Core answer: Density = mass ÷ volume (ρ = m/V), in kg/m³ or g/cm³. Water is exactly 1,000 kg/m³ = 1 g/cm³ — the reference for everything else: anything with density below 1 g/cm³ floats on water, above 1 sinks. Iron is 7.87, aluminum 2.70, gold 19.3, cork ~0.24 g/cm³.
The density table worth memorizing
| Material | Density (g/cm³) | vs water |
|---|---|---|
| Cork | 0.24 | floats high |
| Pine wood | ~0.5 | floats |
| Ice | 0.917 | floats (why icebergs show ~8% above water) |
| Water (4 °C) | 1.000 | reference |
| Seawater | 1.025 | slightly easier to float |
| Aluminum | 2.70 | sinks |
| Iron/steel | 7.87 | sinks |
| Copper | 8.96 | sinks |
| Lead | 11.34 | sinks |
| Gold | 19.30 | sinks hard |
Worked examples
Example 1 — Is the "gold" ring real? A ring weighs 38.6 g and displaces 2.6 mL of water. ρ = 38.6 / 2.6 = 14.8 g/cm³ — far below gold's 19.3, consistent with 14K gold alloy (~13–15) or a fake; pure gold would displace only 2.0 mL. Archimedes' bath test still works.
Example 2 — Fuel tank mass. A 60 L tank of gasoline (ρ ≈ 0.74 kg/L) holds 44.4 kg of fuel — meaningful for a small car's payload, trivial for its range estimate.
Example 3 — Air freight vs sea freight. A 2 m³ box of foam (ρ = 30 kg/m³) weighs 60 kg but sea carriers bill by volume weight for light cargo — density decides which number you pay on.
Common mistakes and myths
- "Heavy means dense" — a ton of styrofoam is heavier than a kilogram of lead; density compares equal volumes.
- Forgetting temperature — water is densest at 4 °C (1.000); hot water expands (~0.958 at 100 °C), which is why hot water rises and lakes freeze from the top.
- Assuming ice sinks — ice is 9% less dense than water, a nearly unique property that keeps aquatic life alive under frozen lakes.
- Mixing units — 1 g/cm³ = 1,000 kg/m³ = 1 kg/L; a factor-of-1,000 slip is the most common student error.
- Using average density for hollow objects — a steel ship floats because its *average* density (steel + air inside) is below 1 g/cm³; the same steel as a solid block sinks instantly.