Density and Pressure

Q: Do I get given the density and pressure formulae in the exam?

No, all three core formulae (, , ) must be recalled, as no formula sheet is provided for this specification.

Q: What value of g should I use for calculations?

Always use N/kg unless the question explicitly states a different value, per Edexcel IGCSE Physics guidance.

Q: How do I convert cm² to m² for pressure calculations?

To convert cm² to m², multiply by : e.g. cm² = m² = m².

Physics· Section 5, spec points 5.1, 5.3-5.7 (2017 spec)· 20 min read

1. Density: Definition, Formula and Unit Conversions★★☆☆☆⏱ 4 min

📘 Definition

Density

$ρ = \frac{m}{V}$

Density is the mass per unit volume of a substance, a characteristic property of a material that does not depend on the amount of substance present.

Example:

Water has a density of 1000 kg/m³, or 1 g/cm³.

All density calculations use the relationship $ρ = m / V$ , where $ρ$ = density, $m$ = mass, $V$ = volume. You must convert units carefully to avoid common errors: 1 g/cm³ = 1000 kg/m³, 1 cm³ = $1 0^{- 6}$ m³.

📐 Worked Example

Calculate the density of a block of aluminium with mass 2700 kg and volume 1 m³. Give your answer in both kg/m³ and g/cm³.

1
Step 1: Recall the density formula
$\rho = \frac{m}{V}$
2
Step 2: Substitute given values in SI units
$\rho = \frac{2700}{1} = 2700 \text{ kg/m}^3$
3
Step 3: Convert to g/cm³ by dividing by 1000
$\rho = \frac{2700}{1000} = 2.7 \text{ g/cm}^3$

2. Practical Investigation of Density★★★☆☆⏱ 5 min

You will be assessed on written descriptions of practical methods to measure the density of three types of material: regular solids, irregular solids, and liquids. All methods follow the same core principle: measure mass and volume separately, then calculate density using $ρ = m / V$ .

Regular solid: Measure mass using a top-pan balance. Measure dimensions using a ruler, calculate volume using the appropriate geometric formula, then compute density.
Irregular solid: Measure mass using a top-pan balance. Fill a eureka can to the spout with water, place a measuring cylinder under the spout, submerge the solid fully, measure displaced water volume, then compute density.
Liquid: Measure mass of an empty beaker, add a known volume of liquid from a measuring cylinder, remeasure total mass, subtract to find liquid mass, then compute density.

📐 Worked Example

A student uses the displacement method to find the density of a small stone. The stone has mass 150 g, and displaces 60 cm³ of water. Calculate the density of the stone in kg/m³.

1
Step 1: Convert mass to kg and volume to m³
$m = 150 \text{ g} = 0.15 \text{ kg}; V = 60 \text{ cm}^3 = 6 \times 10^{-5} \text{ m}^3$
2
Step 2: Apply the density formula
$\rho = \frac{0.15}{6 \times 10^{-5}} = 2500 \text{ kg/m}^3$

Exam tip:

For AO3 practical marks, always mention repeating measurements and calculating a mean to reduce random error, and confirming the object is fully submerged for displacement methods.

3. Pressure in Solids: Force over Area★★★☆☆⏱ 4 min

📘 Definition

Pressure

$p = \frac{F}{A}$

Pressure is the force acting per unit area perpendicular to a surface, measured in pascals (Pa), where 1 Pa = 1 N/m².

Example:

A sharp knife cuts more easily than a blunt one because the force acts over a smaller area, producing higher pressure.

For pressure calculations, $p$ = pressure (Pa), $F$ = force applied perpendicular to the surface (N), $A$ = area over which the force acts (m²). Remember to convert cm² to m² by multiplying by $1 0^{- 4}$ (e.g. 50 cm² = 0.005 m²).

📐 Worked Example

A 50 kg box rests on the floor, with a base area of 0.2 m². Calculate the pressure exerted by the box on the floor. Use $g = 10$ N/kg.

1
Step 1: Calculate the weight of the box (force acting on the floor)
$F = mg = 50 \times 10 = 500 \text{ N}$
2
Step 2: Apply the pressure formula
$p = \frac{F}{A} = \frac{500}{0.2} = 2500 \text{ Pa}$

4. Pressure in Static Fluids★★☆☆☆⏱ 3 min

Fluids (liquids and gases) at rest exert pressure that acts equally in all directions at any given point. This is why a hole in a water bottle will spray water outwards perpendicular to the bottle surface, regardless of the direction of the hole.

✓ Quick check

A scuba diver is 10 m below the surface of the sea. Which direction does the water pressure act on the diver's goggles?
- Only downwards
- Only upwards
- Equally in all directions
- Only sideways
Reveal answer
Equally in all directions —
Pressure in a static fluid acts equally in all directions at the same depth, so the goggles experience pressure from all sides.

5. Fluid Pressure Difference Calculations★★★★☆⏱ 4 min

📘 Definition

Fluid Pressure Difference

$p = h ρ g$

The pressure difference between two points in a static fluid depends only on the vertical height difference between the points, the density of the fluid, and the gravitational field strength. It is independent of the shape or cross-sectional area of the container.

