Physics

6.8 - Pressure Equation & How It Works

7 min

Pressure and its equation

Pressure in fluids

The perpendicular force

Force from pressure

note 1 of 3

Pressure is force per unit area

Pressure tells you how concentrated a force is over the area it acts on.
The same force over a small area gives a high pressure; over a large area it gives a low pressure.
For example, a sharp knife concentrates force onto a tiny area to produce high pressure, while snowshoes spread weight over a large area to produce low pressure.

An upside-down pink triangle and a rounded green block on the same surface under matching downward arrows labelled same force, tagged more pressure with small contact area and less pressure with large contact area.

Fluid pressure

Gases and liquids are both fluids - their particles are free to move around and flow.
As particles move, they collide with surfaces and exert a force on them, creating pressure.
The force from fluid pressure always acts normal (at right angles) to the surface.

A blue cube sits inside a container of liquid with four green arrows pointing at its top, bottom and both sides, joined to a single label reading pressure.

note 2 of 3

Formula for pressure

$p = \frac{F}{A}$

Where:

$p$ = Pressure, in pascals (Pa)
$F$ = Force acting normal to the surface, in newtons (N)
$A$ = Area of that surface, in square metres (m²)

The pressure on a surface is found from the force acting normal to the surface and the area of that surface.

Units:

One pascal is one newton per square metre (1 Pa = 1 N/m²).
1 kilopascal (kPa) = 1,000 Pa.
The same equation works for solids, liquids and gases.

A formula triangle with F in the top section and p and A side by side, separated by a multiplication sign, in the bottom section. — Cover the quantity you want to find to get the equation to use.

note 3 of 3

Worked example - Pressure from force and area

A box rests on the floor. It presses down with a force of 200 N over a contact area of 0.5 m². Calculate the pressure the box exerts on the floor.

A wooden crate rests on the ground, with a blue arrow pointing down from its base labelled 200 N and a green bracket across the base labelled 0.5 m2.

Step 1 - Formula

$p = \frac{F}{A}$

Step 2 - Substitution and calculation

$p = \frac{200}{0.5} = 400 Pa$

The box exerts a pressure of 400 Pa on the floor.

key terms

TermDefinition

PressureThe force acting at right angles to a surface per unit area of that surface.

FluidA liquid or a gas, whose particles can move past one another so it can flow.

NormalA line drawn at right angles to a surface or boundary at the point where a ray or wave meets it. A force or pressure that acts at right angles to a surface is also said to act normal to it.

PascalA unit of pressure equal to one newton per square metre.

end of notes

Key points to remember

Pressure is force per unit area

Pressure tells you how concentrated a force is over the area it acts on.

The same force over a small area gives a high pressure; over a large area it gives a low pressure.

For example, a sharp knife concentrates force onto a tiny area to produce high pressure, while snowshoes spread weight over a large area to produce low pressure.

Formula for pressure

$p = \frac{F}{A}$

Where:

p

= Pressure, in pascals (Pa)

F

= Force acting normal to the surface, in newtons (N)

A

= Area of that surface, in square metres (m²)

The pressure on a surface is found from the force acting normal to the surface and the area of that surface.

Units:

One pascal is one newton per square metre (1 Pa = 1 N/m²).

1 kilopascal (kPa) = 1,000 Pa.

The same equation works for solids, liquids and gases.