What Density Measures
Density is how much mass is packed into a given volume. It is what people mean when they say lead is "heavier" than feathers — a kilogram of each weighs the same, but the lead occupies a tiny fraction of the space.
ρ = m ÷ V
The symbol is the Greek letter rho. The SI unit is kilograms per cubic metre, though grams per cubic centimetre is far more convenient for everyday materials — and the two differ by exactly a factor of 1,000.
Density Units
| Unit | kg/m³ | g/cm³ | lb/ft³ |
|---|---|---|---|
| 1 kg/m³ | 1 | 0.001 | 0.0624 |
| 1 g/cm³ | 1,000 | 1 | 62.43 |
| 1 lb/ft³ | 16.02 | 0.01602 | 1 |
| 1 lb/in³ | 27,680 | 27.68 | 1,728 |
A happy coincidence of the metric system: water has a density of almost exactly 1 g/cm³, because the kilogram was originally defined as the mass of one litre of water. This makes water the natural reference point.
Common Material Densities
| Material | g/cm³ | kg/m³ | lb/ft³ |
|---|---|---|---|
| Air (sea level) | 0.0012 | 1.2 | 0.075 |
| Balsa wood | 0.16 | 160 | 10 |
| Cork | 0.24 | 240 | 15 |
| Petrol | 0.75 | 750 | 47 |
| Ice | 0.917 | 917 | 57 |
| Water | 1.000 | 1,000 | 62.4 |
| Seawater | 1.025 | 1,025 | 64 |
| Brick | 1.9 | 1,900 | 119 |
| Concrete | 2.4 | 2,400 | 150 |
| Aluminium | 2.70 | 2,700 | 169 |
| Steel | 7.85 | 7,850 | 490 |
| Copper | 8.96 | 8,960 | 559 |
| Lead | 11.34 | 11,340 | 708 |
| Gold | 19.30 | 19,300 | 1,205 |
| Osmium (densest element) | 22.59 | 22,590 | 1,410 |
Why Ice Floats
Almost every substance is denser as a solid than as a liquid. Water is the great exception: as it freezes, hydrogen bonds lock the molecules into an open hexagonal lattice that occupies about 9% more space. Ice at 0.917 g/cm³ therefore floats, with roughly 90% of its volume submerged.
This is not a trivial curiosity. If ice sank, lakes and oceans would freeze from the bottom up and never fully thaw, and life as it exists would be impossible.
Specific Gravity
Specific gravity is density relative to water, so it is a pure number with no units. Anything below 1.0 floats in fresh water; above 1.0 it sinks.
It is used heavily in industry precisely because it is unitless: brewers measure the specific gravity of wort to track fermentation, geologists use it to identify minerals, and battery testers use it to judge the state of charge of lead-acid cells.
Density Changes With Temperature and Pressure
Materials expand when heated, so density falls as temperature rises. For gases the effect is dramatic — warm air rises for exactly this reason — while for solids and liquids it is small but measurable.
Water is unusual again: it reaches maximum density at 4°C, not at freezing. This is why deep lakes sit at 4°C at the bottom year round, and why the densest water sinks below both the warmer surface water and the ice above it.
Buoyancy
Archimedes' principle says an object experiences an upward force equal to the weight of the fluid it displaces. An object floats when it can displace its own weight before being fully submerged — which happens exactly when its average density is below the fluid's.
The word average is the key. A steel ship floats because most of its volume is air, so the hull's overall density is far below water's, even though steel itself is nearly eight times denser.
Frequently Asked Questions
How do I find the volume of an irregular object?
Displacement. Submerge it in a measuring container of water and record the rise in level; the volume of water displaced equals the object's volume. This is the method Archimedes is said to have discovered in his bath.
Is density the same as weight?
No. Weight depends on gravity and on how much material there is; density is a property of the material itself, independent of quantity. A gram of gold and a kilogram of gold have identical density.
What is the densest substance?
Osmium, at 22.59 g/cm³, is the densest naturally occurring element. Neutron star material is denser by a factor of around 1014.
Why does oil float on water?
Most oils have a density around 0.9 g/cm³, below water's 1.0. They also do not mix, so the lighter layer stays on top.