What is density and how is it calculated in Physics?

Density is a measure of how much mass is contained in a given volume. It is calculated using the formula: Density = Mass/Volume. In the context of Cambridge IGCSE Physics, understanding density is crucial for solving problems related to Motion, Forces, and Energy, as it helps determine how substances interact with each other.

Why is density important in the study of Motion, Forces, and Energy?

Density plays a vital role in the study of Motion, Forces, and Energy because it affects how objects move and interact. For instance, an object's buoyancy in a fluid is determined by its density relative to the fluid. In Cambridge IGCSE Physics, understanding density helps explain phenomena such as why some objects float while others sink, and how density affects the speed and behavior of moving objects.

How does temperature affect the density of a substance?

Temperature can significantly affect the density of a substance. Generally, as temperature increases, the density of a substance decreases because the particles move faster and spread apart, increasing the volume. This concept is important in Cambridge IGCSE Physics when studying the effects of heat on materials and their subsequent impact on motion and energy transfer.

What are some common methods to measure the density of an irregular object?

To measure the density of an irregular object, one common method is to use water displacement to find the object's volume. First, measure the mass of the object using a balance. Then, submerge the object in a graduated cylinder filled with water and measure the volume of water displaced. The density can then be calculated using the formula: Density = Mass/Volume. This method is often discussed in Cambridge IGCSE Physics practical experiments.

How does density relate to the concept of buoyancy in Physics?

Density is directly related to buoyancy, which is the force that allows objects to float or sink in a fluid. An object will float if its density is less than the fluid's density and sink if it is more. Understanding this relationship is crucial in Cambridge IGCSE Physics, as it helps explain the principles behind ships floating, hot air balloons rising, and the behavior of various materials in different fluids.

Why is "Mixing $\text{g/cm}^{3}$ with $\text{kg/m}^{3}$" a common mistake in Density?

Why it happens: Different question parts use different units. How to avoid it: Convert: 1\,g/cm^3 = 1000\,kg/m^3. Source: 0625/42 — recurring

Why is "Using surface area instead of volume" a common mistake in Density?

Why it happens: Mixing up cm² and cm³. How to avoid it: Volume of a cuboid is l × w × h — three dimensions.

Why is "Inverting the formula ($V/m$)" a common mistake in Density?

Why it happens: Misremembering which is on top. How to avoid it: Density is mass PER unit volume — so mass on top.

Why is "Saying a denser object floats on a less dense one" a common mistake in Density?

Why it happens: Inverting the rule. How to avoid it: Floats only if object density is LESS than fluid density.

Motion, Forces and EnergyCambridge IGCSE Physics (0625)

Density

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Density — Cambridge IGCSE 0625 Physics Extended (2026)

Mass per unit volume. Use $\rho = m/V$ to predict whether something floats. The trickier part is measuring volume of irregular solids and reading the meniscus correctly.

What you’ll learn

Mapped to the Cambridge IGCSE 0625 syllabus (2026-2028).

1.5 — Recall and use $\rho = m/V$ .
1.5 — Describe how to measure the density of a regular and irregular solid, and a liquid.
1.5 — Predict whether an object floats based on density data.

The density formula

$\rho = m/V$ . Two units: $\text{kg/m}^{3}$ and $\text{g/cm}^{3}$ .

$\rho = \dfrac{m}{V}.$

$\rho$ : density ( $\text{kg/m}^{3}$ or $\text{g/cm}^{3}$ ).
$m$ : mass ( $\text{kg}$ or $\text{g}$ ).
$V$ : volume ( $\text{m}^{3}$ or $\text{cm}^{3}$ ).

Worked. A block has mass $240\,\text{g}$ and volume $30\,\text{cm}^{3}$ .

$\rho = 240/30 = 8\,\text{g/cm}^{3} = 8000\,\text{kg/m}^{3}$ .

Conversion. $1\,\text{g/cm}^{3} = 1000\,\text{kg/m}^{3}$ . Water is the easy one to remember: $1\,\text{g/cm}^{3} = 1000\,\text{kg/m}^{3}$ .

$\rho = m/V$ .
Units must be consistent.
$1\,\text{g/cm}^{3} = 1000\,\text{kg/m}^{3}$ .
Water density: $1000\,\text{kg/m}^{3}$ .

Measuring density experimentally

Mass on a balance, volume by geometry (regular) or displacement (irregular).

Regular solid.

Mass: weigh on a balance.
Volume: measure dimensions, calculate (e.g. $V = lwh$ ).
$\rho = m/V$ .

