Angle of Repose Calculator

When granular materials like sand, gravel, or grain are poured onto a horizontal surface, they form a conical pile. The angle of repose ($\theta$) depends on the internal friction of the material. By measuring the height ($h$) and the radius ($r$) of the resulting cone's base, you can find the coefficient of friction ($ heta_{fric}$) using the geometric ratio of height to radius: $\theta_{fric} = \frac{h}{r}$. Taking the inverse tangent (arctan) of this ratio yields the angle of repose: $\text{Angle of Repose} = \arctan\left(\frac{h}{r}\right)$.

Imagine you pour dry sand onto a flat concrete floor, creating a conical pile. You measure the dimensions and find that the height ($h$) of the pile is $1.5$ meters, and the radius ($r$) of the circular base is $2.0$ meters. First, divide the height by the radius to find the frictional tangent: $1.5 / 2.0 = 0.75$. Next, apply the inverse tangent function: $\arctan(0.75) ≈ 36.87^{\circ}$. Thus, the angle of repose for this specific sample of sand is approximately $36.87$ degrees.

Ensure your material is poured slowly from a single central point to form a symmetrical, undisturbed cone. Always measure the radius from the center of the base to the outer edge rather than using the full diameter. Keep in mind that moisture content significantly alters results; wet sand, for example, can stand at much steeper vertical heights due to capillary forces compared to completely dry sand.