Stockpile volume formulas

Cone-shaped pile

For a round pile coming to a point: volume = π × diameter² × height ÷ 12.

Example: a pile 8 m across and 2 m high is π × 64 × 2 ÷ 12 = 33.5 m³.

If you can only measure round the base, diameter = circumference ÷ π.

Ridge or windrow

For a long pile with sloping sides and rounded ends: volume = ½ × width × height × (length − width) + π × width² × height ÷ 12.

The first part is the straight middle section; the second is the two half-cone ends.

Flat-topped pile

For a pile with a flat top (a frustum), use the prismoidal formula: volume = height ÷ 6 × (base area + top area + 4 × middle area).

The middle area is measured halfway up, or estimated from the average of the base and top dimensions.

Why the formula and the real pile disagree

Formulas assume a perfect shape on flat ground. Real piles slump, have bites taken out by loaders, sit on sloping pads and lean against walls. Each of those changes the volume, and none shows up in three tape measurements.

A small error in height matters most: on a cone, 10 cm too high on a 2 m pile overstates the volume by 5%. That is why measuring the real surface beats any formula.

Try the numbers in the free stockpile volume calculator.