Angle of Repose Calculator

Angle of Repose Calculator

Calculate the maximum angle at which granular material remains stable. Essential for mining, agriculture, construction, and material science.

Calculate Angle of Repose

Typical range: 0.3 (smooth) to 1.5 (rough)

Maximum Stable Angle
26.57°
0.4636 rad
degrees

What is Angle of Repose?

The angle of repose is the steepest angle at which a granular material can be piled without flowing or slumping. It represents the balance between gravitational force (trying to make material slide) and friction (resisting the slide). When the angle exceeds this critical point, static friction can no longer hold the material and it slides.

This concept is fundamental in geotechnical engineering, mining operations, agriculture, and material handling. Different materials have different angles of repose depending on particle shape, size, and surface characteristics. Rounded grains have lower angles than angular particles.

The Angle of Repose Formula

θ = arctan(μₛ)
θ = Angle of repose (degrees)
μₛ = Coefficient of static friction

Physics: At the critical angle, the component of gravity along the slope equals maximum static friction. Higher friction = steeper stable slope.

Angles of Repose for Common Materials

Fine Sand: ~30-35° (μ ≈ 0.6)
Coarse Sand: ~32-35° (μ ≈ 0.65)
Gravel: ~35-45° (μ ≈ 0.7-0.9)
Pebbles: ~40-45° (μ ≈ 0.84-0.9)
Iron Ore: ~45-50° (μ ≈ 1.0-1.2)
Coal: ~35-45° (μ ≈ 0.7-0.9)
Crushed Rock: ~45-55° (μ ≈ 1.0-1.4)
Clay (wet): ~35-40° (μ ≈ 0.7-0.84)

Frequently Asked Questions

Why does grain shape affect angle of repose?

Angular particles have higher friction and interlock better. Rounded grains roll easily, reducing friction and steepness.

How is angle of repose measured?

Pour material from a funnel onto a flat surface. Measure the angle from the base to the slope edge. Repeat for accuracy.

Does moisture affect angle of repose?

Yes significantly. Wet material has higher friction due to capillary forces and moisture adhesion, increasing stability angle.

What's friction coefficient for water-saturated sand?

~1.0-1.2 for saturated sand. Much higher than dry sand (0.6-0.7) due to capillary tension.

How does compaction change angle of repose?

Loose material has lower angle. Compacted material interlocks better, creating higher angle of repose.

Why are stockpiles safety concerns?

If angle exceeds repose angle, sudden collapse can occur. Engineering requires safety factors and monitoring for stability.

How is this used in road cut design?

Engineers must ensure cut slopes don't steepen beyond angle of repose for the soil type, with safety margins applied.

What about material particle size?

Smaller particles typically have higher surface area and friction. Larger particles may roll, reducing angle of repose.

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