The pressure formula
Pressure = force ÷ area. Using the formula triangle: Force = Pressure × Area, with force at the top, and pressure and area on the bottom.
Cover the letter you want to find — whatever's left shows the calculation to use.
Worked Example 1
A force of 20N acts on an area of 5m². Find the pressure.
1
Cover "pressure" in the triangle: this leaves force ÷ area
2
Substitute the values: 20 ÷ 5 = 4
Answer4N/m² (4 Pascals)
1N/m² is called 1 Pascal (Pa) — the standard unit of pressure.
Comparing pressure over different areas
The same force spread over a smaller area produces a much higher pressure. This is why a stiletto heel sinks into soft ground, while a snowshoe of the same weight barely leaves a mark.
Both push down with exactly the same 600N force, but the heel's tiny contact area sinks deeply, while the snowshoe's wide area barely dents the surface.
Worked Example 2
A force of 600N acts on a stiletto heel with area 2cm². Find the pressure, then compare it to the same force spread over a snowshoe with area 600cm².
1
Find the pressure from the heel: 600 ÷ 2 = 300
2
Find the pressure from the snowshoe: 600 ÷ 600 = 1
Answer300N/cm² vs 1N/cm² — the heel exerts 300 times more pressure
Rearranging the formula
Worked Example 3
A force of 45N produces a pressure of 90N/m². Find the area.
1
Cover "area" in the triangle: this leaves force ÷ pressure
2
Substitute the values: 45 ÷ 90 = 0.5
Answer0.5m²
Practice questions
Work through each question before checking the answers.
Foundation (Grade 3–5)
Q1A force of 20N acts on an area of 5m². Find the pressure.Foundation
Q2A force of 150N acts on an area of 3m². Find the pressure.Foundation
Q3A pressure of 8N/m² acts over an area of 6m². Find the force.Foundation
Q4A force of 60N produces a pressure of 12N/m². Find the area.Foundation
Q5A force of 400N acts on an area of 0.5m². Find the pressure.Foundation
Higher (Grade 5–7)
Q6A force of 90N acts on an area of 0.3m². Find the pressure.Higher
Q7A pressure of 25N/cm² is applied over an area of 8cm². Find the force.Higher
Q8A force of 500N produces a pressure of 250N/m². Find the area.Higher
Q9A box weighing 240N rests on a base with area 0.6m². Find the pressure it exerts on the ground.Higher
Q10A force of 84N acts on an area of 1.2m². Find the pressure.Higher
Higher — Hard (Grade 8–9)
Q11A cube-shaped block weighing 360N has a base with side length 0.3m. Find the pressure it exerts on the ground.Grade 8–9
Q12A stiletto heel with area 1.5cm² supports a force of 450N. Find the pressure in N/cm², then convert it to N/m² (1m² = 10,000cm²).Grade 8–9
Q13Two boxes exert the same pressure on the ground. Box A has a weight of 180N and base area 0.4m². Box B has a base area of 0.6m². Find the weight of Box B.Grade 8–9
Q14A force of 720N is spread evenly over a rectangular area measuring 1.2m by 0.5m. Find the pressure.Grade 8–9
Q15A circular pillar has a radius of 0.2m and exerts a pressure of 15,000N/m² on the ground (use π = 3.14). Find the force the pillar exerts on the ground.Grade 8–9
Answers
Foundation (Q1–Q5)
Q14N/m²
Q250N/m²
Q348N
Q45m²
Q5800N/m²
Higher (Q6–Q10)
Q6300N/m²
Q7200N
Q82m²
Q9400N/m²
Q1070N/m²
Higher — Hard (Q11–Q15)
Q114000N/m²(area = 0.3 × 0.3 = 0.09m², 360 ÷ 0.09)
Q12300N/cm² = 3,000,000N/m²(450 ÷ 1.5 = 300, 300 × 10,000)
Q13270N(pressure A = 180 ÷ 0.4 = 450N/m², weight B = 450 × 0.6)
Q141200N/m²(area = 1.2 × 0.5 = 0.6m², 720 ÷ 0.6)
Q151884N(area = 3.14 × 0.2² = 0.1256m², 15,000 × 0.1256)
Common mistakes
Common Mistake 1
Confusing force and pressure
A heavier object doesn't always exert more pressure — pressure depends on both the force and the area it's spread over, not force alone.
Common Mistake 2
Using the wrong area
Always use the actual contact area touching the surface, not the object's total surface area or volume.
Common Mistake 3
Forgetting to convert units before comparing
Comparing a pressure in N/cm² directly with one in N/m² without converting first will give a wildly wrong comparison — always match the units.
Common Mistake 4
Forgetting area = length × width for a rectangle
When a question gives two side lengths instead of a single area, calculate the area first before applying the pressure formula.
Exam tips
💡 Exam Tip 1
Draw the F/P/A triangle every time
Sketching the triangle and covering the unknown removes any doubt about whether to multiply or divide.
💡 Exam Tip 2
Remember 1N/m² = 1 Pascal
Questions sometimes give pressure in Pascals (Pa) instead of N/m² — these are exactly the same unit, so no conversion is needed.
💡 Exam Tip 3
Calculate area first if it isn't given directly
For rectangular, square, or circular bases, work out the area as a clearly labelled first step before applying the pressure formula.
💡 Exam Tip 4
Use the stiletto vs snowshoe idea to sense-check
If your answer suggests a small area gives lower pressure than a large area (for the same force), you've likely made an error — smaller area always means higher pressure.
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