions
Should I use diameter or radius?
Use the radius. Divide a measured full base diameter by two.
Does moisture matter?
Yes. Capillary forces and cohesion can substantially change the measured repose angle.
Can I infer a safe excavation slope?
A heap angle is not a geotechnical slope-stability assessment. Soil structure, water and confinement require an appropriate engineering analysis.