Why most aggregate calculators over-order by about a fifth

The error, in one sentence

The compaction factor is the ratio between the loose and compacted densities — so applying a compaction percentage and then converting at a compacted density applies the same correction twice.

Take a patio base: 10 m² at 100 mm compacted depth. That is 1.0 m³ of finished, compacted material in place.

MOT Type 1 is roughly 2,100 kg/m³ compacted and 1,680 kg/m³ loose, and loses about 20% of its loose volume under a compactor — a factor of 1.25 loose per compacted.

There are two correct routes, and they agree:

2.63 against 2.10 is 25% too much stone. On a 40 m² driveway base at 150 mm that is roughly three extra tonnes.

Notice why it is hard to spot: both numbers in the wrong calculation are correct on their own. 1.25 is a real compaction factor. 2.1 t/m³ is a real compacted density. It is using them together that double-counts, and the result looks entirely plausible — it is not out by a factor of ten, just by a fifth.

• Enter 10 m² at 100 mm compacted depth — or 100 sq ft at 4 in.
• Look at the tonnage. For MOT Type 1 it should be about 2.1 tonnes. For US dense-graded base at 2,000 kg/m³ compacted, about 2.0 tonnes.
• If it says 2.6 tonnes, the allowance has been applied twice.
• Then ask which density it used. A calculator that shows its working will tell you. One that does not is asking you to trust an answer you cannot check.

Our own pages are asserted against exactly this test — 10 m² at 100 mm returns precisely compacted volume × compacted density on every base page. That is a test in the codebase, not a claim in the copy. Try it.

This is the part worth sitting with. The error has a direction: it always produces more material, never less.

We are not suggesting anyone does it deliberately. It is a genuinely easy mistake, and we found the same class of error in our own working on the brick coordinating size — entering the bare brick instead of brick-plus-joint gives 71.6 per m² instead of 59.3, a 21% over-order, and it took a failing test to catch it.

But it is worth noticing that a calculator funded by commission on the material has no incentive to find this bug, and one funded by advertising has no incentive to keep it. That asymmetry is the whole reason this site exists — and it is why every figure we use is published with its source and its uncertainty, so you can check us the same way.