How to Convert Volume to Weight
Multiply by density. weight = volume × density, and going the other way, volume = weight ÷ density. Two cubic metres of gravel at 1,600 kg/m³ weighs 3,200 kg. One tonne of that gravel occupies 0.625 m³. The two things that go wrong are mismatched units and using solid density where bulk density belongs — both covered below.
The formula, in three forms
There is only one relationship here, written three ways depending on what you are missing:
| You have | You want | Use | Typical question |
|---|---|---|---|
| Volume + material | Weight | m = ρ × V | "Will my trailer take 3 yards of soil?" |
| Weight + material | Volume | V = m ÷ ρ | "How much space does a tonne of gravel need?" |
| Weight + volume | Density | ρ = m ÷ V | "What is this material?" |
That middle row is the one people underuse, and it is often the commercially important one. Suppliers of gravel, sand, soil and concrete quote by the tonne, while trailers, skips and driveways are measured in volume. Converting between them before you order is what stops a delivery you cannot fit.
Trap one: matching the units
This causes more errors than the formula itself. The volume unit inside the density must match the volume unit you are multiplying by. A density in kg/m³ needs a volume in m³ — not litres, not cubic feet.
| If density is in… | Volume must be in… | Answer comes out in… |
|---|---|---|
| kg/m³ | m³ | kg |
| g/cm³ | cm³ (= mL) | g |
| g/mL | mL | g |
| kg/L | L | kg |
| lb/ft³ | ft³ | lb |
| lb/gal | US gal | lb |
| tonnes/m³ | m³ | tonnes |
Three conversions cover almost everything you will need:
And one shortcut worth memorising, because it collapses most metric problems into arithmetic you can do in your head:
g/cm³ and tonnes/m³ are the same number. Water is 1.0 g/cm³ and 1.0 tonne/m³. Steel is 7.85 g/cm³ and 7.85 tonnes/m³. Gravel is 1.6 g/cm³ and 1.6 tonnes/m³. So if you know a material's density in g/cm³ — the figure most tables give — you can read tonnes per cubic metre straight off it with no conversion at all.
Trap two: bulk density versus solid density
This one produces errors of 40% or more, and it catches people constantly.
A pile of gravel is mostly stone, but partly air. The gaps between the pieces take up space you have to transport and store, but they weigh nothing. So there are two different densities for the same material:
- Solid density — the density of the rock itself, with no gaps. Granite is about 2,700 kg/m³.
- Bulk density — the density of the loose pile, gaps included. Granite gravel is about 1,500–1,700 kg/m³.
Use solid density and your tonne of gravel appears to fit in 0.37 m³. It actually needs 0.625 m³ — nearly 70% more space than you planned for.
| Material | Solid density | Bulk (loose) density | Void space |
|---|---|---|---|
| Gravel / crushed stone | 2,650 kg/m³ | 1,600 kg/m³ | ~40% |
| Sand, dry | 2,650 kg/m³ | 1,600 kg/m³ | ~40% |
| Sand, wet | 2,650 kg/m³ | 1,920 kg/m³ | ~40%* |
| Topsoil, dry | 2,600 kg/m³ | 1,220 kg/m³ | ~53% |
| Topsoil, wet | 2,600 kg/m³ | 1,600 kg/m³ | ~53%* |
| Wood chips | ~700 kg/m³ | ~250 kg/m³ | ~64% |
| Wheat grain | ~1,400 kg/m³ | ~770 kg/m³ | ~45% |
| Snow, fresh | 917 kg/m³ (ice) | ~100 kg/m³ | ~89% |
* The wet rows need a caveat that most density tables skip. Wetting a material does not squeeze the gaps out — the void space stays roughly the same, the voids simply fill with water instead of air. Wet sand is heavier than dry sand not because it has fewer gaps but because its gaps now contain something that weighs 1,000 kg/m³ instead of 1.2. Running the usual "1 − bulk ÷ solid" sum on a wet material gives a void figure that looks lower and is physically meaningless.
Two rules that resolve it: if the material pours, use bulk density. And if a supplier gave you the figure, it is almost certainly bulk density, because that is what they load onto a lorry.
Note the two soil rows. Wet topsoil is roughly 30% heavier than dry for the same volume — which is why a load ordered by volume after a week of rain can overload a trailer that handled the same volume fine in summer.
Density of common materials
Bulk figures where the material is normally loose, solid figures where it is not.
| Material | kg/m³ | g/cm³ | lb/ft³ | tonnes/yd³ |
|---|---|---|---|---|
| Polystyrene foam | 20 | 0.02 | 1.2 | 0.015 |
| Softwood (pine) | 500 | 0.50 | 31 | 0.38 |
| Petrol / gasoline | 750 | 0.75 | 47 | 0.57 |
| Diesel / heating oil | 850 | 0.85 | 53 | 0.65 |
| Ice | 917 | 0.917 | 57 | 0.70 |
| Water | 1,000 | 1.00 | 62.4 | 0.76 |
| Seawater | 1,025 | 1.025 | 64 | 0.78 |
| Topsoil (loose, dry) | 1,220 | 1.22 | 76 | 0.93 |
| Gravel (loose) | 1,600 | 1.60 | 100 | 1.22 |
| Sand (dry, loose) | 1,600 | 1.60 | 100 | 1.22 |
| Asphalt (compacted) | 2,240 | 2.24 | 140 | 1.71 |
| Concrete | 2,400 | 2.40 | 150 | 1.83 |
| Granite (solid) | 2,700 | 2.70 | 169 | 2.06 |
| Aluminium | 2,700 | 2.70 | 169 | 2.06 |
| Steel | 7,850 | 7.85 | 490 | 6.00 |
| Lead | 11,340 | 11.34 | 708 | 8.67 |
| Gold | 19,320 | 19.32 | 1,206 | 14.77 |
Loose material densities vary with moisture, compaction and particle size — treat them as working figures, and use a supplier's own figure when ordering by weight.
