Stockpile Volume Calculator

Stockpile volume calculator: cubic yards and tons in a cone-shaped pile

A stockpile volume calculator treats a loose pile as a cone. Take the base diameter and height, find the radius, and apply cone volume: ⅓ × π × radius² × height, divided by 27 for cubic yards. A gravel pile 20 ft across and 8 ft tall holds 837.8 ft³, or 31.03 yd³, which weighs about 43.4 tons at 1.4 tons per cubic yard.

Use it to check a delivery, take inventory at a yard, or estimate how much material is left in a pile you cannot easily weigh.

The formula in plain words

Imagine an ice cream cone. The cone holds one-third of what a cylinder of the same width and height would hold. A pile of gravel is the same shape, filled to a point.

• Radius = base diameter ÷ 2
• Cubic feet = ⅓ × π × radius² × height
• Cubic yards = cubic feet ÷ 27
• Tons = cubic yards × density (tons per yd³)

The only thing that changes between a pile of sand and a pile of gravel is the density you enter.

Worked examples

1. Gravel pile, 20 ft base, 8 ft tall, 1.4 t/yd³

• Radius: 10 ft
• Cubic feet: ⅓ × π × 10² × 8 = 837.8 ft³
• Cubic yards: 837.8 ÷ 27 = 31.03 yd³
• Tons: 31.03 × 1.4 = 43.44 tons

2. Sand pile, 12 ft base, 5 ft tall, 1.35 t/yd³

• Radius: 6 ft
• Cubic feet: ⅓ × π × 6² × 5 = 188.5 ft³
• Cubic yards: 6.98 yd³
• Tons: 6.98 × 1.35 = 9.42 tons

Example 2 is about 7 yards, which is easy to compare against what you ordered.

Cone volume by size

Densities at 1.4 t/yd³ (gravel) unless noted.

Base × height	Cubic yards	Tons
10 ft × 5 ft	4.85	6.8
12 ft × 5 ft	6.98	9.8
20 ft × 8 ft	31.03	43.4
30 ft × 12 ft	104.72	146.6
40 ft × 12 ft	186.17	260.6

How to measure a pile

• Base diameter: Run a tape across the widest point of the footprint. For a pile that is not round, measure two directions and average them.
• Height: Use a long pole, a laser distance meter from the ground, or a level line against a ladder.
• Ignore the dirt below: Measure from the ground the pile sits on, not from a surrounding berm.
• Repose check: Compare height to diameter. A ratio of about 0.3 to 0.4 is normal for loose dry stone.
• Use the right density: Wet or fines-heavy material weighs more than the table value.

Common mistakes

• Confusing diameter with radius. Halving the diameter is the calculator’s job, so enter the full width.
• Treating a ridge as a cone. A long windrow is a triangular prism. Use the triangular prism volume calculator for that shape.
• Ignoring a flat top. A pile with a flat top is a truncated cone. The frustum volume calculator fits it better.
• Trusting height by eye. A 20 percent overestimate of height makes a 20 percent overestimate of volume.
• Forgetting compaction. Loose pile volume shrinks when the material is spread and packed, so it will not cover as much as its yardage suggests.

Turning tons into truckloads

Delivery trucks differ, so ask your supplier what a load weighs. As an illustration only, if a truck carries 12 tons, the 43.44 ton pile equals 43.44 ÷ 12 = 3.6 loads, so about four trips.

For inventory, repeat the measurement at regular intervals and subtract. If the pile shrinks from 31.03 yd³ to 20 yd³, you have used about 11 yd³, or 15.4 tons at 1.4 tons per yard. Use the same tape points each time so your readings are comparable.

Related calculators

If you know the area you need to cover, the gravel calculator works backward from the size of the job. For pure geometry, use the cone volume calculator, and convert between units with the cubic yard calculator.