Engineering

Angle of Repose Calculation

Calculate the angle of repose from stockpile geometry, coefficient of static friction, or slope percentage, with useful pile and slope outputs.

angle-of-repose-calculation
Use this for quick granular-material and stockpile estimates. Cohesive soils, wet powders, vibration, particle shape, segregation, and wall effects can change the true field angle.
Angle of repose result
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Slope ratio and percent—
Coefficient estimate—
Pile geometry—
Use note—
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How angle of repose is calculated

For a simple conical pile, the angle of repose is the angle between the horizontal ground and the sloping surface of the pile. If pile height and base radius are known, the angle is θ = arctan(H/R). For ideal dry cohesionless material, the angle can also be approximated from friction as tan(θ) ≈ μ.

This friction relationship is commonly presented in basic angle of repose references, including the angle of repose formulation showing θ as the arctangent of the static friction coefficient for a cohesionless material.

Worked example

Pile height = 3 m Base radius = 5 m θ = arctan(3/5) = 30.96° Slope percent = tan(30.96°) × 100 = 60%

The same angle corresponds to an approximate friction coefficient of 0.60 in the simple dry-material model.

Common mistakes in stockpile slope estimates

Do not treat a single angle as permanent for all site conditions. Moisture, particle size distribution, vibration from equipment, wind, loading method, compaction, and segregation can all change the stable slope.

Common questions

  • Many dry granular materials fall roughly in the 25° to 40° range, but the true value is material-specific. Fine powders, wet material, crushed aggregate, rounded grains, and mixed particle sizes can behave very differently.
  • They are related but not always identical. The angle of repose is an observed surface slope for loose material, while internal friction angle is a geotechnical strength parameter usually obtained from shear testing.
  • Use caution. Wet or cohesive soil can stand at steeper short-term angles because of suction or cohesion, then fail when conditions change. A geotechnical stability check is needed for safety-critical slopes.
  • If height and radius are entered, a simple conical stockpile volume can be estimated with V = πR²H/3. Real stockpiles are often irregular, so this is only a geometric approximation.
  • For loose dry granular material, a slope steeper than the stable angle tends to slide or ravel until it returns to a stable angle. In real materials, temporary arching or cohesion can delay failure.