The units of density
Density is mass divided by volume, and its SI unit is the kilogram per cubic metre. In practice almost nobody uses it: laboratories work in grams per cubic centimetre and Anglo-American industry in pounds per cubic foot. The conversion between the first two is easy to remember because the factor is exactly a thousand, which is why water is both 1 g/cm³ and 1,000 kg/m³.
| Unit | Symbol | Equals |
|---|---|---|
| Kilograms per cubic metre | kg/m³ | 1 kg/m³ |
| Grams per cubic centimetre | g/cm³ | 1,000 kg/m³ |
| Grams per millilitre | g/ml | 1,000 kg/m³ |
| Kilograms per litre | kg/l | 1,000 kg/m³ |
| Grams per litre | g/l | 1 kg/m³ |
| Pounds per cubic foot | lb/ft³ | 16.01846337 kg/m³ |
| Pounds per cubic inch | lb/in³ | 27,679.9047102 kg/m³ |
| Ounces per US gallon | oz/gal | 7.48915171 kg/m³ |
How to convert by hand
Every density conversion follows the same procedure: take the amount to the base unit, then from there to the target unit. In practice it is a single multiplication, because the two steps combine into one factor.
Everything passes through kilograms per cubic metre. One gram per cubic centimetre is 1,000, and one pound per cubic foot is 16.018463: that comes from dividing the pound (453.59237 g) by the cubic foot (28.316846 litres).
The equivalents people look up most
| Conversion | Result |
|---|---|
| Water at 4 °C | 1,000 kg/m³ · 1 g/cm³ |
| Air at sea level | 1.225 kg/m³ |
| Olive oil | 916 kg/m³ |
| Reinforced concrete | 2,400 kg/m³ |
| Iron | 7,870 kg/m³ |
| Gold | 19,320 kg/m³ |
Common mistakes
- Mixing up density with specific weight: the second is a force per unit of volume and has gravity built into it.
- Mixing the US gallon with the imperial one. The imperial gallon is 20% larger, so ounces per gallon change value.
- Assuming density is fixed: water changes with temperature, and a gas changes with pressure as well.