Forces and motion · GCSE Physics
Pressure
Teacher-written GCSE Physics revision on pressure: p = F/A in pascals, liquid pressure p = hρg, atmospheric pressure, and why sharp blades and wide tyres are the same equation.
Pressure is force over area: p = F/A, in pascals. Small area, large pressure. In a liquid, p = hρg, so pressure rises with depth.
The important bits
What you need to know
- 1
Pressure p = F / A. Force in newtons, area in square metres, pressure in pascals (Pa). 1 Pa = 1 N/m². Sometimes kPa or N/cm² in applied questions — convert.
- 2
A sharp knife has a small area, so a modest force produces a large pressure and cuts. A tractor tyre has a large area, so the same weight produces a smaller pressure and does not sink as easily.
- 3
Liquid pressure at depth h is p = hρg, with h in metres, ρ in kg/m³, g in N/kg. Pressure acts in all directions and increases with depth, not with the shape of the container’s top.
- 4
Atmospheric pressure is due to the weight of the air. It is about 1.0 × 10⁵ Pa at sea level and falls as you climb because there is less air above you.
- 5
A difference in liquid pressure can cause an upthrust. Objects sink if weight is greater than upthrust; they float if they are equal at some immersion.
- 6
Hydraulic systems (more typical of Triple / Physics in some treatments) use a liquid to transmit pressure: a small force on a small piston can produce a large force on a large piston because p is the same.
- 7
Area must be in m² for pascals. 1 cm² = 1 × 10⁻⁴ m². A 2.0 cm × 2.0 cm shoe-heel is 4.0 × 10⁻⁴ m², not 4.0 m².
- 8
Gases also exert pressure by particle collisions (see gas pressure). Solids transmit forces; the pressure on the floor is still F/A using the contact area.
Quotations worth analysing
Short evidence. Real method.
“Pressure = force / area”
The same force on a quarter of the area quadruples the pressure. That is the nail, the stiletto heel, and the snowshoe.
“The pressure due to a column of liquid p = hρg”
Depth h, not the volume of the lake. Two metres down in a pond or in a reservoir, the extra liquid pressure is the same if ρ matches.
Go deeper
Area is the hidden variable in every pressure question
People say “heavy” when they mean “high pressure”. A tank is heavy; on wide tracks it may still exert a modest pressure. Convert the contact area to m², use the weight in newtons as the force if the object is resting, then divide. Two feet share the weight, so use the total area of both soles if the person is standing still on both. Sitting or standing on one heel changes A and therefore p. In calculations, 60 kg is not a force: W = mg first, then p = W/A. An answer of 0.002 Pa for a person means you used cm² without converting, or divided the wrong way. Typical person-on-floor pressures are tens of kilopascals. Check the order of magnitude before you move on.
Go deeper
Liquid pressure depends on depth, density and g
p = hρg is extra pressure due to the liquid column. At the surface of a lake the extra is zero; 10 m down in fresh water, p = 10 × 1000 × 9.8 = 98 000 Pa, about one atmosphere extra. That is why dams are thicker at the base, and why your ears hurt as you dive. The force on a lock gate is pressure times area, and pressure is larger at the bottom, so the total force is not simply surface pressure times area — Higher treatments may ask you to use the pressure at the midpoint as an estimate. Hydraulics: the liquid is incompressible, p is transmitted, F₂ = pA₂ = F₁ × (A₂/A₁). A car jack is a force multiplier. Flag this as Physics-route depth if your Combined course skipped hydraulics, but p = F/A and p = hρg are widely assessed.
See the idea in action
A 48 kg student stands on both feet. g = 10 N/kg. Weight W = 48 × 10 = 480 N. Each shoe contacts 0.020 m², so total area = 0.040 m². Pressure p = F/A = 480 / 0.040 = 12 000 Pa, or 12 kPa. Standing on one heel of area 8.0 cm² = 8.0 × 10⁻⁴ m², p = 480 / 8.0 × 10⁻⁴ = 600 000 Pa. Same force, much larger pressure. Separately, 2.0 m under a swimming pool: liquid pressure p = hρg = 2.0 × 1000 × 10 = 20 000 Pa above atmospheric.
Exam technique
Turn knowledge into marks
Convert mass to weight before using p = F/A. Convert cm² to m². For liquids, use depth h, not the width of the tank. State the unit as Pa or N/m².
Common mistakes
Do not give these marks away
- 01
Using mass in kilograms as the force in p = F/A, or leaving area in cm².
- 02
Using the volume or surface area of a lake instead of depth in p = hρg.
- 03
Saying a sharp blade has a larger force rather than a smaller area.
A 20 N force is spread over 0.050 m². What is the pressure?
A0.0025 Pa
B1.0 Pa
C400 Pa
D20.05 Pa
Show the answer
400 Pa. p = F/A = 20 / 0.050 = 400 Pa. 0.0025 Pa is A/F, the reciprocal. Always divide force by area.
Quick questions
If this is the bit you searched
What is the unit of pressure?
The pascal (Pa), equal to one newton per square metre. You may also meet kPa or N/cm²; convert to SI for p = F/A.
Why does pressure in a liquid increase with depth?
A deeper point has a taller column of liquid above it, so a larger weight of liquid acts on each unit of area: p = hρg.
Why do snowshoes stop you sinking?
They increase the area, so the same weight produces a smaller pressure on the snow.
Is atmospheric pressure part of p = hρg?
Atmospheric pressure is the pressure due to the air column. Liquid p = hρg is usually the extra pressure due to the liquid. Total pressure at depth is often atmospheric plus hρg.