Pour sand onto a table and it forms a cone with a characteristic slope – the angle of repose. It depends on grain size, shape and moisture. Engineers use it to design hoppers, stockpiles and embankments.
How to use the Angle of Repose Calculator
- Method
- Height of the heap h
- Radius of the heap r
- Coefficient of static friction μ
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the method and enter the heap dimensions or the coefficient of static friction.
Inputs explained
| Field | What to enter |
|---|---|
| Method | Choose one: Heap height and radius, Coefficient of static friction |
| Height of the heap h | Units: m, cm, mm, km, in, ft … |
| Radius of the heap r | Units: m, cm, mm, km, in, ft … |
| Coefficient of static friction μ | A number |
Example values
How the main result changes when Height of the heap h changes and everything else stays at the example values above:
| Height of the heap h (m) | Angle of repose θ (°) |
|---|---|
| 0.75 | 20.556 |
| 1.13 | 29.3578 |
| 1.5 | 36.8699 |
| 1.88 | 43.1524 |
| 2.25 | 48.3665 |
| 3 | 56.3099 |
Formula
θ = arctan(h / r) = arctan(μ_s)
Worked example
Inputs — Method: Heap height and radius; Height of the heap h: 1.5 m; Radius of the heap r: 2 m.
Results — Angle of repose θ = 36.8699 °; Equivalent friction coefficient = 0.75; Heap volume (cone) = 6.2832 m³.
Key terms
- Granular material
- A collection of discrete solid particles.
Frequently asked questions
What is a typical angle of repose for dry sand?
About 30–35°.
Does moisture change it?
Yes – slightly damp sand holds a much steeper slope.
Why does it equal arctan(μ)?
A grain on the slope starts sliding when tan θ exceeds the friction coefficient.
Where is it used?
Designing silos, hoppers, stockpiles and slopes.