Pass an Exam 
Hi, I’m Ari. We can start pressure, force and area from the beginning, work through an example together, or practise a question. Tell me which step is confusing.
GCSE Maths · Ratio & proportion
Pressure, force and area GCSE Questions and Worked Answers
Pressure is force per unit contact area: P = F/A. Rearrange to F = PA or A = F/P when another quantity is missing. Match the area unit to the pressure unit: pascals mean newtons per square metre.
Free AI tutor · GCSE pressure, force and area
Practise GCSE pressure, force and area for free with an AI tutor
Ask Ari for an explanation or work through an original exam-style question together.
AriYour maths coach
Chat cost ≈ $0.000000
Ari is an AI tutor and can make mistakes. Use the worked answers below to check important results.
Start with the meaning
What you need to know about pressure, force and area
Imagine pressing the same block onto soft sand in two positions. On its broad face it spreads its push over a large patch; on its narrow face the push is concentrated into a smaller patch. The force is the push, measured in newtons (N). Pressure measures how much force acts on each unit of the contact area.
See the idea first
Divide the push among units of area
If a 120 N force acts evenly over 60 cm², each square centimetre carries 120 ÷ 60 = 2 N. We write the pressure as 2 N/cm². Let P mean pressure, F force and A contact area: P = F/A. This is average pressure over the area. One pascal, Pa, is 1 N/m², not 1 N/cm².
| Force | Contact area | Force per cm² |
|---|---|---|
| 120 N | 60 cm² | 2 N/cm² |
| 120 N | 30 cm² | 4 N/cm² |
| 120 N | 10 cm² | 12 N/cm² |
From problem to method
Typical problems you need to be able to solve
These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.
Find pressure
What the problem asks: A force of 200 N acts over 0.5 m². Find the pressure.
How to solve it: Divide force by area: 200 ÷ 0.5 = 400 N/m² = 400 Pa.
Find force
What the problem asks: Pressure is 6 N/cm² over 15 cm². Find the force.
How to solve it: Each cm² carries 6 N, so 15 cm² carries 6 × 15 = 90 N. Thus F = PA.
Find contact area
What the problem asks: A 240 N force creates pressure 8 N/cm². Find the area.
How to solve it: At 8 N per cm², 240 N requires 240 ÷ 8 = 30 cm². Thus A = F/P.
A reliable routine
Solve a pressure, force or contact-area problem
Use this when a perpendicular force is spread over a stated contact area and average pressure is required. Division gives force per unit area; multiplication or division reverses the relationship to find a missing quantity.
- Identify P, F and the actual contact area A.
- Make the area units agree with the pressure units.
- Use P = F/A, F = PA or A = F/P for the requested quantity.
- Check units and whether changing the contact area should raise or lower pressure.
Check: For a block resting on one face, use that face's area, not total surface area. Mass in kilograms is not force in newtons; any required conversion must be given.
Fully worked
Pressure, force and area GCSE worked examples
Each solution explains the clue, why the method fits and how to check the result.
Example 1
Pressure in pascals
Question
A 360 N force acts at right angles to a surface over a contact area of 0.12 m². Find the average pressure.
The area is in m², so the result is N/m², or Pa.
Example 2
Force
Question
Pressure is 12 N/cm² over a contact area of 25 cm². Find the force.
Every cm² contributes 12 N.
Example 3
Area
Question
A force of 450 N produces pressure 15 N/cm². Find the contact area.
The pressure denominator tells us the resulting area unit.
Example 4
Rectangular contact
Question
A block exerts 180 N on a face measuring 6 cm by 5 cm. Find the pressure in N/cm².
Contact area:
Pressure:
Do not add the areas of its other faces.
Example 5
Convert before calculating
Question
A 500 N force acts over 200 cm². Find the pressure in Pa.
Using 200 directly would instead give 2.5 N/cm², not 2.5 Pa.
Example 6
Choose the least pressure
Question
A cuboid measures 2 cm × 4 cm × 6 cm and exerts a 48 N force. Find the least possible pressure when it rests flat on a face.
Possible contact areas are 2 × 4 = 8, 2 × 6 = 12 and 4 × 6 = 24 cm². The largest area gives the least pressure at fixed force.
10 original questions · total 25 marks
Pressure, force and area GCSE exam-style questions
Try each question before opening its fully worked answer. The difficulty rises through the set.
Before you startAllow about 30 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed
Find pressure
A force of 90 N acts over 3 m². Find the pressure.
Show worked answer
Small area
A force of 240 N acts over 0.08 m². Find the pressure.
Show worked answer
Find force
Pressure is 500 Pa over 0.4 m². Find the force.
Show worked answer
Find area
A force of 600 N creates 2000 Pa. Find the contact area.
Show worked answer
A face
A 300 N force acts on a rectangular contact area 10 cm by 6 cm. Find pressure in N/cm².
Show worked answer
Two feet
A person exerts 600 N, shared across two feet each with contact area 150 cm². Find average pressure over both feet.
Show worked answer
Total area = 2 × 150 = 300 cm².
Use total force with total area.
Convert area
Find pressure in Pa when 80 N acts over 40 cm².
Show worked answer
Tripled area
At fixed force, contact area triples. How does pressure change?
Show worked answer
Pressure becomes one third of the original.
Greatest pressure
A block exerts 72 N and can rest on faces of area 8, 12 or 24 cm². Find the greatest pressure.
Show worked answer
Choose the smallest area:
A smaller contact concentrates the same force.
Supplied mass conversion
In this model, each kilogram of mass has a weight of 10 N. A 12 kg object rests on 0.03 m². Find the pressure.
Show worked answer
Convert mass to force using the supplied model:
Examiner-style feedback
Common pressure, force and area mistakes
Pressure uses contact area, not the block's total surface area.
Pa requires m²; N/cm² requires cm².
Mass and force are different. Use a supplied weight conversion when needed.
30-second recap
Choose, carry out, check
Translate the wording before you reach for a rule.
- Pressure is force per contact area.
- Match compound units.
- Rearrange for the missing quantity.
- At fixed force, smaller area means greater pressure.
Quick answers
Pressure, force and area FAQ
What is a pascal?
One newton per square metre: 1 Pa = 1 N/m².
Why are snowshoes useful in this model?
They increase contact area, reducing average pressure for the same downward force.
Content standards
Curriculum and rights review
AQA R11 density and pressure are additional Foundation content, also available at Higher. These simplified tasks use force perpendicular to a contact surface. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.
Official specification references