Angle of Repose Calculator

What Is the Angle of Repose?

The angle of repose is the steepest slope a pile of granular material (sand, soil, gravel) can maintain without grains sliding down the sides.

$$\theta_r = \arctan(\mu_s)$$

where $\mu_s$ is the coefficient of static friction between grains.

$$\theta_r = \arctan\left(\frac{h}{r}\right)$$

Measure pile height $h$ and base radius $r$ when friction data is unavailable. Sand with $\mu_s = 0.45$ gives about 24.2°.

What affects the angle of repose?

Particle size, shape, moisture, and friction between grains all influence how steep a pile can become.

Why use height and radius?

Measuring an existing pile lets you estimate the effective friction when tabulated coefficients do not match field conditions.

What is a typical sand angle?

Dry sand often has an angle of repose around 30–35°, depending on grain size and moisture.

Is the angle the same as slope percent?

No, but they are related. Slope percent equals $\tan(\theta) \times 100\%$, which equals $\mu_s$ when using the friction formula.