Physics

9.1 - Density

6 min

Density and its units

Calculating a volume

Measuring a solid's density

Measuring a liquid's density

note 1 of 3

What density is and what it depends on

Density is the mass per unit volume of a substance - a measure of how tightly packed its particles are.
Density depends on what a material is made of and how its particles are arranged - the more tightly packed the particles, the denser the material.
Solids are generally the densest state of matter, liquids slightly less dense, and gases much less dense.

Three boxes of particles labelled solids, liquids and gases, packed tightest to loosest from left to right, above a green double-headed arrow labelled density running from most to least.

Density depends on the material, not the size or shape

Density is a property of the material itself.
A large block of iron and a small iron nail have the same density, even though their masses and volumes are different.
Cutting an object in half halves both its mass and its volume, so its density stays the same.

note 2 of 3

Formula for density

$ρ = \frac{m}{V}$

Where:

$ρ$ = Density, using the Greek letter rho, in kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³)
$m$ = Mass, in kilograms (kg) or grams (g)
$V$ = Volume, in cubic metres (m³) or cubic centimetres (cm³)

Converting between units

1 g/cm³ = 1,000 kg/m³

For example, water has a density of 1 g/cm³, which equals 1,000 kg/m³.

note 3 of 3

Worked example - Using the density formula

Copper has a density of 9.0 g/cm³. Find the mass of 5 cm³ of copper.

Step 1 - Formula

$ρ = \frac{m}{V}$

Step 2 - Rearrange the formula

Make mass the subject:

$m = ρ \times V$

Step 3 - Substitution and calculation

$m = 9.0 \times 5 = 45 g$

So 5 cm³ of copper has a mass of 45 g.

The mass and volume must be in units that match the density. Here density is in g/cm³, so mass is in grams and volume in cubic centimetres.

key terms

TermDefinition

DensityThe mass per unit volume of a substance.

end of notes

Key points to remember

What density is and what it depends on

Density is the mass per unit volume of a substance - a measure of how tightly packed its particles are.

Density depends on what a material is made of and how its particles are arranged - the more tightly packed the particles, the denser the material.

Solids are generally the densest state of matter, liquids slightly less dense, and gases much less dense.

Formula for density

$ρ = \frac{m}{V}$

Where:

ρ

= Density, using the Greek letter rho, in kilograms per cubic metre (kg/m³) or grams per cubic centimetre (g/cm³)

m

= Mass, in kilograms (kg) or grams (g)

V

= Volume, in cubic metres (m³) or cubic centimetres (cm³)

Converting between units

1 g/cm³ = 1,000 kg/m³

For example, water has a density of 1 g/cm³, which equals 1,000 kg/m³.

Worked example - Using the density formula

Copper has a density of 9.0 g/cm³. Find the mass of 5 cm³ of copper.

Step 1 - Formula

$ρ = \frac{m}{V}$

Step 2 - Rearrange the formula

Make mass the subject:

$m = ρ \times V$

Step 3 - Substitution and calculation

$m = 9.0 \times 5 = 45 g$

So 5 cm³ of copper has a mass of 45 g.

The mass and volume must be in units that match the density. Here density is in g/cm³, so mass is in grams and volume in cubic centimetres.