Density Formula

How it works

Density is an intensive property: it belongs to the substance, not to the lump of it in front of you. Cut a block of aluminium in half and each half has half the mass and half the volume, so the density is unchanged. That is what makes it useful for identifying a material and for predicting whether something will float, which it does whenever its density is lower than the fluid around it. The convenient reference is water, which at 4 °C has a density of 999.972 kg/m³ — close enough to 1,000 that one litre weighs almost exactly one kilogram, and one millilitre almost exactly one gram. That equivalence holds for water and nothing else. Flour, cooking oil and honey all have quite different densities, which is why a recipe asking for 200 grams of flour is not asking for 200 millilitres. Density also moves with conditions. Water is at its densest near 4 °C and falls to 997.047 kg/m³ by 25 °C, and gases change far more sharply still, roughly in proportion to pressure and inversely with absolute temperature. That is why a gas density is meaningless unless the temperature and pressure it was measured at are quoted alongside it, and why fuel is sold with a temperature correction.

Variables

• ρDensity (kg/m³ or g/cm³)
• mMass
• VVolume

Worked examples

Practical applications

• Converting a recipe between weight and volume, where only water lets you treat millilitres and grams as interchangeable
• Working out the weight of a load of aggregate, concrete or fuel against a transport or structural limit
• Buoyancy and displacement calculations in naval architecture and civil engineering
• Identifying an unknown material or checking a delivered one, since density is one of its more distinctive properties
• Soil and compaction testing, where achieved density is the acceptance criterion

Common mistakes

• Assuming 1 ml equals 1 g for anything but water. It is close for milk, badly wrong for oil, flour or honey.
• Mixing mass with weight. Density uses mass; weight is a force and changes with gravity while density does not.
• Mixing unit systems. g/cm³ and kg/m³ differ by a factor of exactly 1,000, so 2.70 g/cm³ is 2,700 kg/m³.
• Quoting a gas density without its temperature and pressure. The number means nothing on its own.
• Ignoring temperature for liquids. Water alone varies by about 0.3% between 4 °C and 25 °C, and fuels vary considerably more.

Used in

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