# Angle of Repose Calculator

URL: https://speedycalculator.com/calculators/physics/angle-of-repose/
Last updated: 2026-10-30

> The angle of repose calculator finds the steepest angle at which a pile of granular material – sand, gravel, grain – stays stable, from the height and radius of a heap or from the coefficient of static friction.

## Inputs

- Method
- Height of the heap h (m, cm, mm, km, in, ft, yd, mi)
- Radius of the heap r (m, cm, mm, km, in, ft, yd, mi)
- Coefficient of static friction μ

## Results

- Angle of repose θ
- Equivalent friction coefficient
- Heap volume (cone)

## Formula

```
θ = arctan(h / r) = arctan(μ_s)
```

## Explanation

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

FieldWhat to enterMethodChoose one: Heap height and radius, Coefficient of static frictionHeight of the heap hUnits: m, cm, mm, km, in, ft …Radius of the heap rUnits: m, cm, mm, km, in, ft …Coefficient of static friction μA 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 (°)0.7520.5561.1329.35781.536.86991.8843.15242.2548.3665356.3099

## 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)