Understanding density
Mass divided by volume, with the water anchor.
The units of density, the lucky coincidence that makes water 1 g/cm³, and the temperature dependence that affects everything else.
Mass per volume.
Density (ρ, rho) = mass / volume. SI unit kg/m³. Common alternatives: g/cm³ (same as g/mL), lb/ft³, lb/gal. Conversions are pure scaling between these units.
ρ = mass ÷ volume
The water anchor.
Water at 4°C has density 1000 kg/m³ = 1 g/cm³. This isn't accidental — the kilogram was originally defined (1795) as the mass of one litre of water at this temperature. The base SI unit was redefined in 2019 to be based on Planck's constant, but the historical alignment makes water a convenient reference. Almost every density anyone cares about is expressed relative to water (specific gravity = density ÷ density of water).
Temperature dependence.
Water shrinks as it cools — until 4°C, after which it expands again (the reason ice floats). The 4°C density of exactly 1.000 g/cm³ becomes 0.998 at 20°C and 0.917 for ice at 0°C. For most everyday densities, the temperature variation is small (~1 % across normal ranges) and ignored. For precision applications — chemistry, brewing, fuel-metering — the density table at multiple temperatures matters.
A worked conversion.
Steel has density 7850 kg/m³. Converted: 7.85 g/cm³ (divide by 1000), 490 lb/ft³ (multiply by 0.0624), 65.5 lb/gal (multiply by 0.00835). Same property; four notations across two unit systems. The factors come from chained unit conversions (kg ↔ lb, m³ ↔ ft³ ↔ gal).
Steel density in four units
ρ = 7850 kg/m³
Scaling factors between unit systems.
kg/m³ → g/cm³ × 0.001 ; → lb/ft³ × 0.0624
= 7850 / 7.85 / 490 / 65.5
Densities to memorise.
Air: 1.2 kg/m³ (sea level, 20°C). Water: 1000 kg/m³. Ice: 917. Vegetable oil: 920. Salt water: 1025. Honey: 1420. Aluminum: 2700. Iron/steel: 7850. Lead: 11,340. Gold: 19,320. Mercury: 13,534. The water → metal jump is the one to feel — most metals are 5-20× water density, which is why a chunk of metal in your hand feels surprisingly heavy.
Specific gravity, the dimensionless version.
Specific gravity (SG) = density ÷ density of water. Dimensionless, easy to compare. Steel SG = 7.85; gasoline SG = 0.72; ice SG = 0.92 (less than water, so floats). Most chemistry handbooks list SG rather than absolute density because the cross-system conversion just isn't needed — multiply by 1000 kg/m³ for SI, 62.4 lb/ft³ for imperial.