Conical Stockpile Volume and Tonnage
Volume (cy) and tonnage of a free-standing conical stockpile from its base diameter, angle of repose, and bulk density: height = radius x tan(repose), volume = 1/3 pi r^2 h. A 60 ft pile of stone at 37 degrees stands 22.6 ft and holds ~789 cy (1,065 tons). A survey governs for payment.
Formula and source
radius_ft = base_diameter_ft / 2; height_ft = radius_ft x tan(repose_angle_deg x pi/180); volume_ft3 = (1/3) x pi x radius_ft^2 x height_ft; volume_cy = volume_ft3 / 27; tons = volume_ft3 x density_pcf / 2000.
Right-circular-cone identity by name (angle-of-repose pile); first-principles geometry.
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