Pressure measures how strongly a distributed normal force is applied over an area. If a uniform force $F_\perp$ acts perpendicular to a surface of area $A$, the average pressure is

$$p=\frac{F_\perp}{A}.$$

Pressure is a scalar quantity even though the force producing it has a direction. A fluid at rest pushes perpendicular to any surface it contacts, so pressure is especially natural for liquids and gases.

The SI unit is the pascal:

$$1,\mathrm{Pa}=1,\mathrm{N/m^2}.$$

Common larger units are

$$1,\mathrm{kPa}=10^3,\mathrm{Pa},\qquad 1,\mathrm{bar}=10^5,\mathrm{Pa}.$$

The standard atmosphere is approximately

$$1,\mathrm{atm}=101325,\mathrm{Pa}=101.325,\mathrm{kPa}.$$

Absolute and gauge pressure

Absolute pressure is measured relative to vacuum. Gauge pressure is measured relative to the surrounding atmospheric pressure:

$$p_{\mathrm{gauge}}=p_{\mathrm{absolute}}-p_{\mathrm{atm}}.$$

Thus a tire gauge reading $220,\mathrm{kPa}$ does not mean the gas is at $220,\mathrm{kPa}$ absolute. If atmospheric pressure is about $101,\mathrm{kPa}$, the absolute pressure is approximately

$$p_{\mathrm{absolute}}=220+101=321,\mathrm{kPa}.$$

Gas laws and thermodynamic equations use absolute pressure, because zero pressure in those models corresponds to vacuum rather than to the local atmosphere.

In a gas, countless particle impacts on a container wall produce the average normal force measured macroscopically as pressure. More frequent or stronger impacts produce a larger force per area.