Stockpile volume calculator: cone and windrow piles, with tonnes
Estimate a stockpile's volume and tonnage from its base and height, for a conical pile or a long windrow, in metric or US units. With the formulas, and when a drone survey is worth it instead.
Published · 4 min read · By Malya, the makers of Clarity
A quick estimate of a pile's volume and weight from a tape measure: the base, the height, and what the pile is made of. Pick a conical pile for one dropped from a conveyor or a single point, or a long pile for a windrow pushed up by a loader. Change the units and the numbers convert with them.
Stockpile volume calculator
- Volume
- 628 m³
- Weight
- 1,005 t
- Height used
- 6.00 m
- Footprint
- 314 m²
Cone: V = π × D² × H ÷ 12. Windrow: the two ends make one cone, the middle is a triangular prism, so V = π × W² × H ÷ 12 + (L − W) × W × H ÷ 2. From an angle of repose, H = (W ÷ 2) × tan(angle). Densities are typical loose values; a weighed sample of your own material is better.
How the calculator works
A pile of loose material settles into a cone at its angle of repose, so the cone is the standard model. A long pile is a cone cut in half with a ridge between the halves: the two ends together make one cone, and the middle is a triangular prism as long as the pile minus its width.
| Shape | Volume | Example |
|---|---|---|
| Conical pile | π × D² × H ÷ 12 | D 20 m, H 6 m: 628 m³; at 1.6 t/m³, 1,005 t |
| Long pile (windrow) | π × W² × H ÷ 12 + (L − W) × W × H ÷ 2 | W 20 m, L 45 m, H 6 m: 628 + 1,500 = 2,128 m³ |
| Height from angle of repose | H = (W ÷ 2) × tan(angle) | W 20 m at 35°: H = 7.0 m |
Where a formula goes wrong
- The pile is not a cone. A loader working the face cuts it back into a wall; rain slumps it; two products pushed together make a ridge. The formula still answers, about a shape that is not there.
- The ground is not flat. On a slope, the height measured on the downhill side overstates the pile and the uphill side understates it. A height of 6 m against 5.5 m is 9% of the volume.
- The height is a guess. The peak of a large pile is rarely reachable. Working from the angle of repose is better than eyeballing, but a degree either way is a few percent of the volume.
- Density. Volume times density is weight only if the density is right: loose against compacted, dry against wet, can differ by fifteen percent.
When to measure the real shape instead
A drone survey measures the surface of the pile itself, millions of heights across it, and subtracts the ground underneath. No shape is assumed, so a worked face, a slump or a merged pile is measured as it is. The part that still needs judgement is the base under the pile, which is explained step by step in how to measure stockpile volume with a drone, and for a yard full of piles at month end, in stockpile inventory for quarries.
Clarity measures piles on the orthomosaic and terrain model you already have (Studio, $50 a month) or on the maps it makes from your photos (Enterprise), prints the base it used beside every volume, and turns volume into tonnes with a density per measurement. The demo quarry in every free account has piles to try it on.
Questions people ask
How do you calculate the volume of a stockpile?
For a pile dropped from one point, treat it as a cone: volume equals pi times the base diameter squared times the height, divided by 12. For a long pile, treat the two rounded ends as one cone and the middle as a triangular prism: add pi times the width squared times the height over 12 to the middle length times the width times the height over 2. Multiply the volume by the material's density to get tonnes.
How accurate is a stockpile volume calculator?
As accurate as the pile is a cone. A fresh conical pile on flat ground measured carefully comes within five to ten percent. A pile that has been worked by a loader, slumped, or sits on sloping ground can be out by twenty percent or more, because the real shape is not the one the formula assumes. A drone survey measures the actual surface instead, which is why it is the method for inventory.
What is the angle of repose?
The steepest angle at which a loose material stands without sliding. Dry sand stands at about 30 to 35 degrees, gravel and crushed stone at about 35 to 40. For a conical pile the height is half the base diameter times the tangent of that angle, so a pile can be estimated from its footprint alone, which helps when the top cannot be reached.
How do I convert cubic yards of gravel to tons?
Multiply the cubic yards by the loose density in pounds per cubic yard and divide by 2,000. Loose gravel and crushed stone are typically 2,500 to 2,900 pounds per cubic yard, so about 1.25 to 1.45 US tons per cubic yard. A weighed sample of your own material is the number to use for anything that will be invoiced.
Do it in Clarity.
Explore is free, with no card and no expiry: a real quarry, already flown, to try every tool on. Studio is $50 a month for up to five sites of your own ground, from the orthomosaic and terrain model you already have. Enterprise processes your photos.
Read next
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- How to measure stockpile volume with a droneThe flight, the surface, the base under the pile, and the one choice that changes the number most.
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