Angle of Repose Calculator
Angle of Repose Results
What Is the Angle of Repose?
The angle of repose is the maximum angle between a pile of material and the horizontal ground before the material starts to slide.
Picture pouring sand onto the ground. It forms a cone-shaped pile. The slope of that pile is the angle of repose.
- A low angle means the material spreads easily
- A high angle means the material is rough, sticky, or angular
Each material has its own typical range.
Why the Angle of Repose Matters
Knowing the angle of repose helps prevent failures and design mistakes.
Common uses include:
- Designing safe soil slopes and embankments
- Planning stockpiles for sand, gravel, coal, or grain
- Designing hoppers, silos, and conveyor systems
- Estimating flow behavior of powders and bulk solids
- Understanding landslide and slope stability risks
If the slope is steeper than the angle of repose, failure is likely.
What the Angle of Repose Calculator Does
This calculator estimates the angle of repose using three different methods:
- Direct Measurement
- Material Type Estimation
- Empirical Formula
Each method fits a different situation, from quick field checks to engineering estimates.
Method 1: Direct Measurement (Height and Radius)
This is the most straightforward and reliable method when you can measure a real pile.
What You Enter
- Pile height
- Pile radius
- Units (meters, feet, centimeters, or inches)
How It Works
The calculator converts all units to meters and applies this formula:
Angle of Repose = arctan(height ÷ radius)
Outputs
- Angle in degrees
- Angle in radians
- Slope ratio (shown as 1:x)
When to Use This Method
- Field measurements
- Lab experiments
- Stockpile inspections
- Educational demonstrations
Tip: Take multiple measurements and average them for better accuracy.
Method 2: Estimate by Material Type
This method gives a realistic estimate when direct measurement is not possible.
Material Categories Included
- Soil
- Sand
- Gravel
- Powder
- Grain
- Industrial materials
Each category includes specific materials with typical angle ranges.
Extra Adjustments
The calculator refines the estimate using:
- Moisture content
- Particle size
Examples:
- Slight moisture often increases the angle for sand and soil
- High moisture reduces the angle for fine powders
- Larger particles usually form steeper piles
When to Use This Method
- Early design planning
- Feasibility studies
- Educational use
- Quick estimates
This method balances speed with reasonable accuracy.
Method 3: Empirical Formula
This is the most technical option and works well for engineering estimates.
What You Enter
- Cohesion
- Internal friction angle
- Bulk density
- Surface roughness
How the Calculator Adjusts the Angle
- Internal friction sets the base angle
- Cohesion increases stability
- Dense materials raise the angle
- Rough surfaces increase resistance
The final value is limited to a realistic range to avoid extreme results.
When to Use This Method
- Engineering calculations
- Material behavior analysis
- Research and modeling
- When lab data is available
This method gives insight into why the angle changes.
Understanding the Results
The calculator provides three outputs:
1. Angle of Repose (Degrees)
This is the main value used in practice.
General interpretation:
- Below 20°: Very free-flowing or wet material
- 20° to 30°: Fine or moist materials
- 30° to 40°: Typical soils and sands
- 40° to 50°: Coarse or angular materials
- Above 50°: Highly stable, rough, or cohesive material
2. Angle in Radians
Used mainly in scientific and mathematical work.
3. Slope Ratio
Shown as 1:x, meaning 1 unit of height for x units of horizontal distance.
This is useful in slope design and drawings.
Built-In Interpretation Text
The calculator also explains the result in plain language. It tells you:
- Whether the angle is low, moderate, or high
- What that means for material behavior
- How the chosen calculation method affects accuracy
This makes the tool helpful even for non-specialists.
Factors That Affect the Angle of Repose
Even with good calculations, real-world results can vary.
Key factors include:
- Particle shape (rounded vs angular)
- Size distribution
- Moisture content
- Compaction
- Surface roughness
- Testing method
Always treat calculated values as informed estimates, not absolute limits.
Best Practices When Using the Calculator
- Use direct measurement whenever possible
- Double-check units before calculating
- Avoid relying on a single value for critical designs
- Combine results with field data and safety factors
- Remember that natural materials are rarely uniform