Formula
Density is the mass per unit volume: ρ = m / V.
ENT-level problem
Find the buoyant force acting on a steel ball of volume $V = 0.001$ m³ that is fully submerged in water. The density of water is $\rho = 1000$ kg/m³, $g = 10$ m/s².
By Archimedes' law the buoyant force equals the weight of the water displaced by the body:
$$F = \rho g V = 1000 \cdot 10 \cdot 0.001 = 10 \text{ N}$$
Density shows how much mass fits into a unit of volume. In SI it is measured in kilograms per cubic metre (kg/m³); for liquids and solids grams per cubic centimetre are often used.
Density does not depend on the size of the body: a chip of ice and an iceberg made of the same ice have the same density. Water has 1000 kg/m³ (1 g/cm³); ice is lighter than water, which is why it floats.
In SI — kg/m³. Also commonly g/cm³: 1 g/cm³ = 1000 kg/m³.
Pure water at 4 °C has 1000 kg/m³ (1 g/cm³). It serves as the reference when comparing densities.
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