Mass from Volume and Density

The multiplication, and the word that does the damage

Mass is volume times density, and nothing on this page disputes that. What the page is about is that DENSITY is not one number. For a single material there are routinely five: the density of the solid particles, the bulk density of the material loose, the same material compacted, the same material dry, and the same material saturated. They differ by tens of percent, they are all called density in conversation, and the calculation cannot tell which one it has been given.

For a manufactured solid — steel, glass, aluminium — this hardly matters, because the material has one density and it is well established. For anything granular, porous or placed, it matters more than the geometry does.

Rolled sections: the table, not the arithmetic

A rolled steel section's mass per unit length is PUBLISHED, and the published figure is the one to use. Computing it instead — as a web rectangle plus two flange rectangles times the density of steel — understates it, because a rolled section has root radii where the web meets the flanges and, on older profiles, tapered flanges. That material is real and the rectangle model throws it away.

The discrepancy is a few percent on a typical universal beam, which sounds tolerable until it is applied to a tonnage for pricing or to a crane lift. It also runs consistently in one direction — always short — so it does not average out across a schedule the way a random error would.

Hollow sections carry the same lesson in a different form: a square hollow section has corner radii inside and out, so its area is not the outer square less the inner square. And the wall thickness in the designation is nominal; the design thickness a standard assigns is slightly under it. The site's steel-section calculators work from published section properties for exactly this reason, and the pages say so.

Five densities, and how to tell which one you have

PARTICLE or SOLID density is the density of the material itself with no voids — the figure for steel, glass or the mineral grains of a soil. It is the only one of the five that is a property of the substance rather than of a sample.

BULK density is mass divided by the total volume the material occupies, voids included. It is what a delivered load has, and it changes with how the load settled on the way.

DRY, BULK and SATURATED unit weights are the same material at three moisture states. For a soil, they can differ by a fifth or more between dry and saturated, which is why a geotechnical report states which it is quoting.

SUBMERGED unit weight is the saturated figure less the unit weight of water — buoyancy, applied to the soil skeleton. It is the one used below a water table, and it is dramatically smaller: subtracting roughly 9.81 kN per cubic metre from a saturated soil removes about half its effective weight. Using the bulk figure below the water table roughly doubles the load a retaining wall or a footing is designed against, and using the submerged figure above it halves a load that is real.

The practical rule is that a density quoted without a state is a density that has to be chased. This site's reference table carries the state alongside each figure for that reason.

Where it fails: moisture, and the tonne that is less material

Aggregate, sand and topsoil are bought by mass and used by volume, and water is carried in the price. A load delivered after rain weighs more and spreads no further — so a tonne of wet sand is less sand than a tonne of dry sand, by exactly the mass of the water in it.

The effect is largest on fine materials, which hold the most water per unit volume, and it is invisible at the weighbridge because the ticket records mass and nothing else. Where the quantity matters, ordering by volume rather than by mass moves the risk to the supplier; where it must be by mass, the allowance is a judgement about the weather and belongs on the page rather than buried in a density.

The same mechanism explains why a stockpile measured by survey and a stockpile weighed over a bridge rarely agree. Neither is wrong; they are measuring a material whose bulk density changed between them.

Where it fails: the volume is not solid

The density is only half the input; the other half is whether the volume is GROSS or NET. A hollow concrete block wall is mostly void, so its self-weight from gross dimensions times the density of concrete is far too heavy — the figure needed is the net solid volume, plus any grouted cells.

The same distinction runs through steel decking, void-formed slabs, cored planks and every hollow section. And it moves during construction: an ungrouted masonry wall and the same wall after grouting are two different loads, and the temporary case is often the one the falsework was designed for.

Where a page here takes a wall area rather than a volume, it is because the net-to-gross ratio is a property of the unit and is carried in the data rather than being asked of the reader. The published figures are per unit of wall face for that reason, and the assumption is stated on the page.

The alternative: weigh it

For anything already in existence, the alternative to computing a mass is measuring one, and it is better. A weighbridge ticket, a load cell on a crane, or a sample of known volume on a scale all produce the actual figure for the actual material, including whatever moisture and grading it happens to have.

The computed figure is the right tool for something not yet made — a section to be ordered, a pour to be planned, a lift to be rigged before the panel is on site. Its job is to be close enough to make a decision and to be transparent about the density it assumed.

The one case where the computation beats the measurement is a SAFETY margin: a glass panel lift or a crane pick is planned on a computed mass deliberately, because the plan has to exist before the object does, and the assumptions can then be checked rather than discovered. Every one of those pages states its density so that the check is possible.