What is pressure?

A force distributed over a surface

Pressure is a physical quantity that measures the effect of a force distributed over a surface. The smaller the surface a force is applied to, the greater the pressure, even if the force itself doesn't change.

The pressure formula

The fundamental relation is:

P = F / S

where:

• P is the pressure, in pascal (Pa)
• F is the pressing force, in newton (N), perpendicular to the surface
• S is the surface over which the force is applied, in m^2

One pascal corresponds to a force of one newton applied over a surface of one square meter (1 Pa = 1 N/m^2). The hectopascal (1 hPa = 100 Pa) is also used for weather forecasting, or the bar (1 bar = 100,000 Pa).

Concrete example

A 60 kg person (weight of about 600 N) exerts a very different pressure depending on whether they wear flat-soled shoes or stiletto heels: the contact surface on the ground goes from several hundred cm^2 to a few cm^2, which can multiply the pressure by 50 or more.

Common pitfall

Don't confuse force and pressure: two objects can have the same weight and exert very different pressures if their contact surfaces differ. Always check that S is indeed the surface actually in contact, and not a volume or another quantity.