Stockpile Volume Calculator: Cone, Frustum and Windrow Volume

A stockpile keeps its shape in its slopes. A rectangular formula applied to a pile base gives a box the pile never was, so this calculator uses the shape the pile actually holds: a cone, a circular flat-top frustum, or a triangular windrow. It keeps the loose volume and the optional mass figure as separate results.

How much material does a stockpile hold?

Enter the pile shape, the base size, and the vertical height. The calculator works out the loose volume for one pile, then the total for identical piles. It shows a mass figure only when you enter a bulk density for this material and condition.

Use the result in 3 stages. Record the loose volume first, the implied side-slope angle second, and the density used third, only when a mass figure was requested. Each record answers a different project question, and the third record is what makes a mass figure checkable later.

When should you use this stockpile calculator?

Use it for one regular pile shape whose dimensions stay constant: a single cone, a circular flat-top pile, or a straight windrow with a constant triangular section and vertical ends. Run it separately for each pile or section that changes shape or size.

Use the measure a stockpile guide for the tape-and-rod method behind these readings. Use the stockpile formulas and survey guide when the pile is rectangular on top, irregular, or needed as a payment quantity.

Which measurements do you need?

You need the shape, the base size, and the vertical height. You need a bulk density only when you want a mass figure.

Base diameter

Measure across the pile base, through its centre, at the base level the height is measured from. Take two readings at right angles where the base is not clearly circular, and record both before choosing a representative diameter. A diameter taken at the wrong level, such as across a raised pad edge, moves the whole result.

Top diameter

Measure across the flat top of a flat-top pile only. The top must be smaller than the base. A top diameter equal to or larger than the base diameter describes a different shape, and the calculator rejects it with a named error.

Windrow length and base width

Measure the windrow length along the ridge and the base width across the ridge, perpendicular to its length, both at the base level. The length must be at least the base width. A length shorter than the width is not an elongated windrow, and the calculator rejects it.

Vertical height

Measure the vertical height from the chosen base level to the peak or flat top. Do not measure along the sloped side. A slope-length reading is always longer than the vertical height, and it inflates the volume.

Identical piles

Count only piles that match the entered shape and dimensions. A pile that differs in any dimension gets its own calculation, and the results are added afterwards.

Bulk density

Enter a bulk density only from project data for this material, supplier, moisture, and compaction state. The field starts blank. The page gives no density table, because a table value for a named material can still be wrong for the pile on site.

What formulas does the calculator use?

The calculator applies the formulas in this order, with no hidden allowance added at any stage.

1. Cone: radius = base diameter ÷ 2. Volume = π × radius² × height ÷ 3.
2. Flat-top pile: base radius = base diameter ÷ 2, top radius = top diameter ÷ 2. Volume = π × height ÷ 3 × (base radius² + base radius × top radius + top radius²). A top diameter of 0 gives the cone volume, which is the correct limit case.
3. Windrow: volume = length × base width × height ÷ 2. This is a triangular prism, so it treats both ends as vertical and the section as constant.
4. Total loose volume = one-pile volume × identical piles.
5. Display conversions: imperial primary yd³ = ft³ ÷ 27, secondary ft³; metric primary m³, secondary L = m³ × 1,000.
6. Mass, only when a density is entered: metric tonnes = total m³ × density in kg/m³ ÷ 1,000; imperial short tons = total ft³ × density in lb/ft³ ÷ 2,000.

What does the implied side-slope angle check?

The calculator derives a side-slope angle from the dimensions you entered: cone, atan(height ÷ base radius); flat-top pile, atan(height ÷ (base radius − top radius)); windrow, atan(2 × height ÷ base width). The angle is a consistency check, not a material property. Compare it with the project's own material data. An angle steeper than the material can hold means at least one dimension is wrong, usually a height measured along the slope or a base diameter taken short. Re-measure before using the volume. The calculator never supplies an angle for a material, because the angle a material holds depends on the material, particle shape, and moisture.

