What is pressure?
Force is a push or a pull. Area is how much surface something covers.
Pressure tells us how strongly a force is spread over an area. It is the force on each square metre.
P = F ÷ A
- P = pressure, in pascals (Pa)
- F = force pressing straight on the surface (the 'force of pressure'), in newtons (N)
- A = area, in square metres (m²)
1 Pa = 1 N/m². This is a small pressure, so we often use kilopascals: 1 kPa = 1000 Pa.
If you know the pressure and area you can find the force: F = P × A.
Bigger area, smaller pressure (and the other way)
For the same force:
- Small area → big pressure. Needles, nails, knife edges, the studs on football boots and an axe blade all use this to cut or grip.
- Big area → small pressure. Wide school-bag straps, snowshoes, camel feet, tank tracks, the wide base of a building, and the many tyres on a truck spread the force so it does not sink or hurt.
This is why you can lie on a bed of many nails but would never step on one nail: the force is shared by hundreds of tiny areas.
Pressure in liquids
Liquids have weight, so they press on the bottom and sides of their container.
- Liquid pressure increases with depth: more liquid is above, pushing down.
- At the same depth, a liquid presses equally in all directions.
- A denser liquid (like sea water or mercury) presses more at the same depth.
The rule is P = ρ g h, where ρ (rho) is the density in kg/m³, g ≈ 10 N/kg (9.8 more exactly) and h is the depth in m. In water, pressure grows by about 10 000 Pa (10 kPa) for every metre you go down.
Uses: dams are thicker at the bottom; water tanks are kept high so taps get strong flow; a submarine must have very strong walls.
Pressure in gases and air pressure
A gas is made of tiny particles moving fast in all directions. They hit the walls again and again. Each hit is a tiny push. All the pushes together make gas pressure.
- Less volume → more pressure (if temperature stays the same): squeeze the gas into half the space and the particles hit the walls twice as often, so the pressure doubles. This is why a bicycle pump gets hard to push.
- Higher temperature → more pressure (if volume stays the same): hot particles move faster and hit harder and more often. That is why a closed can must not be heated, and why tyres are checked when cool.
The air above us also presses. Atmospheric pressure at sea level is about 101 000 Pa (101 kPa), like the weight of a 10-tonne lorry on each square metre. We do not get crushed because the fluids inside our body push back equally. Air pressure is lower on mountains, because there is less air above.
Fluids in the body: blood pressure
The heart is a pump. When it squeezes, it pushes blood into the arteries and the pressure on the artery walls rises. When it relaxes, the pressure falls.
- Doctors write blood pressure as two numbers, for example 120/80 mmHg (millimetres of mercury, an old pressure unit; 1 mmHg ≈ 133 Pa).
- The top number (systolic) is when the heart squeezes; the bottom number (diastolic) is when it rests.
- Blood pressure is measured at the level of the heart, because liquid pressure changes with height. In a standing person, the pressure in the feet is higher than in the head.
- A drip (IV bag) is hung high above the patient so the liquid pressure is enough to flow into a vein.
Very high blood pressure for a long time can damage the heart and arteries, so it is checked regularly in adults.
Try it: predict, then check
In the 3D free play, set the force to 100 N. Predict: if you halve the area from 200 cm² to 100 cm², what happens to the pressure? Move the slider and check. (It doubles: 5000 Pa → 10 000 Pa.)
Key formulas and definitions
- P = F ÷ A (pressure = force ÷ area)
- F = P × A and A = F ÷ P
- 1 Pa = 1 N/m²; 1 kPa = 1000 Pa
- Liquid pressure: P = ρ g h (grows with depth)
- Gas: smaller volume or higher temperature → higher pressure
- Atmospheric pressure at sea level ≈ 101 kPa; 1 mmHg ≈ 133 Pa
Worked examples
1. A box weighing 200 N stands on an area of 0.5 m². Find the pressure.
P = F ÷ A = 200 ÷ 0.5 = 400 Pa.
2. A girl of weight 500 N stands on both feet, total area 0.025 m². What pressure does she put on the floor?
P = 500 ÷ 0.025 = 20 000 Pa = 20 kPa.
3. She now stands on one foot (area 0.0125 m²). What happens to the pressure?
The area halves, so the pressure doubles: 500 ÷ 0.0125 = 40 000 Pa.
4. A drawing pin is pushed with 10 N. The point has an area of 0.000 000 1 m² (10⁻⁷ m²). Find the pressure.
P = 10 ÷ 10⁻⁷ = 10⁸ Pa = 100 000 000 Pa. That huge pressure lets the pin go into wood.
5. A force of 60 N gives a pressure of 1500 Pa. What area is it acting on?
A = F ÷ P = 60 ÷ 1500 = 0.04 m².
6. Find the water pressure (not counting air) 5 m below the surface of a pool. Take ρ = 1000 kg/m³ and g = 10 N/kg.
P = ρ g h = 1000 × 10 × 5 = 50 000 Pa = 50 kPa.
7. Air at sea level presses with about 100 000 Pa. What force does it put on a table top of 1.5 m²?
F = P × A = 100 000 × 1.5 = 150 000 N. The air below the table pushes up almost the same, so the table does not break.
Common mistakes
- Thinking a bigger force always means a bigger pressure. Area matters too: the same force on a big area gives a small pressure.
- Forgetting to change cm² into m². 1 m² = 10 000 cm², so 50 cm² = 0.005 m².
- Thinking liquids press only downwards. At any depth they press equally in all directions, including sideways and upwards.
- Using mass instead of weight for the force. A 50 kg person has a weight of about 500 N (mass × 10).