Stockpile Volume Calculator
The stockpile volume calculator estimates the volume of a material pile using either a conical or frustum (truncated cone) model. Enter the base diameter, optional top diameter (for frustum piles with a flat top), height, and optional bulk density to compute the volume in cubic feet or meters and the estimated weight in tons. This calculation is used in quarrying, mining, agriculture, and construction to estimate material inventory from simple field measurements.
Stockpile volume formulas
Cone: V = (1/3) * pi * r1^2 * h
Frustum: V = (pi * h / 3) * (r1^2 + r1*r2 + r2^2)
where r1 = D1/2 (base radius), r2 = D2/2 (top radius)
Weight = V (in cubic yards) * bulk density (tons/cy)
If D2 = 0 the frustum formula reduces to the cone formula. Convert: 1 cubic foot = 0.037037 cubic yards = 0.028317 cubic meters.
Bulk density reference values
- Dry sand: approximately 1.30 to 1.40 tons per cubic yard.
- Gravel (crushed): approximately 1.35 to 1.50 tons per cubic yard.
- Topsoil (loose): approximately 1.00 to 1.20 tons per cubic yard.
- Coal (bituminous): approximately 0.75 to 0.85 tons per cubic yard.
- Always use laboratory or certified scale measurements when precise inventory is critical.
Stockpile volume calculator: frequently asked questions
What shape is a typical material stockpile?
Most stockpiles form a cone or truncated cone (frustum). A free-standing pile of material such as gravel, sand, or aggregate typically forms a cone when poured from a single point. When spread with machinery or built against a wall, it forms a frustum with a flat top.
What is angle of repose?
The angle of repose is the natural slope angle a loose material assumes when piled. Dry sand is about 30-35 degrees. Gravel is 35-40 degrees. The height of a conical stockpile depends on its base diameter and the angle of repose: h = (d/2) * tan(angle of repose).
How do I convert volume to weight (tons)?
Weight = volume (cubic yards) * bulk density (tons per cubic yard). Common bulk densities: dry sand = 1.3 t/cy; gravel = 1.4 t/cy; crushed stone = 1.5 t/cy; topsoil = 1.1 t/cy; coal = 0.8 t/cy. Enter the bulk density in the weight field for automatic conversion.
How accurate is the cone formula for stockpile estimation?
The cone formula gives a good estimate for symmetrical free-standing piles. Actual volumes may differ due to irregular shapes, compaction, and material segregation. For precise inventory, laser scanning or GPS surveys with terrain modeling software are more accurate.
What is a frustum and how do I measure it?
A frustum is a cone with the top cut off, creating a flat circular top. Measure the diameter at the base (D1), the diameter at the top flat area (D2), and the height (h). The frustum volume = (pi * h / 3) * (r1^2 + r1*r2 + r2^2) where r1 = D1/2 and r2 = D2/2.
Official sources
- USGS: USGS geospatial and volume measurement references.
- NIST: NIST unit conversions (cubic feet, yards, meters).
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.