Percentage Change
Percentage change measures how much a quantity has increased or decreased relative to its original value.
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Percentage change measures how much a quantity has increased or decreased relative to its original value.
- Change divided by original, times 100
- A 20 percent rise multiplies by 1.2
- A 20 percent fall multiplies by 0.8
🧠 Quick quiz
Three questions. Score 2 or more to complete the topic.
What is Percentage Change?
Within Mathematics, which covers numbers, algebra, geometry, trigonometry and statistics from first principles to exam level, this topic explains Percentage Change. Maths builds step by step, so each topic here gives you a rule, a picture and a quick check you can use on homework and in exams.
Check that you can explain Percentage Change in your own words and give one example from everyday life. If you can do that, you have understood the core idea.
Understanding Percentage Change gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
Percentage Change in detail
Percentage change measures how much a quantity has increased or decreased compared with its original value: change ÷ original × 100. If a price rises from £40 to £50, the change is £10, so the increase is 10 ÷ 40 × 100 = 25%.
A multiplier method is faster for repeated work: increasing by 20% means multiplying by 1.2, and decreasing by 20% means multiplying by 0.8. Always compare against the original, not the new value. Percentage change is used for sales, profit and loss, population growth and inflation.
How the interactive helps you understand Percentage Change
Watch the growth curve in the interactive. Use any sliders or buttons it offers to change the values and see how the growth curve responds.
Before you change anything, predict the result. Then change one value at a time and check whether your prediction was right. This is a quick way to build a correct mental model of Percentage Change.
Real-life uses and examples
- Spot Percentage Change in exam questions, where it often sits inside a short word problem.
- Check a homework answer about Percentage Change by estimating first, then working it out step by step.
- Use Percentage Change when comparing prices, discounts or recipe quantities in everyday life.
Common mistakes to avoid
- Forgetting units, signs or brackets when you apply Percentage Change.
- Memorising the steps for Percentage Change without checking why they work.
- Learning the definition without testing it. Use the quiz and the interactive to check that you can apply the idea.
Frequently asked questions about Percentage Change
What is Percentage Change?
Percentage change measures how much a quantity has increased or decreased relative to its original value.
What are the most important points about Percentage Change?
The main points are: Change divided by original, times 100; A 20 percent rise multiplies by 1.2; A 20 percent fall multiplies by 0.8.
Why is Percentage Change useful?
Understanding Percentage Change gives you a reliable method you will reuse in later maths units, in science lessons and in data work.
How can I practise Percentage Change?
Open the interactive at the top of this page and change the controls one at a time. Predict the result before each change, then take the three-question quiz. A score of two or more marks the topic as complete on this device.
Which topics are related to Percentage Change?
Related topics in Mathematics include Proportion, Laws of Indices, Standard Form.