The formula
tonnes = area × depth × density ÷ 1,000
Where it comes from
The sum is the same as for gravel and only the density changes, but it changes a lot: sand weighs about 1,600 kg per cubic metre and potting compost barely 400. That fourfold difference is why sand is sold by the tonne and compost by the litre, and why comparing prices "per bag" between the two means nothing at all.
How to work it out by hand
- Multiply the area by the depth in metres
- Add the settlement allowance
- Multiply by the density of the material you are using
- Divide by a thousand for the tonnes
What is worth knowing
A sand bed for block paving goes 3 to 5 cm deep and is screeded without compacting, because the blocks themselves bed it down when vibrated. Topsoil for a new lawn wants 10 to 15 cm, which is what the roots need, and it is worth mixing it into the ground below rather than leaving it as a separate layer: otherwise the roots reach the change in texture and stop going down. Potting compost is a different thing altogether and is not soil: it is peat, fibre and perlite, made to hold water and stay open, and it will not take compaction.