Pressure is the force acting on each unit of area, so p = F ÷ A. It appears whenever a question asks why something sinks into soft ground, why a nail is sharpened, or how much force a hydraulic piston can give.
This skill opens pressure in solids and fluids and is used again in every later lesson of the module.
What does the equation say?
The same force spread over a small area gives a large pressure. Spread it over a large area and the pressure is small. That is why a high-heeled shoe marks a soft floor more than a flat shoe does, even on the same person.
The equation can be rearranged in three ways:
- pressure = force ÷ area, p = F ÷ A
- force = pressure × area, F = p × A
- area = force ÷ pressure, A = F ÷ p
Units: force in newtons (N), area in square metres (m²), pressure in pascals (Pa), where 1 Pa = 1 N/m².
How to set up any pressure question
- Write down what you are given, with units.
- Convert the area to m² if it is in cm². Divide by 10 000, because 1 m² = 10 000 cm².
- Check that the force is in newtons. If a mass is given, see avoiding mass where a force is required.
- Write the equation and substitute.
- Give the answer with a unit, and check that the size is sensible.
Worked example
A closed box has a weight of 240 N. Its base measures 0.30 m by 0.20 m.
The box is then stood on its smallest face, which measures 0.20 m by 0.10 m. Find the pressure in each position. (Invented example data.)
Step 1, first area: 0.30 × 0.20 = 0.060 m².
Step 2, first pressure: p = 240 ÷ 0.060 = 4000 Pa.
Step 3, second area: 0.20 × 0.10 = 0.020 m².
Step 4, second pressure: p = 240 ÷ 0.020 = 12 000 Pa.
Check: the area became three times smaller (0.060 ÷ 0.020 = 3), so the pressure is three times larger (12 000 ÷ 4000 = 3). The weight did not change, only the area in contact.
The mistake to watch for
A common slip is to leave an area in cm² and still call the answer pascals.
Mistaken answer: a force of 240 N on an area of 600 cm² gives p = 240 ÷ 600 = 0.4 Pa.
The equation was right, but 600 cm² is not 600 m². The answer is 0.4 N/cm², not 0.4 Pa.
The correction is to convert first: 600 cm² = 600 ÷ 10 000 = 0.060 m². Then p = 240 ÷ 0.060 = 4000 Pa. A pressure of 0.4 Pa would be far too small for a 240 N load, and that size check catches the slip.
Check yourself
Try these, then open each answer.
1. A force of 500 N acts on an area of 0.25 m². Find the pressure.
Show answer
p = F ÷ A = 500 ÷ 0.25 = 2000 Pa
2. The pressure under a platform is 15 000 Pa and its area is 0.40 m². What force does it carry?
Show answer
F = p × A = 15 000 × 0.40 = 6000 N
3. Which gives the larger pressure: 800 N on 0.50 m², or 300 N on 0.10 m²?
Show answer
First: 800 ÷ 0.50 = 1600 Pa. Second: 300 ÷ 0.10 = 3000 Pa. The second gives the larger pressure, even though its force is smaller, because its area is much smaller.
Where this leads next
Next, see how depth creates pressure in liquid pressure under stated conditions. The pressure practice set mixes all the skills in this module.
Some students can do these one-step questions but lose the thread when a question hides the area or gives a mass. Our teachers look for exactly that in online one-to-one Physics tuition.