How Do You Calculate Pressure (P = F/A)?

For IB Physics SL and HL, calculate pressure by dividing the perpendicular force acting on a surface by the area over which that force acts:

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

Pressure is measured in pascals (Pa), where $1\ \mathrm{Pa} = 1\ \mathrm{N\,m^{-2}}$.

The Reasoning

In topic B.3 Gas laws, pressure is defined as the perpendicular force per unit area:

• $P$ is pressure in pascals (Pa).
• $F$ is the force acting perpendicular to the surface in newtons (N).
• $A$ is the area in square metres ($\mathrm{m^2}$).

Gas pressure arises because gas particles collide with a surface and undergo changes in momentum. These collisions exert a force; dividing the total perpendicular force by the area gives the pressure.

The equation can be rearranged as $F = PA$ or $A = \frac{F}{P}$. Select the form that isolates the required quantity, then check dimensional consistency. For example, pressure multiplied by area gives $$, so the result is a force.

If a piston area is $300\ \mathrm{cm^2}$, convert it by multiplying by $10^{-4}$: $300 \times 10^{-4} = 0.030\ \mathrm{m^2}$. Squaring the centimetre-to-metre conversion is essential because area has two dimensions. Complete this conversion before inserting values into the equation.

Worked Example

A gas exerts a perpendicular force of $600\ \mathrm{N}$ on a piston with area $0.030\ \mathrm{m^2}$. Therefore:

$$P = \frac{600}{0.030} = 2.0 \times 10^4\ \mathrm{Pa}$$

So the gas pressure is $2.0 \times 10^4\ \mathrm{Pa}$, or $20\ \mathrm{kPa}$.

A common misconception is to substitute area in $\mathrm{cm^2}$. The area must first be converted into $\mathrm{m^2}$: $1\ \mathrm{cm^2} = 1.0 \times 10^{-4}\ \mathrm{m^2}$. Also use only the component of force perpendicular to the surface.

Exam Technique

For a Calculate question, show the equation, substitution, and final value with a unit. Check that force is in newtons and area is in square metres before substituting; incorrect area conversion is the most frequent source of powers-of-ten errors.