Worked examples, both directions
Volume → weight: will the trailer take it?
You need 3 cubic yards of topsoil. Your trailer is rated to 1,500 kg.
- Convert volume: 3 yd³ × 0.7646 = 2.294 m³
- Pick the density: dry topsoil, 1,220 kg/m³
- Multiply: 2.294 × 1,220 = 2,798 kg
Nearly twice the trailer's rating — and if it has rained, wet topsoil at 1,600 kg/m³ makes it 3,670 kg. Two trips minimum, and that is before considering the axle rating.
Weight → volume: how much space does a tonne need?
A supplier quotes gravel at £45 per tonne. You have a bay 2 m × 1.5 m × 0.5 m.
- Bay volume: 2 × 1.5 × 0.5 = 1.5 m³
- Rearrange: mass = ρ × V = 1,600 × 1.5 = 2,400 kg
- That is 2.4 tonnes, so order 2.4 t — about £108
Weight → volume: the reverse check
One tonne of gravel: V = 1,000 ÷ 1,600 = 0.625 m³, or 0.82 cubic yards. Useful as a mental anchor — a tonne of gravel is roughly three-quarters of a cubic yard.
Water: the anchor that makes everything easier
Water is the reference point the whole metric system was built around, and it makes mental estimation possible:
| Volume of water | Weighs |
|---|---|
| 1 mL / 1 cm³ | 1 g |
| 1 litre | 1 kg |
| 1 cubic metre | 1 tonne (1,000 kg) |
| 1 US gallon | 8.33 lb |
| 1 imperial gallon | 10.0 lb |
| 1 cubic foot | 62.4 lb |
Because those numbers are exact by design, every other material becomes a multiple of water. Steel is 7.85× water. Concrete 2.4×. Petrol 0.75×. Once you know a material's specific gravity — its density relative to water — you can convert anything: a cubic metre of concrete weighs 2.4 tonnes because concrete is 2.4× water and a cubic metre of water is 1 tonne.
For water specifically, including how the figure shifts with temperature, see the water weight calculator.
A note on "weight" versus "mass"
Strictly, the formula gives mass. Weight is the force gravity exerts on that mass and is measured in newtons. On Earth the distinction never matters, because gravity is effectively constant and we use kilograms and pounds for both.
It matters in exactly three places: physics coursework, anywhere off Earth's surface, and engineering calculations that need force rather than mass. Everywhere else, "how much does this weigh" and "what is its mass" have the same practical answer. The mass vs volume vs density guide goes into the distinction properly.
Common mistakes
- Mismatched units. Density in kg/m³ multiplied by a volume in litres gives an answer 1,000× too large. Match them first, every time.
- Solid density on a loose material. The 40%-plus error. Gravel, sand, soil, grain, chips and snow all need bulk density.
- Ignoring moisture. Wet sand and wet soil are 25–30% heavier than dry for the same volume.
- Confusing the three "tons". A metric tonne is 1,000 kg (2,205 lb), a US short ton is 2,000 lb (907 kg), a UK long ton is 2,240 lb (1,016 kg). A price "per ton" can mean any of them.
- Forgetting compaction. Material delivered loose and then compacted shrinks — hardcore and topsoil typically settle 20–30%. Order by the loose volume you need to place, not the finished compacted volume.
- Assuming a container's rated volume is the usable volume. Tanks, skips and bags are rarely filled to their geometric capacity.
Frequently asked questions
How do you convert volume to weight?
Multiply the volume by the density of the material: weight = volume × density. Two cubic metres of gravel with a bulk density of 1,600 kg/m³ weighs 2 × 1,600 = 3,200 kg, or 3.2 tonnes. The only requirement is that the volume unit matches the volume unit inside the density figure.
How do you convert weight to volume?
Divide the weight by the density: volume = weight ÷ density. One tonne of gravel at 1,600 kg/m³ occupies 1,000 ÷ 1,600 = 0.625 m³. This is the direction most people need when a supplier quotes by the tonne and they need to know whether it will fit in a trailer or a skip.
What is the formula for mass from density and volume?
Mass = density × volume, written m = ρV. It is a rearrangement of the definition of density, ρ = m/V. The three forms are ρ = m/V, m = ρV, and V = m/ρ. Knowing any two of the three quantities gives you the third.
Why does a tonne of gravel take up more space than a tonne of rock?
Because a pile of gravel is mostly stone but partly air. The gaps between the pieces are counted in the volume you have to store or transport but contribute no weight. Solid granite has a density around 2,700 kg/m³, while gravel made from the same rock has a bulk density around 1,500–1,700, because roughly 40% of the pile is empty space. Always use bulk density for anything loose and granular.
How much does a litre of water weigh?
One litre of water weighs almost exactly one kilogram, and one cubic metre weighs one tonne. This is the most useful anchor in the whole subject because it was designed that way: the kilogram was originally defined as the mass of one litre of water. Every other material can then be described as a multiple of water — steel is 7.85 times heavier for the same volume, petrol 0.75 times.
Do I use weight or mass in these calculations?
Strictly the formula gives mass, in kilograms or pounds-mass. Weight is a force and is measured in newtons. In everyday use on Earth the distinction never matters, because gravity is effectively constant, and kilograms and pounds are used for both. It only becomes important in physics problems, in aerospace, or anywhere gravity differs from Earth's surface.