Force calculations
Force calculations using pressure and area are crucial in understanding how different surfaces interact with forces in real life. Whether it’s how a knife slices through food or how snowshoes keep you from sinking into deep snow, learning how to calculate force from pressure and area helps explain many everyday phenomena in engineering, nature, and design. Jump to the questions
Practise now
Calculate the force using the formula: Force = Pressure × Area. Give your answer in Newtons (N).
Topic guide
What this worksheet practises
This worksheet focuses on using the formula relating Force, Pressure, and Area. This is a common cross-curricular topic that appears in both mathematics and physics exams.
Key method
The core relationship is given by the formula: Pressure = Force ÷ Area. A formula triangle is highly recommended here.
- Draw a triangle with Force (F) at the top, and Pressure (P) and Area (A) at the bottom.
- Identify which two values you have been given in the question.
- Cover up the value you want to find with your thumb. The remaining letters show you the calculation to perform.
- If P and A are next to each other at the bottom, it means multiply (F = P × A).
- If F is over P or A, it means divide (P = F ÷ A, or A = F ÷ P).
Worked example
A box exerts a force of 120 Newtons on the ground. The base of the box has an area of 4 m². Calculate the pressure exerted by the box.
Step 1: Identify the knowns. Force (F) = 120 N. Area (A) = 4 m².
Step 2: We want to find Pressure (P). Covering P on the triangle leaves F over A.
Therefore, Pressure = Force ÷ Area.
Step 3: Substitute the numbers.
Pressure = 120 ÷ 4.
Step 4: Perform the calculation.
Pressure = 30.
Step 5: Add the correct units. Because Force was in N and Area in m², the pressure is N/m².
The pressure is 30 N/m².
Common mistakes to avoid
The most common mistake is multiplying the two numbers together regardless of what they represent. If you are given Force and Area, you must divide them. Also, be careful with units. If the force is in Newtons and the area is in cm², the pressure must be given as N/cm², not N/m².
Things to remember
Pressure is essentially a measure of how "concentrated" a force is. A stiletto heel exerts a massive pressure because its area is tiny, meaning the force is divided by a very small number. Flat shoes exert low pressure because the area is large.