Irregular solid.

Mass: weigh on a balance.
Volume: water-displacement method.
- Half-fill a measuring cylinder, record $V_{1}$ .
- Lower object in (fully submerged), record $V_{2}$ .
- Volume $= V_{2} - V_{1}$ .
$\rho = m/V$ .

Liquid.

Mass empty measuring cylinder.
Pour in a known volume, mass again.
Mass of liquid = (mass + cylinder) − (cylinder).
$\rho = m/V$ .

Worked. Empty cylinder: $80\,\text{g}$ . With $50\,\text{cm}^{3}$ liquid: $124\,\text{g}$ .

Mass of liquid: $124 - 80 = 44\,\text{g}$ .
$\rho = 44/50 = 0.88\,\text{g/cm}^{3}$ .

Regular solid: geometry for volume.
Irregular solid: water displacement.
Liquid: cylinder + balance.
Always read meniscus at the bottom.

Floating and sinking

Object floats if its density is less than the fluid's density.

Rule. An object placed in a fluid will:

Float if its density is less than the fluid's.
Sink if its density is greater than the fluid's.
Stay where placed (suspended) if equal.

Worked. A wooden block has density $0.6\,\text{g/cm}^{3}$ . Will it float in water ( $1\,\text{g/cm}^{3}$ )?

$0.6 < 1$ → floats.

Worked. Iron has density $7.9\,\text{g/cm}^{3}$ . In water it sinks.

Hot vs cold liquids. Heating a liquid usually decreases its density (particles spread out). That's why hot air rises, and convection currents form.

Floats: $\rho_{\text{object}} < \rho_{\text{fluid}}$ .
Sinks: $\rho_{\text{object}} > \rho_{\text{fluid}}$ .
Hot fluid is less dense than cold (usually).

How it’s examined

Density appears every Paper 2 (2-3 marks: calculate or compare densities) and most Paper 4s as part of a multi-step practical question. Examiner reports flag two errors: unit confusion ( $\text{g/cm}^{3}$ vs $\text{kg/m}^{3}$ ), and meniscus mis-readings on the volume.

Sources: Cambridge IGCSE Physics 0625 syllabus 2026-2028 (1.5); 0625/42 Oct/Nov 2024 — Q5 (density practical); 0625 Examiner Reports 2022-2024. Last reviewed 2026-05-06.

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Step-by-step worked examples — Density

Step-by-step solutions to past-paper-style questions on density, written exactly the way a tutor would explain them at the board.

