Pressure measures how concentrated a force is over a given area: 100 N spread over 2 m² gives 50 N/m². The formula P = F ÷ A connects pressure, force, and area — rearrange it to find whichever quantity you need. Pressure sits alongside speed and density as one of the three compound measures on the GCSE specification.
What is pressure?
Pressure is defined as the force acting perpendicular to a surface divided by the area of that surface:
Pressure = Force ÷ Area
The key idea is concentration: the same force produces higher pressure when it acts on a smaller area. This is why a drawing pin can be pushed into cork (tiny tip area, very high pressure) even though a thumbhumb pushes with the same force that would barely dent an open palm.
Pressure is a compound measure — it is defined by a formula involving two other quantities — just like speed (distance ÷ time) and density (mass ÷ volume).
What is the formula and how is it rearranged?
P = F / A
Rearranging gives the other two forms:
- F = P × A (force, given pressure and area)
- A = F / P (area, given force and pressure)
The formula triangle for pressure, force and area — written with F at the top, P and A at the bottom — is a reliable visual aid. Cover the quantity you want to find; if the other two are side by side, multiply; if one is on top of the other, divide.
What units does pressure use?
The standard unit of pressure in the SI system is the pascal (Pa), where:
1 Pa = 1 N/m² (one newton per square metre)
Other units you may encounter at GCSE:
| Unit | Equivalent | Context |
|---|---|---|
| Pa (pascal) | N/m² | Gases, standard pressure |
| kPa (kilopascal) | 1000 Pa | Atmospheric pressure, tyre pressure |
| N/cm² | 10 000 Pa | Solid objects on surfaces |
Always check the units in the question. If force is in N and area is in cm², your pressure comes out in N/cm², not Pa. Convert areas to m² if you need an answer in Pa.
How do you calculate pressure?
Worked example: A box weighs 60 N and rests on a floor. Its base is a rectangle 0.5 m × 0.3 m. Calculate the pressure it exerts on the floor.
- Force = 60 N.
- Area = 0.5 × 0.3 = 0.15 m².
- P = F/A = 60/0.15 = 400 Pa (N/m²).
How do you calculate force from pressure and area?
Worked example: The pressure of gas inside a piston is 250 000 Pa. The face of the piston has an area of 0.008 m². What force does the gas exert on the piston?
- P = 250 000 Pa, A = 0.008 m².
- F = P × A = 250 000 × 0.008 = 2000 N.
How do you calculate area from force and pressure?
Worked example: A rucksack exerts a force of 40 N on a shelf. The pressure between the bag and the shelf is 500 N/m². What is the contact area?
- F = 40 N, P = 500 N/m².
- A = F/P = 40/500 = 0.08 m².
How does pressure compare to speed and density?
| Compound measure | Formula | Units |
|---|---|---|
| Speed | Speed = Distance/Time | m/s, km/h |
| Density | Density = Mass/Volume | g/cm³, kg/m³ |
| Pressure | Pressure = Force/Area | Pa (N/m²), N/cm² |
All three share the same structure: a quantity defined as one thing divided by another. In all three cases, the formula triangle method works identically. Mixing up which quantity goes on top (force, not area, goes on top for pressure) is the most common error, so writing the formula P = F/A at the top of your working is a simple safeguard.
Frequently asked questions
Does it matter whether I use N/m² or Pa?
They are the same unit: 1 Pa = 1 N/m². In GCSE questions, the expected unit is usually stated in the question or the answer line. If neither is given, state your unit clearly — "400 Pa" and "400 N/m²" are both correct and carry the same mark.
Why do pointed heels cause more damage to wooden floors than flat shoes?
Both a stiletto heel and a flat shoe might carry the same force (the person's weight). But a stiletto heel concentrates that force onto an extremely small area, producing a very high pressure — sometimes thousands of N/cm² — which exceeds the compressive strength of wood. A flat sole spreads the same force over a much larger area, reducing pressure to a safe level. This is exactly the P = F/A formula in action.
How do I convert between N/cm² and N/m² (Pa)?
1 m² = 10 000 cm², so 1 N/m² = 1/10 000 N/cm², or equivalently 1 N/cm² = 10 000 Pa. To convert a pressure in N/cm² to Pa, multiply by 10 000. For example, 3 N/cm² = 3 × 10 000 = 30 000 Pa.
Is pressure the same as stress in engineering?
In everyday GCSE maths, "pressure" and "stress" both refer to force per unit area. In engineering and physics, stress is the more general term (it can act in any direction and includes shear), while pressure usually refers to force acting perpendicular to (normal to) a surface. At GCSE level the distinction is not tested — treat them as the same concept.
For compound measures practice at GCSE with Professor Pi, visit aitutors.me.