Pressure formula: p = F ÷ A
Pressure = force normal to a surface ÷ area of that surface, or p = F/A. p is the pressure in pascals (Pa), F is the force in newtons (N) and A is the area in square metres (m²). It belongs to the separate Physics courses, and in those exams the equation sheet prints it for you.
Equation
p = F ÷ A
| Symbol | Quantity | Unit |
|---|---|---|
p | pressure | Pa |
F | force | N |
A | area | m² |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | p = F/A |
| AQA Combined Science (8464) | Not in this specification | |
| Edexcel Physics (1PH0) | Recall | P = F/A |
| Edexcel Combined Science (1SC0) | Not in this specification | |
| OCR Gateway Physics A (J249) | Recall | p = F/A |
| OCR Twenty First Century Physics B (J259) | Recall | p = F/A |
Calculator: p = F ÷ A
Why area matters
Pressure tells you how concentrated a force is. The same push spread over a big area gives a low pressure. Squeeze it onto a tiny area and the pressure shoots up.
That is why snowshoes stop you sinking into snow, and why a drawing pin goes into a board so easily. Your thumb presses on the wide head. The same force comes out through a point with a very small area, so the pressure there is huge.
One pascal is one newton on each square metre, which is a very small pressure. Everyday values are often in thousands of pascals, so kPa (kilopascals) turns up a lot.
The word normal in the equation means at right angles to the surface. Only the part of the force that pushes straight into the surface counts.
Board forms and which courses include it
- AQA Physics (8463): p = F/A.
- Edexcel Physics (1PH0): P = F/A, with a capital P.
- Both OCR courses, Gateway Physics A (J249) and Twenty First Century Physics B (J259): p = F/A.
This one is for separate Physics only. It is not in AQA Combined Science (8464) or Edexcel Combined Science (1SC0). On OCR J259 it sits in the normal recall list, since that whole course is Physics.
Each of these courses marks it for recall. You will still find it on the sheet in the exam. The AQA equation list shows where it sits among AQA's 35.
Rearranging p = F/A
- F = p × A
- A = F ÷ p
The force is often a weight, so the force equations and W = m g may come first. Pressure in a liquid has its own equation: see pressure in a liquid. For gases, try the gas law page.
Worked examples
p
- Change the area to m²: 1 m² = 10 000 cm², so 300 cm² = 0.03 m²
- p = F ÷ A
- p = 45 ÷ 0.03
- p = 1500 Pa
1500 Pa
F
- F = p × A
- F = 200 000 × 0.02
- F = 4000 N
4000 N
A
- 2 kPa = 2000 Pa
- A = F ÷ p
- A = 700 ÷ 2000
- A = 0.35 m²
0.35 m²
Common mistakes
- Dividing cm² by 100 to get m². A square metre holds 100 × 100 = 10 000 square centimetres, so divide by 10 000.
- Turning the equation upside down. Area goes on the bottom: a bigger area must give a smaller pressure.
- Using a mass in kg as the force. Turn it into a weight in newtons first.
Build speed at making F or A the subject with the Equation Rearranger.
Questions people ask
Why do knives cut better when they are sharp?
A sharp edge has a tiny area. The force from your hand then makes a much higher pressure on the food.
Is N/m² the same as Pa?
Yes. One pascal is one newton per square metre, so you can write either.