1Density of a regular solid
Core• regular
Question
A metal block has dimensions $4\,\text{cm} \times 5\,\text{cm} \times 2\,\text{cm}$ and mass $312\,\text{g}$ . Find its density.
Step-by-step solution
1. Step 1
  Volume.
  $V = 4 \times 5 \times 2 = 40\,\text{cm}^{3}$
2. Step 2
  $\rho = \dfrac{m}{V}$ .
  $\rho = \dfrac{312}{40} = 7.8\,\text{g/cm}^{3}$
Answer
$7.8\,\text{g/cm}^{3}$ (likely iron)
2Density of an irregular solid
Extended• Adapted from 0625/42 May/Jun 2024 Q4• irregular
Question
A stone of mass $135\,\text{g}$ is lowered into water in a measuring cylinder; the level rises from $50\,\text{cm}^{3}$ to $95\,\text{cm}^{3}$ . Find the density.
Step-by-step solution
1. Step 1
  Volume by displacement.
  $V = 95 - 50 = 45\,\text{cm}^{3}$
2. Step 2
  Density.
  $\rho = \dfrac{135}{45} = 3.0\,\text{g/cm}^{3}$
Answer
$3.0\,\text{g/cm}^{3}$
3Float or sink prediction
Extended• floating
Question
Object: density $0.8\,\text{g/cm}^{3}$ . Liquid: water ( $1.0\,\text{g/cm}^{3}$ ). Will it float?
Step-by-step solution
1. Step 1
  Object density < liquid density → floats.
Answer
Yes — it floats.
4Find mass from density and volume
Core• rearrange
Question
$200\,\text{cm}^{3}$ of mercury has density $13.6\,\text{g/cm}^{3}$ . Find the mass.
Step-by-step solution
1. Step 1
  $m = \rho V$ .
  $m = 13.6 \times 200 = 2720\,\text{g}$
Answer
$2720\,\text{g} = 2.72\,\text{kg}$
5Density of a regular cylinder
Core• regular, cylinder
Question
A solid metal cylinder has radius $2.0\,\text{cm}$ , height $10\,\text{cm}$ and mass $354\,\text{g}$ . Find its density. Take $\pi = 3.14$ .
Step-by-step solution
1. Step 1
  Volume of cylinder $V = \pi r^{2} h$ .
  $V = 3.14 \times (2.0)^{2} \times 10 = 125.6\,\text{cm}^{3}$
2. Step 2
  Density.
  $\rho = \dfrac{354}{125.6} \approx 2.82\,\text{g/cm}^{3}$
Answer
$\rho \approx 2.82\,\text{g/cm}^{3}$
6Convert density from $\text{g/cm}^{3}$ to $\text{kg/m}^{3}$
Extended• Adapted from 0625/22 May/Jun 2023 Q5• units, conversion
Question
Aluminium has density $2.7\,\text{g/cm}^{3}$ . Convert this to SI units, and find the mass of $0.5\,\text{m}^{3}$ of aluminium.
Step-by-step solution
1. Step 1
  Use $1\,\text{g/cm}^{3} = 1000\,\text{kg/m}^{3}$ .
  $\rho = 2.7 \times 1000 = 2700\,\text{kg/m}^{3}$
2. Step 2
  $m = \rho V$ in SI.
  $m = 2700 \times 0.5 = 1350\,\text{kg}$
Answer
$\rho = 2700\,\text{kg/m}^{3}$ ; $m = 1350\,\text{kg}$ .
Examiner tip
The examiner report flags candidates often forget the factor of $1000$ in the unit conversion and quote $2.7\,\text{kg/m}^{3}$ — three orders of magnitude wrong.
7Predict floating with density comparison
Extended• floating, concept
Question
A block of mass $480\,\text{g}$ has dimensions $10\,\text{cm} \times 8\,\text{cm} \times 6\,\text{cm}$ . Will it float in water ( $1.0\,\text{g/cm}^{3}$ ) and in mercury ( $13.6\,\text{g/cm}^{3}$ )?
Step-by-step solution
1. Step 1
  Volume.
  $V = 10 \times 8 \times 6 = 480\,\text{cm}^{3}$
2. Step 2
  Block density.
  $\rho = \dfrac{480}{480} = 1.0\,\text{g/cm}^{3}$
3. Step 3
  Compare. In water, $\rho_{\text{block}} = \rho_{\text{water}}$ — the block JUST floats (neutrally buoyant). In mercury, $\rho_{\text{block}} < \rho_{\text{mercury}}$ — it floats easily.
Answer
In water: neutrally buoyant. In mercury: floats.
8Find a missing dimension given the density
Extended• rearrange, geometry
Question
A rectangular brass slab of density $8.4\,\text{g/cm}^{3}$ has mass $672\,\text{g}$ and a square base of side $4.0\,\text{cm}$ . Find its thickness.
Step-by-step solution
1. Step 1
  Volume from $V = m/\rho$ .
  $V = \dfrac{672}{8.4} = 80\,\text{cm}^{3}$
2. Step 2
  Thickness from volume = base area × thickness.
  $t = \dfrac{V}{A} = \dfrac{80}{4.0 \times 4.0} = 5.0\,\text{cm}$
Answer
Thickness $= 5.0\,\text{cm}$
Examiner tip
The 2024 mark scheme awards method marks for explicit rearrangement of $\rho = m/V$ before substituting numbers.
9Average density of a solid plus liquid mixture
Extended• mixture, concept
Question
A flask contains $300\,\text{g}$ of water ( $\rho = 1.0\,\text{g/cm}^{3}$ ) and a sealed sand bag of $400\,\text{g}$ with volume $200\,\text{cm}^{3}$ . Find the average density of the contents.
Step-by-step solution
1. Step 1
  Water volume.
  $V_{w} = \dfrac{300}{1.0} = 300\,\text{cm}^{3}$
2. Step 2
  Total mass and volume.
  $m_{T} = 300 + 400 = 700\,\text{g};\ V_{T} = 300 + 200 = 500\,\text{cm}^{3}$
3. Step 3
  Average density.
  $\rho_{\text{avg}} = \dfrac{700}{500} = 1.4\,\text{g/cm}^{3}$
Answer
$1.4\,\text{g/cm}^{3}$
10A* — overall density of a hollow shape
Challenge• hollow, synoptic
Question
A spherical metal shell of outer radius $5.0\,\text{cm}$ and inner radius $4.0\,\text{cm}$ has mass $1240\,\text{g}$ . Find (a) the density of the metal it is made from and (b) its average density (treating the air cavity as massless). Take $\pi = 3.14$ .
Step-by-step solution
1. Step 1
  Outer volume.
  $V_{\text{out}} = \tfrac{4}{3}\pi (5.0)^{3} \approx 523\,\text{cm}^{3}$
2. Step 2
  Inner volume.
  $V_{\text{in}} = \tfrac{4}{3}\pi (4.0)^{3} \approx 268\,\text{cm}^{3}$
3. Step 3
  Volume of metal alone.
  $V_{\text{metal}} = 523 - 268 = 255\,\text{cm}^{3}$
4. Step 4
  Density of the metal.
  $\rho_{\text{metal}} = \dfrac{1240}{255} \approx 4.86\,\text{g/cm}^{3}$
5. Step 5
  Average density uses outer volume.
  $\rho_{\text{avg}} = \dfrac{1240}{523} \approx 2.37\,\text{g/cm}^{3}$
Answer
Metal density $\approx 4.86\,\text{g/cm}^{3}$ ; average density $\approx 2.37\,\text{g/cm}^{3}$ .
Examiner tip
The examiner report flags candidates often divide total mass by total (outer) volume to get the metal's density — that mixes the two questions. Subtract the cavity volume for the material's density.

