## Pressure

Pressure (the symbol: p) is the force per unit area applied in a direction perpendicular to the surface of an object. Gauge pressure (also spelled gage pressure)[a] is the pressure relative to the local atmospheric or ambient pressure.

Pressure is the effect of a force applied to a surface. Pressure is the amount of force acting per unit area. The symbol of pressure is p.

### Formula:

Mathematically:

where:

p is the pressure,
F is the normal force,
A is the area of the surface area on contact

Pressure is a scalar quantity. It relates the vector surface element (a vector normal to the surface) with the normal force acting on it. The pressure is the scalar proportionality constant that relates the two normal vectors:

The minus sign comes from the fact that the force is considered towards the surface element, while the normal vector points outward.

It is incorrect (although rather usual) to say “the pressure is directed in such or such direction”. The pressure, as a scalar, has no direction. It is the force given by the previous relationship to the quantity that has a direction, not the pressure. If we change the orientation of the surface element, the direction of the normal force changes accordingly, but the pressure remains the same.

Pressure is transmitted to solid boundaries or across arbitrary sections of fluid normal to these boundaries or sections at every point. It is a fundamental parameter in thermodynamics, and it is conjugate to volume.