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.
Example
You enter
- Pile base diameter (ft) 60
- Angle of repose (degrees) 37
- Loose bulk density (pcf) 100
You get
- Pile height 22.6 ft
- Volume (ft³) 21306.6
- Volume (cy) 789.13
- Tonnage 1,065 tons
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
Scopeheight = 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 or tableradius_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.
Source and editionRight-circular-cone identity by name (angle-of-repose pile); first-principles geometry.
Free accessThe cone-volume and angle-of-repose relations are public geometry and soil-mechanics practice.
What governsEstimate. AHJ and licensed professional govern.
API field namesbase_diameter_ft, repose_angle_deg, density_pcf, height_ft, volume_ft3, volume_cy, tons
- Angle of repose 37 degrees default (granular material runs ~30-40 degrees); moisture and angularity steepen itsoil-mechanics practice
- Bulk density 100 pcf default loose (the material governs); a survey governs for paymentmaterials practice