Density is a physical quantity that tells us how much mass fits into a unit of volume of a given substance. It lets us tell materials apart, check whether an object will sink in water, and convert mass into volume and back. In this article we show the density formula, the SI units, and the calculations using a concrete example.
The density formula
Density, denoted by the Greek letter ρ (rho), is calculated by dividing the mass of a body by its volume:
- ρ = m / V — density equals mass divided by volume
- m = ρ × V — mass equals density times volume
- V = m / ρ — volume equals mass divided by density
These three rearrangements of the same formula are enough to solve most problems.
SI units
In the SI system density is expressed in kilograms per cubic metre (kg/m³). In laboratory practice grams per cubic centimetre (g/cm³) are used more often. The conversion is simple:
- 1 g/cm³ = 1000 kg/m³
- Mass m — kilogram (kg) or gram (g)
- Volume V — cubic metre (m³), litre (l) or cubic centimetre (cm³)
For reference: the density of water is 1000 kg/m³ (1 g/cm³), and that of iron is about 7870 kg/m³.
Worked example
We have a metal cube with a mass of m = 540 g and a volume of V = 200 cm³. We calculate the density.
- We apply the formula ρ = m / V.
- We substitute: ρ = 540 g / 200 cm³.
- We calculate: ρ = 2.7 g/cm³.
- In SI units: ρ = 2.7 × 1000 = 2700 kg/m³.
A density of 2.7 g/cm³ corresponds to aluminium. This shows that density helps identify materials.
Will an object sink?
Comparing the density of a body with the density of a liquid tells us whether the body floats or sinks:
- When the body's density is lower than the liquid's density — the body floats.
- When the body's density is higher — the body sinks.
- When the densities are equal — the body stays suspended.
Wood (about 700 kg/m³) floats on water because its density is lower than 1000 kg/m³, while the aluminium cube from our example will sink.
How to measure volume?
For regular solids we calculate the volume using geometric formulas, for example a rectangular block V = a × b × c. For irregular solids we use the displacement method: we place the body into a measuring cylinder with water and read off the rise in the liquid level.
Second example: finding the mass
We want to calculate the mass of 3 litres of cooking oil with a density of ρ = 920 kg/m³.
- We apply the formula m = ρ × V.
- We convert the volume into cubic metres: V = 3 l = 0.003 m³.
- We substitute: m = 920 × 0.003.
- We calculate: m = 2.76 kg.
Three litres of oil weigh 2.76 kg, that is less than three litres of water (3 kg), because oil has a lower density.
Density of typical substances
For comparison it is worth knowing the approximate densities:
- Air — about 1.2 kg/m³
- Pine wood — about 500 kg/m³
- Water — 1000 kg/m³
- Aluminium — 2700 kg/m³
- Iron — 7870 kg/m³
- Gold — 19 300 kg/m³
These values let you quickly judge whether a calculated density makes physical sense.
Most common mistakes
- Inconsistent units — grams with cubic metres give a wrong result. Reduce the data to a single system.
- Confusing mass with weight — mass is in kilograms, while weight is a force in newtons.
- Wrong rearrangement — when looking for volume we divide mass by density, not the other way around.
- Confusing litres with cubic metres — 1 m³ is 1000 litres.
Frequently asked questions
- Does density depend on temperature? Yes. Most substances expand when heated, so their density decreases. Data is usually given for a temperature of 20°C.
- Why does ice float on water? Ice has a lower density (about 917 kg/m³) than liquid water (1000 kg/m³), which is why it floats on the surface.
- Which unit should I choose? In school problems g/cm³ is convenient, while in engineering calculations kg/m³ is used.
Summary
Density ρ = m / V is the ratio of mass to volume. In the SI system we measure it in kg/m³, and in the laboratory in g/cm³ (1 g/cm³ = 1000 kg/m³). Knowing two of the three quantities, you can easily find the third and check what material you are dealing with.
Work out density, mass or volume: Density Calculator →