Angle of Repose Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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When you need a quick angle of repose check, the best result is one you can explain, not just copy. Stress, strain, stiffness, and section properties are tightly tied to geometry, so a correct formula can still give the wrong engineering answer when the wrong dimension is entered. The calculator below uses a narrow equation set and shows the output in a form that is easy to sanity-check.

What this calculator does

Use the Angle of Repose Calculator when you want angle of repose from Height of the heap, Radius of the heap without building a broader simulation. Supporting cards, if present, expose useful consequences of the same equation rather than introduce unrelated assumptions.

How to use it

Use measured or specified values for Height of the heap, Radius of the heap. Let the page handle supported unit conversions, but keep the physical convention consistent across the fields. If you are comparing two scenarios, change only the quantity you intend to test so the effect is easy to interpret.

How the calculation works

If a static-friction coefficient is entered, the page uses θ = atan(μ). Otherwise it can derive θ = atan(h/r) from pile height and radius, and then μ = tanθ. This is the simple limiting-friction geometry used by the calculator.

Example

Using the default example on the page (Height of the heap = 0.35 m; Radius of the heap = 0.96 m), the calculator returns angle of repose of 20.031013 deg. Try increasing one input while holding the others fixed; the response should match the dependence shown in the formula above.

How to interpret the result

The angle of repose describes the modeled specimen or section, not every possible failure mode. A useful check is whether increasing a numerator term raises the answer and increasing a denominator term lowers it as the equation predicts.

Limitations and notes

The simple angle-friction equivalence is an idealized granular/static relation. Particle shape, moisture, compaction, vibration, cohesion, size distribution, and whether the material is being poured or drained can change the measured angle of repose.