Example:

The pressure at the bottom of a 1 m tall water tank is 10,000 Pa higher than the pressure at the top, regardless of how wide the tank is.

For these calculations, $p$ = pressure difference (Pa), $h$ = vertical height difference (depth) between the two points (m), $ρ$ = density of the fluid (kg/m³), $g$ = 10 N/kg unless stated otherwise.

📐 Worked Example

Calculate the pressure difference between the surface of a swimming pool and a point 2 m below the surface. The density of water is 1000 kg/m³, use $g = 10$ N/kg.

1
Step 1: Recall the fluid pressure difference formula
$p = h\rho g$
2
Step 2: Substitute the given values
$p = 2 \times 1000 \times 10 = 20000 \text{ Pa} = 20 \text{ kPa}$

Exam tip:

Always use vertical height for $h$ , not diagonal length if the container is sloped. The shape of the container does not affect the pressure difference, only the vertical depth matters.

6. Common Pitfalls

Wrong move:

Using g = 9.81 N/kg for calculations

Why:

The Edexcel IGCSE specification explicitly states to use g = 10 N/kg unless the question says otherwise, so using 9.81 will lead to incorrect answers and lost marks.

Correct move:

Always use g = 10 N/kg unless a different value is given in the question.

Wrong move:

Forgetting to convert cm² to m² for pressure calculations, using cm² directly in the formula

Why:

Pressure is in pascals, which is N/m², so area must be in m². Using cm² will give a value 10,000 times larger than the correct answer.

Correct move:

Multiply any area given in cm² by $1 0^{- 4}$ to convert to m² before substituting into $p = F / A$ .

Wrong move:

Using the volume of the container instead of displaced volume for irregular solid density calculations

Why:

The displacement method uses the volume of water pushed out by the solid, which equals the volume of the solid itself, not the total volume of the container.

Correct move:

Measure only the volume of water that flows out of the eureka can or the increase in water level in the measuring cylinder when the solid is submerged.

Wrong move:

Assuming pressure in a fluid only acts downwards

Why:

Pressure in a static fluid acts equally in all directions at a given depth, so objects under water experience pressure from all sides, not just above.

Correct move:

State that pressure acts equally in all directions when describing fluid pressure in exam answers.

Wrong move:

Converting g/cm³ to kg/m³ by multiplying by 100 instead of 1000

Why:

1 g/cm³ = 1000 kg/m³, as 1 kg = 1000 g and 1 m³ = 1,000,000 cm³, so the conversion factor is 1000.

Correct move:

Multiply density in g/cm³ by 1000 to get density in kg/m³, or divide kg/m³ by 1000 to get g/cm³.

7. Quick Reference Cheatsheet

Formula	Variables	Units to Use	Key Note
$ρ = m / V$	$ρ$ = density, $m$ = mass, $V$ = volume	$ρ$ : kg/m³ or g/cm³; $m$ : kg or g; $V$ : m³ or cm³	1 g/cm³ = 1000 kg/m³; match units to required output
$p = F / A$	$p$ = pressure, $F$ = force, $A$ = area	$p$ : Pa (N/m²); $F$ : N; $A$ : m²	Convert cm² to m²: × $1 0^{- 4}$ ; use only contact area
$p = h ρ g$	$p$ = pressure difference, $h$ = vertical height, $ρ$ = fluid density, $g$ = gravitational field strength	$p$ : Pa; $h$ : m; $ρ$ : kg/m³; $g$ : 10 N/kg	Independent of container shape; use vertical depth, not diagonal length

8. Frequently Asked

Do I get given the density and pressure formulae in the exam?

No, all three core formulae ( $ρ = m / V$ , $p = F / A$ , $p = h ρ g$ ) must be recalled, as no formula sheet is provided for this specification.

What value of g should I use for calculations?

Always use $g = 10$ N/kg unless the question explicitly states a different value, per Edexcel IGCSE Physics guidance.

How do I convert cm² to m² for pressure calculations?

To convert cm² to m², multiply by $1 0^{- 4}$ : e.g. $200$ cm² = $200 \times 1 0^{- 4}$ m² = $0.02$ m².

Going deeper

syllabusEdexcel IGCSE Physics (4PH1) SpecificationRefer to section 5 for full topic guidance

What's Next

Now that you have mastered density and pressure for Edexcel IGCSE Physics, you are ready to move on to the next topics in the Solids, Liquids and Gases unit. Next, you will learn about specific heat capacity and changes of state, which build on your understanding of mass and energy transfers in materials. Following that, you will cover the gas laws, including the relationship between pressure, volume and temperature of gases, which extends your knowledge of pressure in fluids. Make sure you practise as many exam-style questions on density and pressure as possible to reinforce your recall of the three core formulae and unit conversion skills, as these are frequently tested in both Paper 1 and Paper 2 of the exam, as well as in the Double Award specification.