Key Formulae — Density

The formulae you need to memorise for density on the Cambridge IGCSE 0625 paper, with every variable defined in plain English and a note on when to use it.

Density
$\rho = \dfrac{m}{V}$
$\rho$
density (kg/m³ or g/cm³)
$m$
mass
$V$
volume
When to use
Density problems for any homogeneous substance.
Density unit conversion
$1\,\text{g/cm}^{3} = 1000\,\text{kg/m}^{3}$
When to use
Switching between $\text{g/cm}^{3}$ and $\text{kg/m}^{3}$ .

Key Definitions and Keywords — Density

Definitions to memorise and the exact keywords mark schemes credit for density answers — sharpened from recent examiner reports for the 2026 0625 sitting.

Density
Examiner keyword
Mass per unit volume of a substance.
Volume by displacement
Examiner keyword
Volume of an irregular object found from the rise in water level when fully submerged.

Common Mistakes and Misconceptions — Density

The traps other students keep falling into on density questions — taken from recent Cambridge IGCSE 0625 examiner reports and mark schemes — and how to avoid them.

✕Mixing $\text{g/cm}^{3}$ with $\text{kg/m}^{3}$
0625/42 — recurring
Why it happens
Different question parts use different units.
How to avoid it
Convert: $1\,\text{g/cm}^{3} = 1000\,\text{kg/m}^{3}$ .
✕Using surface area instead of volume
Why it happens
Mixing up cm² and cm³.
How to avoid it
Volume of a cuboid is $l \times w \times h$ — three dimensions.
✕Inverting the formula ( $V/m$ )
Why it happens
Misremembering which is on top.
How to avoid it
Density is mass PER unit volume — so mass on top.
✕Saying a denser object floats on a less dense one
Why it happens
Inverting the rule.
How to avoid it
Floats only if object density is LESS than fluid density.

Practice questions

Exam-style questions with step-by-step worked solutions. Try one before checking the method.

Past paper style quiz

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Video lesson

Short walkthrough of the concepts students most often get stuck on.

Density — frequently asked questions

The things students keep getting wrong in this sub-topic, answered.

Density

Short Study Notes in the form of Slides

Detailed Study Notes

What you’ll learn

How it’s examined

1Density of a regular solid

2Density of an irregular solid

3Float or sink prediction

4Find mass from density and volume

5Density of a regular cylinder

6Convert density from g/cm3\text{g/cm}^{3}g/cm3 to kg/m3\text{kg/m}^{3}kg/m3

7Predict floating with density comparison

8Find a missing dimension given the density

9Average density of a solid plus liquid mixture

10A* — overall density of a hollow shape

Density

Density unit conversion

Density

Volume by displacement

✕Mixing g/cm3\text{g/cm}^{3}g/cm3 with kg/m3\text{kg/m}^{3}kg/m3

✕Using surface area instead of volume

✕Inverting the formula (V/mV/mV/m)

✕Saying a denser object floats on a less dense one

Practice questions

Past paper style quiz

Assess your understanding

Video lesson

Density — frequently asked questions

6Convert density from $\text{g/cm}^{3}$ to $\text{kg/m}^{3}$

✕Mixing $\text{g/cm}^{3}$ with $\text{kg/m}^{3}$

✕Inverting the formula ( $V/m$ )