Pressure, Force and Area
Pressure, force and area are linked by pressure = force ÷ area. It shows how concentrated a force is, so 100 N spread over 2 m² gives 50 N/m². Rearrange it to get force = pressure × area.
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Pressure, Force and Area Basics
- Force is a push or pull measured in newtons (N).
- Area is the size of a flat surface measured in square metres (m²).
- Pressure shows how concentrated a force is, measured in pascals (Pa).
Using the Pressure Triangle
- Cover the value you want to find to reveal its formula.
- Two values side by side means multiply: .
- One value above another means divide: and .
Finding Force
- To find force, multiply pressure by area.
- 500 Pa .
Finding Area
- To find area, divide force by pressure.
- Total ski area = 800 N ÷ 2000 .
- Then ÷ 2 skis = each.
Finding Pressure
- First find one support's area: .
- Then × 4 supports for the total area: .
- To find pressure, divide force by area: Pa.
Practice Questions
Test your understanding
A fridge pushes down on the floor with a force of 1000 N over an area of . Find the pressure.
Correct! 🎉 +10 pointsCorrect! 🎉 Worth 10 XPNot quite right
Use pressure = force ÷ area.
So .
Dividing by 0.5 is the same as multiplying by 2, so the answer is bigger than 1000, not smaller: spreading 1000 N over only half a square metre gives 2000 N on every square metre.
The pressure is 2000 N/m².
A crate presses on the ground with a pressure of 900 N/m² over an area of . Find the force.
Correct! 🎉 +10 pointsCorrect! 🎉 Worth 10 XPNot quite right
Rearrange pressure = force ÷ area to get force = pressure × area.
So .
Each square metre carries 900 N, and there are 2 square metres, so the total force is 1800 N.
A force of 1800 N produces a pressure of 1200 N/m². Find the area it acts on.
Correct! 🎉 +20 pointsCorrect! 🎉 Worth 20 XPNot quite right
Use area = force ÷ pressure.
So .
The area is .
A wardrobe has a rectangular base measuring by . It presses on the floor with a force of 1350 N. Find the pressure on the floor.
Correct! 🎉 +20 pointsCorrect! 🎉 Worth 20 XPNot quite right
First find the area of the base. For a rectangle, area = length × width .
Then use pressure = force ÷ area. So .
The pressure is 1500 N/m².
Check three things: , not 9; the force must be divided by the area (), not by a single side length; and because you are dividing by a number smaller than 1, the answer is bigger than 1350, not smaller.
A square paving slab has sides of . The pressure on it is 2000 N/m². Find the force acting on the slab.
Correct! 🎉 +20 pointsCorrect! 🎉 Worth 20 XPNot quite right
First find the area of the slab. For a square, area = side × side .
Then use force = pressure × area. So .
The force is 500 N.
Take care to multiply by the area (), not by a side length () and not by the perimeter (), and to multiply rather than divide, since force = pressure × area.
A box with a square base presses on the ground with a force of 800 N. The pressure on the ground is 3200 N/m². Find the length of one side of the square base.
Correct! 🎉 +30 pointsCorrect! 🎉 Worth 30 XPNot quite right
First find the area of the base using area = force ÷ pressure. So .
For a square base, area = side × side, so the side is the square root of the area: .
The side length is .
Three steps are easy to get wrong: stopping at the area () instead of square rooting it, squaring the area instead of rooting it (), and dividing the wrong way round (, which would give a side of ).
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Interactive Activity
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Frequently asked questions
The questions students bump into most on this topic
Force is a push or a pull, such as the weight of a delivery box pressing on the floor, measured in newtons. Area is the size of the flat surface it presses on, in square metres. Pressure is how concentrated the force is over that area, in pascals. The same force on a smaller area gives a higher pressure, which is why a point digs in.
Pressure = force ÷ area. Rearranged, force = pressure × area and area = force ÷ pressure. The pressure triangle has force on top with pressure and area underneath: cover the one you want, multiply if the other two are side by side, divide if one is above the other. Keep force in newtons, area in square metres and pressure in pascals.
Divide the force by the area, working out the area first if it is not given. A bed weighing 1,200 N stands on 4 supports, each 1 m by 0.5 m. One support is 1 × 0.5 = 0.5 m², so the total area is 4 × 0.5 = 2 m². The pressure on the floor is 1,200 ÷ 2 = 600 pascals.
Multiply the pressure by the area. A wardrobe’s base covers 2 m² and presses on the floor with a pressure of 500 pascals, so the force is 500 × 2 = 1,000 newtons. Check the units first: pressure in pascals and area in square metres give a force in newtons.
Divide the force by the pressure. A skier weighs 800 N and the skis press on the snow with a pressure of 2,000 pascals, so the total ski area is 800 ÷ 2,000 = 0.4 m². There are two skis, so each one has an area of 0.4 ÷ 2 = 0.2 m². Read the question to the end before you stop.
Force is measured in newtons, N. Area is measured in square metres, m². Pressure is measured in pascals, Pa, and one pascal is one newton per square metre, so the unit itself says “force divided by area”. If a question gives an area in square centimetres, convert it before you use the formula.
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