Angle of Repose Calculator
Calculate the angle of repose for granular materials using friction coefficient or pile geometry
Calculate Angle of Repose
Typical range: 0.2 - 1.5 for most granular materials
Angle of Repose Results
Formula used: θ = arctan(μs)
Friction coefficient: μs = 0
Material flow: Flows easily
Flow Characteristics
Example Calculation
Sand Pile Example
Material: Dry sand
Static friction coefficient: μs = 0.45
Measured pile height: 0.35 m
Measured pile radius: 0.96 m
Calculation Results
From friction: θ = arctan(0.45) = 24.2°
From geometry: θ = arctan(0.35/0.96) = 20.0°
Analysis: Measured angle is lower, indicating the sand may be more humid or compacted
Common Material Properties
Key Facts
Lower angles indicate better flow properties
Moisture content significantly affects the angle
Particle size and shape influence flow behavior
Temperature can affect cohesive forces
Understanding Angle of Repose
What is Angle of Repose?
The angle of repose is the steepest angle at which a granular material can be piled without slumping. It represents the balance between gravitational forces trying to make the material flow and friction forces resisting that flow.
Physical Principles
- •Directly related to the coefficient of static friction
- •Determined by particle size, shape, and surface texture
- •Affected by moisture content and cohesive forces
- •Independent of pile size for uniform materials
Mathematical Relationships
θ = arctan(μs)
From friction coefficient
θ = arctan(h/r)
From pile geometry
Where:
- θ: Angle of repose
- μs: Static friction coefficient
- h: Height of the pile
- r: Radius of the pile base
Applications
Civil Engineering
- • Slope stability analysis
- • Embankment design
- • Retaining wall calculations
- • Foundation design
Industrial Applications
- • Bulk material handling
- • Silo and hopper design
- • Conveyor system design
- • Storage facility planning
Mining & Agriculture
- • Ore stockpile management
- • Grain storage design
- • Material flow optimization
- • Equipment sizing