Pressure describes how a force is spread over the area it acts on. The same load can produce enormous pressure when it acts on a small area, or a tiny one when it is spread over a large area. In this article we explain the pressure formula, the SI units, and we show the calculations using an example.
The pressure formula
Pressure, denoted by the letter p, is calculated by dividing the pressing force by the area it acts on:
- p = F / S — pressure equals force divided by area
- F = p × S — force equals pressure times area
- S = F / p — area equals force divided by pressure
It is important that the force acts perpendicular to the surface.
SI units
In the SI system we measure pressure in pascals (Pa):
- Force F — newton (N)
- Area S — square metre (m²)
- Pressure p — pascal (Pa), where 1 Pa = 1 N/m²
In practice larger units are used: 1 kPa = 1000 Pa, and 1 hPa (hectopascal) = 100 Pa. Atmospheric pressure is about 1013 hPa.
Why does a small area give high pressure?
The smaller the area the same force acts on, the greater the pressure. That is why a sharp knife cuts more easily than a blunt one, and why a person on skis does not sink into the snow, even though without skis they would. Skis spread the weight over a larger area, reducing the pressure.
Worked example
A crate presses on the floor with a force of F = 800 N, and its base has an area of S = 2 m². We calculate the pressure.
- We apply the formula p = F / S.
- We substitute: p = 800 N / 2 m².
- We calculate: p = 400 Pa.
The crate exerts a pressure of 400 pascals on the floor.
The effect of changing the area
If the same crate stood on a smaller base with an area of 0.5 m², the pressure would be: p = 800 / 0.5 = 1600 Pa. The area has decreased fourfold, while the pressure has increased fourfold. This shows the inverse proportionality between area and pressure.
Second example: force from pressure
A piston with an area of S = 0.01 m² operates under a pressure of p = 200 000 Pa (200 kPa). We calculate the pressing force.
- We apply the formula F = p × S.
- We substitute: F = 200 000 × 0.01.
- We calculate: F = 2000 N.
The piston exerts a force of 2000 newtons. This is the principle behind hydraulic systems, in which a small pressure over a large area produces an enormous force.
Pascal's law
Pressure exerted on an enclosed liquid spreads evenly through it in all directions. This is Pascal's law, on which the operation of hydraulic presses, jacks and braking systems is based. Thanks to it, a small force applied to a small piston can produce an enormous force on a large piston, as long as the pressure in the liquid stays the same. The ratio of the forces equals the ratio of the areas of the two pistons, which lets you multiply the force many times over while keeping the same pressure.
Units of pressure outside the SI system
Apart from the pascal, in practice we come across other units of pressure, depending on the field. Car tyre pressure is given in bars (1 bar = 100 000 Pa) or pounds per square inch (psi). Blood pressure is measured in millimetres of mercury (mmHg), and the weather is described in hectopascals. In physics calculations it is always worth reducing the values to pascals to keep the formulas consistent. Knowing the conversions makes it easier to compare data from different sources.
Hydrostatic pressure
In a liquid there is also hydrostatic pressure, which depends on depth. It is calculated from the formula p = ρ × g × h, where ρ is the density of the liquid, g the acceleration due to gravity, and h the depth. That is why the pressure increases with immersion, as divers can feel.
Most common mistakes
- Area in cm² instead of m² — 1 m² is 10 000 cm², so this mistake greatly distorts the result.
- Confusing force with mass — in the formula we substitute the force in newtons, not the mass in kilograms.
- A non-perpendicular force — the formula assumes pressure perpendicular to the surface.
- Confusing pascals with hectopascals — 1 hPa is 100 Pa, which matters for atmospheric pressure.
Frequently asked questions
- What is atmospheric pressure? On average about 1013 hPa, that is 101 300 Pa at sea level.
- Why do tyres have high pressure? Because the small contact patch with the road has to carry the weight of the vehicle, which requires high pressure inside.
- How does pressure depend on depth? It increases linearly with depth according to the formula p = ρ × g × h.
Summary
Pressure p = F / S is the force per unit area, expressed in pascals. The smaller the area, the greater the pressure for the same force. Keep an eye on the SI units, especially converting square centimetres into square metres.
Convert and calculate pressure: Pressure Converter →