Pressure is the force acting on each unit of area: pressure = force ÷ area. A greater force or a smaller area gives a greater pressure.
This lesson starts the force and pressure topic. Once it feels secure, go on to comparing pressure in fluids.
What do I need for every calculation?
Force in newtons, area in square metres and pressure in pascals. If the area is given in cm², convert it before you divide.
To rearrange, use force = pressure × area, and area = force ÷ pressure. A triangle with F on top and P and A below helps you remember the three forms.
Worked example: a box on a table
An invented box weighs 120 N. It can rest on its small face of 200 cm² or on its large face of 800 cm².
Step 1: convert the areas. 200 cm² = 200 ÷ 10 000 = 0.02 m². 800 cm² = 800 ÷ 10 000 = 0.08 m².
Step 2: pressure on the small face. 120 ÷ 0.02 = 6 000 Pa.
Step 3: pressure on the large face. 120 ÷ 0.08 = 1 500 Pa.
Step 4: compare. The box exerts four times the pressure on its small face, because the area is four times smaller while the force is the same. The force on the table is the box’s weight in both cases.
The mistake that costs marks
The common slip is to divide by the area in cm² directly: 120 ÷ 200 = 0.6, then write “0.6 Pa”. That number is in newtons per cm², so writing Pa is wrong.
The correct approach converts first. Writing “200 cm² = 0.02 m²” on its own line takes a few seconds and keeps the answer in pascals. A quick sense check helps too: 6 000 Pa is 6 kilopascals, a sensible size for a box on a table.
Rearranging the formula
Sometimes the question gives the pressure and asks for the force or area. An invented foot-stamp leaves a pressure of 40 000 Pa over 0.0150 m². Force = P × A = 40 000 × 0.0150 = 600 N.
For area, a 500 N person standing so that the pressure is 25 000 Pa needs an area of 500 ÷ 25 000 = 0.02 m². Always check the unit of the answer against the quantity asked.
Check yourself
An invented suitcase weighs 90 N and stands on 150 cm². Calculate the pressure in pascals and say what happens to the pressure if it is laid flat on 600 cm².
Answer
Area = 150 ÷ 10 000 = 0.015 m². Pressure = 90 ÷ 0.015 = 6 000 Pa.
Laid flat: area = 600 ÷ 10 000 = 0.06 m², so pressure = 90 ÷ 0.06 = 1 500 Pa. The pressure becomes one quarter of the original, because the area is four times larger for the same force.
What to study next
Continue with comparing pressure in fluids, where the same idea applies to liquids. Drill the conversions with the units and significant-figure checker.
To keep track of which slips you make, use the mistake log and paper-error review. If you want a teacher to check your working line by line, see online one-to-one Science tuition.