The Density Formula
Density is defined as mass per unit volume:
ρ = m / V
Where ρ (rho) is density, m is mass, and V is volume. This can be rearranged to solve for any variable:
- Find density: ρ = m / V
- Find volume: V = m / ρ
- Find mass: m = ρ × V
Common Density Units
| Unit | Equivalent to 1 kg/m³ | Common Use |
|---|---|---|
| kg/m³ | 1 (SI unit) | Engineering, physics |
| g/cm³ | 0.001 | Chemistry, materials science |
| g/mL | 0.001 | Liquids, lab work |
| kg/L | 0.001 | Liquids, beverages |
| lb/ft³ | 0.06243 | US construction |
| lb/in³ | 0.00003613 | US manufacturing |
| lb/gal | 0.008345 | US liquids |
Densities of Common Materials
| Material | kg/m³ | g/cm³ |
|---|---|---|
| Air (20°C) | 1.204 | 0.001204 |
| Water (4°C) | 1,000 | 1.000 |
| Ice | 917 | 0.917 |
| Concrete | 2,400 | 2.4 |
| Aluminum | 2,700 | 2.7 |
| Steel | 7,850 | 7.85 |
| Copper | 8,960 | 8.96 |
| Gold | 19,320 | 19.32 |
Temperature and Pressure Effects
Density changes with temperature and pressure. For solids and liquids, the change is small. For gases, density is heavily affected — doubling pressure doubles gas density, and increasing temperature decreases it.
Water is an exception: its density increases from 0°C to 4°C, then decreases. This anomalous behavior is why ice forms on the surface of lakes rather than the bottom.
Practical Applications
- Buoyancy: Objects float if their density is less than the fluid they're in
- Material identification: Density helps identify unknown metals and minerals
- Quality control: Density changes indicate contamination or composition changes
- Engineering: Density determines weight of structures, fuel loads, and material selection
- Cooking: Oil floats on water (0.91 g/cm³ vs 1.0 g/cm³) — useful in food science