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Density guide

What is density and how is it calculated?

Density (ρ, the Greek letter rho) is one of the most fundamental physical properties of matter. It describes how much mass is packed into a given volume. In other words,, how "heavy" a material is for its size. Dense materials feel heavy even in small amounts; low-density materials are light and bulky. Understanding density explains why ships float, why helium balloons rise, why oil floats on water, and why gold is so valuable by the ounce.

The density formula

The relationship between density, mass, and volume is one of the simplest and most powerful equations in physics:

Rearranged to solve for the other two variables:

The SI unit of density is kilograms per cubic metre (kg/m³). In chemistry and everyday contexts, grams per cubic centimetre (g/cm³) is equally common and is numerically equal to grams per millilitre (g/mL) and kilograms per litre (kg/L).

Worked example: finding density

A block of aluminium has a mass of 2.7 kg and a volume of 1 litre (0.001 m³). What is its density?

Converting: 2,700 kg/m³ = 2.7 g/cm³. This matches the known density of aluminium (2.70 g/cm³), confirming the calculation.

Worked example: finding volume

You need to find the volume of a gold ingot that weighs 400 grams. Gold's density is 19.3 g/cm³.

A 400 gram bar of gold is smaller than a matchbox. This is why gold is so valuable per unit volume — it is extraordinarily dense.

Why objects float or sink: Archimedes' principle

An object floats in a fluid if its average density is less than the density of the fluid. This is Archimedes' principle: a submerged object displaces a volume of fluid equal to its own volume, and experiences a buoyant force equal to the weight of that fluid.

• Wood (500–900 kg/m³) floats on water (1000 kg/m³) because its density is less than water's.
• Steel (7,850 kg/m³) sinks in water, yet a steel ship floats because its overall average density (steel hull + air inside) is less than water.
• Hot-air balloons rise because heated air is less dense than the surrounding cooler air — the balloon's total average density falls below that of the atmosphere.
• Helium balloons rise because helium (0.164 kg/m³) is far less dense than air (1.225 kg/m³).

Density and temperature

Density is not fixed — it changes with temperature and pressure. Most materials expand when heated (thermal expansion), increasing volume while mass stays constant, which reduces density. Water is a famous exception: it is densest at 4°C (999.97 kg/m³) and expands when cooled further to 0°C (ice at 917 kg/m³), which is why ice floats.

Gases are highly compressible: doubling the pressure (at constant temperature) roughly doubles the density. The density of air at sea level is about 1.225 kg/m³, but at 10,000 metres altitude it falls to about 0.414 kg/m³, which is why high-altitude mountaineers experience "thin air."

Specific gravity

Specific gravity (SG), also called relative density, is the ratio of a substance's density to the density of a reference substance (usually water at 4°C = 1,000 kg/m³ = 1.000 g/cm³):

Because the reference density is 1 g/cm³, specific gravity is numerically equal to density in g/cm³ and is dimensionless. Materials with SG > 1 sink in water; materials with SG < 1 float. This makes specific gravity a quick check without needing units.

Applications of density

• Material identification: Every pure substance has a characteristic density. Measuring the density of an unknown sample and comparing it to reference values can identify the material (or detect counterfeits — a fake gold coin will have a lower density than pure gold).
• Engineering and construction: Structural engineers use density to calculate the weight of beams, slabs, and columns from their dimensions. Getting density wrong can lead to catastrophic underestimates of structural loads.
• Medicine: Bone mineral density (BMD) scans measure how compact bone tissue is — lower-than-normal density indicates osteoporosis. Blood density and urine density are diagnostic markers for various conditions.
• Food science: The density of liquids like milk, beer, and wine is used for quality control and to measure concentration. Hydrometers (floats that sink to a calibrated depth) measure density directly.
• Geology: Rock and mineral densities help geophysicists model Earth's interior. Seismic wave velocities depend on rock density and elastic moduli.

Unit conversions at a glance

Disclaimer

Results are calculated from the values you enter. Reference densities are approximate values at standard conditions (20°C, 1 atm) unless otherwise noted. Actual values vary with temperature, pressure, purity, and alloy composition.