⛰️ Angle of Repose Calculator
Find the angle of repose of a cone-shaped pile of granular material from its height and base diameter.
What the angle of repose is
The angle of repose is the steepest angle, measured from the horizontal, at which a granular material (like sand, gravel, or grain) can be piled without slumping. For a naturally formed cone-shaped pile, it can be found from the pile’s height and base radius using angle = arctan(height / base radius).
How this calculator works
Enter the height of the pile and the diameter of its base. The calculator finds the base radius, computes the angle of repose using the arctangent relationship, and also estimates the pile’s volume using the cone volume formula, V = (1/3)πr²h.
The angle of repose depends on a material’s grain shape, size, and moisture content, and typically ranges from about 25° for fine dry sand to over 45° for coarse, angular gravel. This calculator is for general engineering and educational planning purposes.