Density, mass and volume
Density (ρ, the Greek letter rho) is the mass of a material per unit of volume:
ρ = m ÷ V
It is expressed in kg/m³ in the SI system, in g/cm³ (the same number as kg/L) in labs and cooking, and in lb/ft³ or lb/gal in the US. Knowing any two of density, mass and volume gives the third: m = ρ × V and V = m ÷ ρ.
Specific gravity compares a density with that of water (1,000 kg/m³, 62.4 lb/ft³ or 8.34 lb/gal). A specific gravity below 1 floats in water, above 1 sinks.
Worked example: 10 lb of liquid in a 1 gallon container
- Convert: 10 lb = 4.536 kg and 1 gal = 3.785 L.
- Density: 4.536 ÷ 0.003785 = 1,198 kg/m³, or 74.8 lb/ft³, about 10 lb/gal.
- Specific gravity: 1.198. The liquid sinks in water: it could be a heavy syrup or an antifreeze concentrate.
Densities of common materials
| Material | kg/m³ | lb/ft³ | Specific gravity |
|---|---|---|---|
| Air (sea level, 68 °F) | 1.2 | 0.075 | 0.0012 |
| Pine wood | 500 | 31 | 0.50 |
| Gasoline | 740 | 46 | 0.74 |
| Ice | 917 | 57 | 0.92 |
| Water | 1,000 | 62.4 | 1.00 |
| Seawater | 1,025 | 64 | 1.03 |
| Honey | 1,420 | 89 | 1.42 |
| Concrete | 2,400 | 150 | 2.4 |
| Aluminum | 2,700 | 169 | 2.7 |
| Steel | 7,850 | 490 | 7.85 |
| Copper | 8,960 | 559 | 8.96 |
| Gold | 19,300 | 1,205 | 19.3 |
Practical uses
- Weight of a load: a cubic yard of concrete (0.765 m³) weighs about 0.765 × 2,400 = 1,835 kg, or 4,050 lb.
- Fuel: a 15 gallon tank of gasoline weighs about 15 × 6.2 = 93 lb.
- Identifying a material: a ring that weighs 10 g and displaces 0.52 mL of water has a density of 19.2 g/cm³, consistent with gold.
- Shipping and storage: bulk materials are often priced by weight but stored by volume.
Measuring density at home
Weigh the object on a kitchen scale, then measure its volume by the water it displaces in a measuring cup (Archimedes’ method). For liquids, weigh a known volume and subtract the weight of the container.
Good to know
Density changes with temperature, because most materials expand when they warm. Water is densest at 39 °F (4 °C), which is why ice floats and lakes freeze from the top. Gases are far more sensitive: air is about 10% less dense at 90 °F than at 32 °F.