Sheet № 227 · Foundation + Higher · AQA · Edexcel · OCR
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 sy
§Key definitions
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.
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.
Answer:
The pressure is 500 Pa.
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?
§Formulas to memorise
Pressure = Force / Area, or P = F / A
Force = Pressure x Area, or F = P x A
Area = Force / Pressure, or A = F / P
Pressure is measured in pascals (Pa) or N/m². 1 Pa = 1 N/m².
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.
Write down the formula — P = F / A.
Identify which quantity you need to find — and rearrange if necessary.
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.
Substitute — the values into the formula and calculate.
State the units — in your answer.
Worked example
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:
⚠ 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.