Pressure, Force and Area
Simple Explanation
Pressure measures how concentrated a force is, over the area it acts on: P = F/A. The same force pushed through a smaller area produces a much bigger pressure, and vice versa.
Why Do We Need It?
Pressure — not force alone — is what determines whether something cuts, punctures, or supports weight without sinking, which is why so much everyday design (knife blades, snow shoes, tyres) is really about controlling pressure.
Formula
Pressure
P = F / A
Pressure measures how concentrated a force is — the same force spread over a smaller area produces a much bigger pressure.
- P
- — pressure, in pascals (Pa), where 1 Pa = 1 N/m²
- F
- — force applied perpendicular to the surface, in newtons (N)
- A
- — area over which the force acts, in square metres (m²)
When to use it: Whenever the pressure produced by a force acting over a known area needs to be found (or either of the other two quantities, given the other two).
Worked Example
Find the pressure under a table leg
A table leg exerts a force of 200 N on the floor through a contact area of 0.002 m². Find the pressure on the floor.
Why Does This Work?
Dividing the total force by the area it is spread over gives exactly how much force acts on each individual unit of area — which is the definition of pressure.
Real-Life Example
Why snow shoes work
A person wearing snow shoes can walk on soft snow without sinking, while the same person in regular boots sinks straight in.
Snow shoes spread the person's weight (the same force) over a much larger area, greatly reducing the pressure on the snow beneath each footstep.
Practice
A force of 60 N acts over an area of 0.5 m². Find the pressure.
EasyA drawing pin has a point of area 0.000001 m² (1 mm²), pushed in with a force of 5 N. Find the pressure at the point.
MediumCommon mistake
Confusing force and pressure — a very large force spread over a huge area can produce a small pressure, while a small force concentrated on a tiny area (like a needle point) can produce an enormous pressure.
Quick Review
- P = F/A
- Pressure is measured in pascals (Pa), where 1 Pa = 1 N/m².
- A smaller area concentrates the same force into a much bigger pressure.