How to estimate stockpile tonnage from pile geometry

Most desks don't have a surveyor on retainer for every yard they track. You get a site visit, a photo, maybe a tape measure and a rangefinder, and you need a tonnage number before the call. This is the geometry method, the one traders and stockpile clerks have used since before anyone had a drone.

Getting the volume first: which shape are you looking at

Pile shape depends on how the stacker built it, so start there, not with a formula.

A conveyor-fed pile that's been left alone usually comes out close to a cone or a truncated cone (a frustum, where the top's been pushed flat by a dozer or clipped by a reclaimer). For a full cone with base diameter D and height H:

V = (π/12) × D² × H

For a frustum with top diameter d and bottom diameter D, over height H:

V = (πH/12) × (D² + Dd + d²)

Where stackers run back and forth along a rail, the material builds into an elongated ridge, what most yards call a windrow or long pile. Treat the middle section as a triangular prism and the two ends as half-cones:

V ≈ (1/2) × W × H × (L − W) + (π/12) × W² × H

where W is the base width, H the peak height, and L the total length. It's a rough fit, not an exact one. Real piles sag, settle unevenly, and get re-profiled by loaders, so the formula gets you in the right range, not to the decimal.

Measure height off the actual peak, not an edge estimate. A few meters of error in H moves the volume more than the same error in diameter does, because height scales linearly while area scales with the square of the radius in the cone term.

Converting cubic metres to tonnes: the density problem

Volume alone doesn't tell the desk anything. You need bulk density, and this is where most back-of-envelope estimates go wrong.

Bulk density varies by material, moisture content, and how long the pile has sat. A freshly stacked coal pile runs looser than one that's had weeks of its own weight compacting the base. Thermal coal commonly reports in a bulk density band around 0.8 to 1.0 t/m³, iron ore fines somewhere in the 2.1 to 2.5 t/m³ range, copper concentrate around 1.8 to 2.2 t/m³, but these are general reference ranges, not a substitute for the assay or shipping spec for the cargo on that pad. Rain adds mass and can also cause the pile to pack tighter, so a density figure taken from a dry-season disclosure won't hold through monsoon season at a tropical port.

Multiply volume by the density figure appropriate to that material and moisture state, and you have a tonnage estimate. Multiply by a density that's six months stale, or borrowed from a different mine's spec sheet, and you have a number that looks precise and isn't.

Where the geometry estimate breaks down

The formulas assume a clean, single, undisturbed shape. Yards rarely give you that.

Benching, where a loader cuts a working face into the pile for reclaim, turns a simple cone into a stepped shape no formula above covers well. Segregation by particle size, with fines settling toward the base and coarser material rolling to the outer slope, means a single density figure applied across the whole pile is an average covering a range that's quite wide. Multiple piles pushed together at a crowded terminal blur the base footprint you'd need for a clean diameter reading in the first place.

None of that makes the geometry method useless. It makes it a point estimate, good for one gut-check on one day. What a desk wants is the direction of travel: is the pile at the port building or drawing down week over week, and is that consistent with what the shipment manifests say. A single measurement can't answer that on its own, you need the same site read the same way on a schedule. That repeat read, tracked as a volumetric trend per named site rather than recalculated from scratch each time, is the gap Bulk Stockpile Index was built to close.

If the desk is tired of reverse-engineering pile tonnage from a photo every time a disclosure looks off, a weekly series across the sites you already track is worth a look.