Density
Density tells you how much mass is packed into a given volume. One formula, one experiment, and a set of unit conversions that cause most of the lost marks.
1. The formula
Density = mass ÷ volume ρ = m / V
Units: kg/m³, or g/cm³.
Rearranged: m = ρ V and V = m / ρ
Example: a block of mass 240 g and volume 30 cm³.
- ρ = 240 ÷ 30 = 8 g/cm³
Use MASS, not weight. Density is mass per unit volume — confusing the two was a recorded error. Mass is in kg or g; weight is a force in newtons.
Keep your units consistent: kg with m³, or g with cm³. Mixing them is the most common error here.
2. Density is a property of the material
Density does NOT change when you change the amount of a substance.
A small block of aluminium and a large one have the same density. If you double the volume, you also double the mass, so the ratio is unchanged.
Two opposite errors were recorded here: thinking density and volume have no relationship, and thinking that if volume increases, density increases. Neither is right. For a fixed mass, density and volume are inversely related — but for the same material, density is simply constant.
Typical values:
| Substance | Density |
|---|---|
| Water | 1000 kg/m³ = 1 g/cm³ |
| Air | 1.2 kg/m³ |
| Aluminium | 2700 kg/m³ |
| Iron | 7900 kg/m³ |
| Gold | 19 300 kg/m³ |
Water’s density — 1 g/cm³ or 1000 kg/m³ — is worth memorising. It is the reference for floating and sinking, and it appears constantly.
3. Unit conversion
1 g/cm³ = 1000 kg/m³
Why: 1 m³ = 100 × 100 × 100 = 1 000 000 cm³, and 1 kg = 1000 g, so the factor is 1 000 000 ÷ 1000 = 1000.
Volume conversions:
- 1 m³ = 1 000 000 cm³
- 1 cm³ = 1 ml
- 1000 cm³ = 1 litre
Volume conversions CUBE the length factor. Going from cm to m divides lengths by 100, so volumes divide by 100³ = 1 000 000. Confusion converting centimetres to metres for a volume was a recorded error.
Convert to kilograms and cubic metres if the question wants SI units — tutors flagged this specifically.
4. Measuring density
Regular solid
- Measure the mass on a balance
- Measure the dimensions with a ruler and calculate the volume (l × w × h for a cuboid)
- ρ = m / V
Irregular solid — the displacement method
- Measure the mass on a balance
- Part-fill a measuring cylinder with water; record V₁
- Fully submerge the object; record V₂
- Volume = V₂ − V₁
- ρ = m / V
The object must be fully submerged and must sink. For a floating object, hold it under with a thin rod, or use a displacement (eureka) can and collect the overflow.
Be ready to describe this experiment in words. Tutors noted it is an “explanatory question” — you may be asked to explain how you would determine the density, so learn the steps as a method, not just a formula.
Liquid
- Measure the mass of an empty measuring cylinder
- Pour in the liquid and record the volume
- Measure the mass again
- Mass of liquid = final − empty
- ρ = m / V
Subtract the container’s mass. Forgetting this is the standard error in the liquid method.
Improving accuracy:
Take two or three readings and average them — advice given directly in lessons. Also read the bottom of the meniscus at eye level, and dry the object before weighing it.
5. Floating and sinking
An object floats if its density is less than the density of the fluid. It sinks if its density is greater.
So anything with density under 1000 kg/m³ floats in water.
Why a steel ship floats: steel is far denser than water, but the ship is hollow. Its average density — including the air inside — is less than water’s, so it floats.
Why oil floats on water: oil is less dense (≈ 900 kg/m³).
Density and temperature: heating usually makes a substance expand, so the same mass occupies a larger volume and the density decreases. This is what drives convection currents.
6. Mistakes that cost marks
Using weight instead of mass.
Mixing units — g with m³, or kg with cm³.
Converting volume with a linear factor instead of cubing.
Thinking density changes with the amount of a substance.
Not fully submerging the object in the displacement method.
Forgetting to subtract the container mass for a liquid.
Reading the top of the meniscus.
Comparing to the wrong value for water’s density.
Omitting units.
Frequently asked questions
What is the formula for density? ρ = m / V — mass divided by volume.
What are the units? kg/m³ or g/cm³.
What is the density of water? 1000 kg/m³, or 1 g/cm³.
How do I convert g/cm³ to kg/m³? Multiply by 1000.
Does density change if I use more of the substance? No — density is a property of the material.
How do I find the density of an irregular object? Measure its mass, then find its volume by displacement, and divide.
How do I find the density of a liquid? Measure the mass of the cylinder empty and full, subtract, and divide by the volume.
When does an object float? When its density is less than that of the fluid.
Why does a steel ship float? Its average density, including the air inside, is less than water’s.
What happens to density when a substance is heated? It usually decreases, because the substance expands.
Quick revision checklist
- I know ρ = m/V and can rearrange it
- I know the units and keep them consistent
- I use mass, not weight
- I know water is 1000 kg/m³ = 1 g/cm³
- I can convert between g/cm³ and kg/m³
- I cube the factor for volume conversions
- I know density doesn’t depend on the amount
- I can describe the method for a regular solid
- I can describe the displacement method in full
- I can describe the method for a liquid, subtracting the container mass
- I know how to improve accuracy
- I can predict floating and sinking
- I can explain why a steel ship floats
- I give units on every answer
These notes cover density in the Cambridge IGCSE Physics (0625) syllabus and are written for Grade 9–11 / Year 10–11 students. They are based on teaching patterns observed across a large set of one-to-one IGCSE Physics lessons, with particular attention to the errors students make most often and the wording examiners reward. Always check the current syllabus and formula list for your own exam series.
Finished this topic?
Saved on this device — no account needed.