Physics

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Angle of Repose Calculator.

Calculate the angle of repose from a coefficient of friction.

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angle: 26.565051

angle

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Use Cases

Material Handling Design

Engineers use the angle of repose to design hoppers, silos, and conveyor systems to ensure bulk materials flow properly and do not clog.

Example: Designing a storage silo for sand with a friction coefficient of 0.6 gives an angle of about 31 degrees.

Geotechnical Engineering

In soil mechanics, the angle of repose helps assess slope stability and the behavior of granular soils in embankments and foundations.

Example: Evaluating the stability of a gravel slope with a friction coefficient of 0.8.

Frequently Asked Questions

What is the angle of repose?
The angle of repose is the steepest angle at which a pile of granular material remains stable without sliding. It is determined by the coefficient of friction between the particles and the surface.
How is the angle of repose calculated?
The angle of repose (θ) is calculated using the inverse tangent of the coefficient of friction: θ = arctan(μ). Simply enter the coefficient of friction into the calculator to get the angle in degrees.
What units does the calculator use?
The calculator takes the coefficient of friction as a dimensionless number (no units) and outputs the angle in degrees. The coefficient of friction is a ratio of frictional force to normal force.

Tips & Common Mistakes

Tips

  • Ensure the coefficient of friction is accurate for your specific material and surface conditions, as it can vary with moisture and particle size.
  • The angle of repose is typically measured for dry, loose materials; for cohesive materials, the angle may be higher.
  • Use the calculated angle as a reference for design, but always verify with physical testing for critical applications.
  • Remember that the coefficient of friction is dimensionless, so no unit conversion is needed.

Common Mistakes to Avoid

  • Using the coefficient of static friction when the material is already in motion; use the appropriate coefficient for the condition.
  • Assuming the angle of repose is the same as the angle of internal friction; they are related but not identical.
  • Forgetting that the calculator gives the angle in degrees, not radians, so check your expected output.

Last updated: August 13, 2026