Stockpile Volume Formula: Cone and Windrow Piles to Tons

Whether you are checking a delivery, counting what is left in the yard or figuring out how many loader buckets a pile holds, the stockpile volume formula comes down to a little geometry. Most piles of gravel, sand, millings or dirt settle into one of two shapes: a cone, or a long ridge called a windrow. Measure a few distances, plug them in, and you have cubic yards. Multiply by a density and you have tons.

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The formulas at a glance

Pile shape	Volume formula
Cone	V = π × r² × h ÷ 3
Cone, from circumference	V = C² × h ÷ (12 × π)
Cone, from angle of repose	V = π × r³ × tan(angle) ÷ 3
Windrow (ridge with rounded ends)	V = (b × h ÷ 2) × L + π × r² × h ÷ 3
Flat-topped cone (frustum)	V = π × h ÷ 3 × (R² + R × r + r²)

Here r is the base radius, h the height, C the circumference around the toe, b the base width of a windrow (twice its end radius), L the length of the straight middle section, and R and r the bottom and top radii of a flattened pile. Work in feet, then divide the cubic feet by 27 for cubic yards.

Measuring a cone pile

Circumference. Walk a long tape around the toe of the pile, following where the slope meets the ground. That is easier and more accurate than guessing the center for a radius.
Height. On a small pile, lay a straight board from the peak and measure down. On a big one, measure the slope length up the face from the toe to the peak, then use height = √(slope² − r²), with r = C ÷ 6.283.
Plug in. Use V = C² × h ÷ 37.7 (12π rounded).

Example (made-up numbers): a pile measures 60 feet around and 8 feet high. V = 60 × 60 × 8 ÷ 37.7 ≈ 764 cubic feet, about 28.3 cubic yards. As a check, the radius is about 9.55 feet, so the side slope is about 8 ÷ 9.55, which is roughly a 40 degree angle. That is in line with a natural gravel pile.

Using the angle of repose

The angle of repose is the steepest slope a loose material holds before it starts sliding. Because a free-dumped pile settles near that angle, you can estimate height from the base alone. One widely used engineering reference table gives these values:

Gravel: about 40 degrees
Sand, dry: about 35 degrees
Sand, damp: about 40 degrees
Crushed stone: about 30 degrees
Loose earth: about 28 degrees

Moisture, particle shape, fines and how the pile was built all shift the real angle, so measure the height when you can and use the angle as a cross-check. A pile that a loader has pushed up and tracked over will be steeper and denser than a free-dumped one.

Measuring a windrow pile

Long piles built by a conveyor or by trucks dumping in a line are best treated as a triangular prism in the middle with half a cone on each end. The two half cones add up to one full cone.

Measure the base width b across the middle and the height h.
Measure the length L of the straight section, from where one rounded end starts to where the other begins.
Middle volume = b × h ÷ 2 × L. End volume = π × (b ÷ 2)² × h ÷ 3.

Example (made-up numbers): a ridge 16 feet wide, 6 feet high, with a 40 foot straight section. Middle: 16 × 6 ÷ 2 × 40 = 1,920 cubic feet. Ends: π × 8 × 8 × 6 ÷ 3 ≈ 402 cubic feet. Total ≈ 2,322 cubic feet, about 86 cubic yards.

From cubic yards to tons

Stockpiles are loose material, so use a loose density, not a compacted one. Planning figures from our calculators:

Material	Tons per cubic yard (loose, dry)
#57 stone	1.40
Crusher run / dense grade	1.50
Pea gravel	1.35
Concrete sand (dry)	1.35
Fill dirt	1.10

So the 28.3 yard cone of #57 is about 28.3 × 1.4 ≈ 40 tons, and the 86 yard crusher run windrow is about 86 × 1.5 ≈ 129 tons. Wet material weighs more per yard. If it matters, weigh a few loader buckets on a truck scale and use your own number. The gravel, crushed stone, sand and topsoil calculators do the conversion both ways.

Tips for better numbers

Split odd piles. A pile pushed against a wall is roughly half a cone. A lumpy pile can be broken into a few simple shapes and added up.
Watch the toe. Most error comes from where you decide the pile ends. Measure where the slope meets firm ground, not the loose spill around it.
Remember the ground. If the pile sits in a hollow or on a slope, the visible shape is not the whole volume.
Count loads as a check. Compare against the number of dump truck loads delivered or loader buckets moved.
Go high-tech for big inventory. Quarries and large contractors usually measure piles by GPS survey or drone photos, which handle irregular shapes far better than a tape.

Questions people ask

What is the formula for a cone-shaped stockpile?

Volume = π × r² × h ÷ 3, where r is the radius of the base and h is the height. With feet in, the answer is cubic feet. Divide by 27 for cubic yards.

How do I measure the radius of a big pile?

Walk a tape around the bottom to get the circumference, then divide by 2π, about 6.283. You can also use the shortcut volume = C² × h ÷ (12π), where C is the circumference.

How do I find the height of a pile without climbing it?

Measure the slope length from the toe to the peak and the radius, then height = √(slope² − radius²). Or use the angle of repose: height ≈ radius × tan(angle).

What is the angle of repose of gravel?

One widely used engineering table lists gravel at about 40 degrees, dry sand about 35, damp sand about 40 and crushed stone about 30. Real piles vary with moisture, particle shape and how the pile was built.

How do I convert stockpile volume to tons?

Multiply cubic yards by the material's loose density in tons per cubic yard. Planning figures in our calculators include 1.4 for #57 stone, 1.5 for crusher run and about 1.35 for dry concrete sand.

How accurate is a tape-measure stockpile estimate?

Good enough for ordering and rough inventory if the pile is close to a cone or windrow shape. Lumpy piles, piles against a wall and very large inventories are usually measured by survey or drone instead.

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