Stockpile Shape Volume Calculator
Each shape uses its exact solid-geometry volume formula.
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How to use this calculator
- Pick the stockpile shape: 0 for a conical (single dumped cone) pile, 1 for a wedge / windrow (a long ridge with sloped ends), or 2 for a truncated cone (a flat-topped pile).
- Enter the pile height and the dimensions your shape needs — base diameter for conical and truncated cone (plus top diameter for truncated), or base width and straight ridge length for a wedge / windrow.
- Optionally add the material's bulk density in t/m³ to convert the volume into an estimated mass in tonnes.
How it works
Each shape uses its exact solid-geometry volume formula. A conical pile is V = (1 ÷ 3)·π·r²·h. A truncated cone (frustum) is V = (1 ÷ 3)·π·h·(R² + R·r + r²), where R and r are the base and top radii. A wedge / windrow is modelled as a triangular prism of length L plus one full cone made from its two rounded end slopes: V = ½·W·h·L + (1 ÷ 3)·π·(W ÷ 2)²·h.
Multiplying the volume by the bulk density gives an estimated in-place mass: mass (t) = volume (m³) × density (t/m³). Because bulk density depends heavily on moisture, particle size and compaction, the tonnage is an estimate — the geometry is exact but the material behaviour is not.
Worked example
Volume and tonnage of a conical sand pile. A conical stockpile has a base diameter of 10 m and a height of 4 m. Choose shape 0 (conical). The radius is 5 m, so V = (1 ÷ 3) × π × 5² × 4 = 104.72 m³, over a footprint of 78.54 m². Entering a bulk density of 1.6 t/m³ for damp sand gives an estimated mass of 104.72 × 1.6 = 167.55 t.
Common mistakes
- Entering a radius where the tool asks for a diameter (or vice versa). The base and top fields are diameters — the full width across the pile — and the tool halves them internally.
- Confusing loose bulk density with solid (particle) density. Use the loose or heaped bulk density of the piled material, not the density of the solid rock or grain, or the tonnage will be far too high.
- Treating the result as survey-grade. Real piles rarely form perfect cones — the angle of repose, wind, moisture and reclaim change the true shape, so verify important quantities with a field survey.
Frequently asked questions
Which shape should I choose for my stockpile?
Use conical (0) for material tipped from a single point that forms a symmetrical cone. Use wedge / windrow (1) for a long ridge built by a travelling conveyor or dozer, with sloped conical ends. Use truncated cone (2) for a flat-topped pile — for example one that has been reclaimed or built to a level crest.
What bulk density should I use?
Use the loose or heaped bulk density of the actual piled material, not solid density. Typical values are roughly 1.4–1.6 t/m³ for sand and gravel, 1.5–1.8 t/m³ for crushed rock, and 0.7–0.9 t/m³ for wood chips — but always confirm with a lab test or supplier data for accuracy.
Why is my calculated tonnage different from the weighbridge?
The volume is exact for the shape you entered, but real piles deviate from ideal geometry and bulk density changes with moisture and compaction. A conical pile is also fixed by its natural angle of repose, so the height and diameter are not independent. Treat the result as a planning estimate and reconcile against surveyed volumes or weighbridge data.
Related tools
- Cone Volume Calculator
- Pyramid Volume Calculator
- Density Mass Volume Calculator
- Bin and Hopper Volume Calculator
- Frustum Volume Calculator
- Average End Area Volume Calculator
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