Energy and particles · GCSE Physics
Density
Teacher-written GCSE Physics revision on density: ρ = m/V with mass in kilograms and volume in cubic metres, plus the required practical for regular and irregular solids and liquids.
Density is mass over volume. Convert to kilograms and cubic metres, or keep grams and centimetres cubed together — never mix them.
The important bits
What you need to know
- 1
Density ρ = m / V. SI units: kilograms per cubic metre (kg/m³). Grams per cubic centimetre (g/cm³) are also used: 1 g/cm³ = 1000 kg/m³.
- 2
Solids are usually denser than liquids, which are denser than gases, because particles are closer together. Ice is an exception: it is less dense than water, so it floats.
- 3
For a regular solid, measure mass on a balance and find volume from lengths (cube, cuboid, cylinder). Repeat lengths and average.
- 4
For an irregular solid, measure mass, then find volume from the displacement of water in a measuring cylinder or a eureka can.
- 5
For a liquid, measure the mass of a measuring cylinder, add a known volume of liquid, then subtract to get the mass of liquid. ρ = m/V.
- 6
1 cm³ = 1 × 10⁻⁶ m³. 1 ml = 1 cm³. Mixing cm³ with kilograms is the usual way to get an answer 1 000 000 times too big or too small.
- 7
Density is a property of the material, not of the size of the sample. Halving the mass and the volume leaves ρ unchanged.
- 8
Floating: an object floats on a liquid if its average density is less than the density of the liquid.
Quotations worth analysing
Short evidence. Real method.
“Density = mass / volume”
The triangle is only useful after the units match. Write m in kg and V in m³, or both in g and cm³, then divide.
“The density of a material is the mass per unit volume.”
Per unit volume is the point: two blocks of the same metal have the same density even if one is larger, because mass and volume scale together.
Go deeper
The density practical is a measurement story, not a formula recitation
Mass is the easy part: zero the balance, place the object, record to the precision of the instrument, repeat if the question asks. Volume is where marks leak. A regular cuboid needs three lengths, each repeated, then V = l × w × h. An irregular stone needs displacement: the rise in water level is the volume, but the stone must be fully submerged and not splash. A eureka can pours the displaced water into a measuring cylinder, which is cleaner for larger objects. For a liquid, subtract the empty-cylinder mass. Then calculate ρ = m/V and give the unit that matches the measurements. Two or three repeats, then a mean, is what “take repeats” is for: spotting a rogue splash, not decorating the table.
Go deeper
Unit conversions decide whether the number is believable
Water is about 1.0 g/cm³ or 1000 kg/m³. If you calculate 0.001 kg/m³ or 1 000 000 g/cm³, the conversion has gone wrong. 1 cm³ = 1 × 10⁻⁶ m³, so a 25 cm³ rubber stopper is 2.5 × 10⁻⁵ m³. A 20 g stopper is 0.020 kg, so ρ = 0.020 / 2.5 × 10⁻⁵ = 800 kg/m³, which is a sensible polymer. Staying in grams and centimetres cubed gives 20 / 25 = 0.80 g/cm³, the same material. Pick one system and stay in it. Ice at about 920 kg/m³ is less dense than water, which is why icebergs float — a particle-model exception students should be ready to name.
See the idea in action
A metal cube has mass 0.216 kg. Each side is 3.0 cm = 0.030 m. Volume V = 0.030³ = 2.7 × 10⁻⁵ m³. Density ρ = m/V = 0.216 / 2.7 × 10⁻⁵ = 8000 kg/m³. Checking in centimetres: mass = 216 g, V = 27 cm³, ρ = 216 / 27 = 8.0 g/cm³, which is 8000 kg/m³. The two unit systems agree, so the conversion is safe.
Exam technique
Turn knowledge into marks
Show mass and volume measurements, then ρ = m/V with units. Convert 1 cm³ = 1 × 10⁻⁶ m³ if you need kg/m³. For irregular objects, write that the displaced water volume equals the object’s volume.
Common mistakes
Do not give these marks away
- 01
Mixing cm³, ml and m³ in the same line, or using mass in grams with volume in cubic metres.
- 02
Forgetting to subtract the empty measuring cylinder when finding the mass of a liquid.
- 03
Saying a larger block of the same metal is denser because it is heavier.
A 0.040 kg object displaces 20 cm³ of water. What is its density in kg/m³?
A2.0 kg/m³
B800 kg/m³
C2000 kg/m³
D8000 kg/m³
Show the answer
2000 kg/m³. 20 cm³ = 20 × 10⁻⁶ m³ = 2.0 × 10⁻⁵ m³. ρ = 0.040 / 2.0 × 10⁻⁵ = 2000 kg/m³. 800 kg/m³ would be 50 cm³; 2.0 kg/m³ forgot the conversion.
Quick questions
If this is the bit you searched
How do you measure the density of an irregular object?
Measure mass on a balance. Find volume from the displacement of water in a measuring cylinder or eureka can, then use ρ = m/V.
Why is ice less dense than water?
As water freezes, the particle arrangement becomes more open, so the same mass occupies a larger volume. That is why ice floats.
What are the SI units of density?
Kilograms per cubic metre (kg/m³). Grams per cubic centimetre are often easier in a school lab: 1 g/cm³ = 1000 kg/m³.
Does cutting an object in half change its density?
No. Mass and volume both halve, so ρ = m/V stays the same for a uniform material.