Worked imperial example: conical pile

A conical aggregate pile has a 30 ft base diameter and a 12 ft vertical height. One pile is measured, and no density is entered.

Report the planning result as 104.720 yd³ loose, together with the 30 ft base diameter, the 12 ft vertical height, and the 38.7° implied angle. The cubic-yard conversion does not change the loose state.

Worked metric example: flat-top pile

A flat-top pile has a 10 m base diameter, a 4 m top diameter, and a 3 m vertical height. One pile is measured, and no density is entered.

Report the planning result as 122.522 m³ loose, together with both diameters and the 3 m height. A 45.0° implied angle is steep for many loose materials, so this pile's dimensions deserve a second check before the figure is used.

Worked metric example: windrow with a mass stage

A windrow is 20 m long, 6 m wide at the base, and 2.5 m high. The project density for this material and condition is 1,600 kg/m³, entered by the user.

Report 150 m³ loose and 240 t, with the 1,600 kg/m³ density named beside the mass figure. Without that density record, the mass figure cannot be checked later. The material and soil guide explains how moisture and handling change the density a pile shows.

How are changing piles and hidden bases handled?

A regular-shape formula covers only the shape it names. A pile that changes width or height along its length, a windrow with tapered ends, a pile with hollows or shoulders, two piles merged into one mass, and a pile backed against a wall all fall outside one formula. Split the pile into measured sections, apply end corrections, or use a surface survey, as the formulas and survey guide sets out. A base that cannot be seen, such as a pile sitting in a hollow or on uneven ground, needs a stated base surface before any formula result means anything. Record the base surface with the dimensions, not after the result.

What does the loose volume not include?

The loose volume is the volume the pile occupies in its measured state. It does not convert to a bank volume, a compacted volume, or a haulage quantity by itself. Settlement after measurement, moisture change, handling loss, and the difference between a loose pile and material in the ground all sit outside this calculation. The haulage and ordering guide covers the step from a loose pile figure to a delivery plan, and the Aggregate Weight-Volume Converter handles a separate weight-to-volume conversion once a density is confirmed. Truck loads and legal payload are not calculated here.

Common stockpile calculation mistakes

• Using a rectangular formula (length × width × height) on a cone or windrow. The box overstates the pile by a wide margin.
• Measuring height along the sloped side instead of vertically. The slope length is always longer, and the volume follows it upward.
• Entering a radius where the calculator asks for a diameter, or a diameter where a radius is expected. The volume changes by a factor of 4.
• Using the top diameter of a flat-top pile as its base diameter. The frustum formula needs both, and swapping them changes the result.
• Treating a windrow's tapered ends as vertical without noting it. The prism formula then overstates the ends.
• Taking a density from a generic table and reporting the mass as measured. Density belongs to a specific material and condition, and the page keeps the field blank until project data supplies it.
• Carrying a planning formula result into a payment quantity. A payment quantity needs the project's survey method and specification, as the common mistakes guide also warns.

Questions about stockpile quantity

Which shape should I pick for a pile with a rounded top?

Pick the shape the pile most closely matches and record the mismatch. A rounded top sits between a cone and a flat-top pile, so neither formula is exact. A surface survey gives the defensible figure when the quantity matters.

Can I use this calculator for a pile inside a bunker or against a wall?

No. A wall changes the pile shape, and the cone, frustum, and windrow formulas all assume a free-standing pile on a level base. Measure the bunker as sections or use a survey.

Why does the calculator ask for no density by default?

Because no single density fits every pile of a named material. Moisture, compaction, particle shape, and supplier all move the value. A blank field forces the density to come from project data, and the mass figure then carries a record that can be checked.

What if my windrow ends taper?

Split the windrow into a central constant section and separate end sections, or use a surface survey. The windrow formula in this calculator treats both ends as vertical, and the result note on the page states that limit.

Does the calculator convert loose volume to bank volume?

It does not. Loose, bank, and compacted volumes are separate states, and the conversion between them needs project data about the material and its handling. The worked example guide shows a loose-volume check reconciled against a delivery ticket without converting states.