Enter your pile's height and base radius (or use friction coefficient) to calculate the Angle of Repose — the steepest stable slope angle for any granular material. The calculator also returns the result in radians, estimated pile volume, and a flow behavior classification based on the computed angle.
Angle of Repose
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Angle in Radians
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Flow Classification
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Pile Volume
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Estimated Pile Mass
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Friction Coefficient (μ)
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The angle of repose is the steepest angle at which a heap of granular material can remain stable without slumping. It is measured between the surface of the pile and the horizontal plane, and is an intrinsic property of the material influenced by particle size, shape, moisture, and surface friction.
Use the formula θ = arctan(H / R), where H is the vertical height of the pile and R is the base radius. For example, a pile 3 m tall with a 5 m base radius gives θ = arctan(3/5) ≈ 30.96°. This calculator performs this calculation automatically.
The formula is θ = arctan(μs), where μs is the static friction coefficient between particles. A friction coefficient of 0.6 corresponds to an angle of approximately 30.96°. This relationship assumes a simplified model of particle-on-particle static friction.
Dry sand typically has an angle of repose between 30° and 35°. Moist soil ranges from 35° to 45°. Fine powders like flour can be as low as 25°–30°, while rough angular gravel can exceed 45°. Wet or cohesive materials can behave differently due to surface tension and cohesion effects.
The static angle of repose is the maximum angle at which a pile remains stable when at rest. The dynamic (or kinetic) angle of repose is the angle the surface settles to after material has been disturbed or is flowing. The dynamic angle is generally a few degrees lower than the static angle.
Water creates surface tension bridges between particles (capillary cohesion), which adds an apparent cohesive force that allows steeper pile angles. However, very high moisture levels can act as a lubricant, reducing the angle. The relationship is non-linear and depends on particle size and wettability.
Angular, irregular particles interlock more effectively and produce higher angles of repose compared to smooth, spherical particles. Rounded grains roll easily over each other, leading to lower repose angles. This is why crushed rock has a higher angle than river-worn pebbles of the same mineral composition.
Yes — the angle of repose is a key parameter in hopper and silo design. Hopper walls are often angled steeper than the material's repose angle to ensure reliable gravity flow. However, for cohesive materials, flow function analysis (e.g., Jenike method) is also recommended alongside repose angle data.