Pressure, Force and Area –

Pressure, force and area questions appear on GCSE Maths papers as part of compound measures — alongside speed-distance-time and density-mass-volume. You are expected to use and rearrange the formula P = F/A, convert units where necessary, and apply the formula in real-world contexts such as building foundations, snowshoes and hydraulic systems. This topic is examined at both Foundation and Higher tier and typically carries 3 to 5 marks. This guide covers the formula, rearrangements, unit conversions and worked examples.

What Is Pressure?

Pressure measures how much force is spread over a given area. A large force over a small area creates high pressure; the same force over a large area creates low pressure.

Key Formulas

Units

• Force is measured in newtons (N).
• Area is measured in square metres (m²) or square centimetres (cm²).
• Pressure is measured in pascals (Pa) or N/m². 1 Pa = 1 N/m².
• If area is in cm², pressure will be in N/cm².

Step-by-Step Method

1. Write down the formula P = F / A.
2. Identify which quantity you need to find and rearrange if necessary.
3. Check units are consistent. If force is in N and area is in m², pressure will be in N/m² (Pa). Convert if the question requires different units.
4. Substitute the values into the formula and calculate.
5. State the units in your answer.

Worked Example 1 — Foundation Level

Question: A box exerts a force of 200 N on the ground. The base of the box has an area of 0.4 m². Calculate the pressure.

Working:

P = F / A = 200 / 0.4 = 500 N/m² (or 500 Pa)

Answer: The pressure is 500 Pa.

Worked Example 2 — Higher Level

Question: A woman weighs 600 N. She stands on one foot. The area of the sole of her shoe is 120 cm². Calculate the pressure in N/cm² and convert to Pa.

Working:

Step 1: P = F / A = 600 / 120 = 5 N/cm²

Step 2: Convert area to m²: 120 cm² = 120 / 10000 = 0.012 m²

Step 3: P = 600 / 0.012 = 50,000 Pa

Answer: The pressure is 5 N/cm² or 50,000 Pa.

Worked Example 3 — Exam Style

Question: A machine applies a pressure of 800 Pa to a surface. The force applied is 2400 N. Calculate the area of the surface in m².

Working:

Rearrange: A = F / P = 2400 / 800 = 3 m²

Answer: The area of the surface is 3 m².

Common Mistakes

• Forgetting to convert area units. If area is given in cm², convert to m² by dividing by 10,000 before using the formula if you need the answer in Pa (N/m²).
• Mixing up the rearrangements. Use the formula triangle: P at the top, F and A at the bottom. Cover the one you want to find.
• Omitting units in the answer. Pressure without units is meaningless. Always state N/m², Pa or N/cm².
• Confusing pressure with force. Pressure is force per unit area, not just force. A heavier object does not always exert more pressure — it depends on the area of contact.

Exam Tips

• Draw and label the formula triangle at the start of your answer. This shows the examiner you know all three rearrangements and earns method marks.
• Questions often compare two scenarios (e.g., standing on two feet versus one foot). Calculate pressure for each case separately before comparing.
• If the question involves real-world context (e.g., why snowshoes stop you sinking), explain that spreading the force over a larger area reduces the pressure.
• Always give your final answer with the correct units clearly stated.

Practice Questions

Q1 (Foundation): A force of 450 N acts on an area of 1.5 m². What is the pressure?

Q2 (Foundation): A pressure of 250 Pa acts on an area of 2 m². What is the force?

Q3 (Higher): A brick exerts a force of 30 N. It can be placed on its side (area 60 cm²) or its end (area 20 cm²). Calculate the pressure for each position and state which gives greater pressure.

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Related Topics

• Compound Measures: Density and Pressure
• Speed, Distance and Time
• Unit Conversions

Summary

• Pressure = Force / Area (P = F / A). Rearrange to find F or A when needed.
• Pressure is measured in pascals (Pa) or N/m². 1 Pa = 1 N/m².
• The same force over a smaller area produces higher pressure.
• Always check that force and area are in compatible units before calculating.
• To convert cm² to m², divide by 10,000.
• Draw the formula triangle to help you rearrange quickly and earn method marks.
• State the correct units in every answer.