How to Calculate Percentage Change
Percentage change is a core GCSE and IGCSE Maths skill that tells you how much a value has increased or decreased compared with its original amount. In this guide you will learn the standard method step by step, including how to spot increases vs decreases, how to avoid using the new value by mistake, and how to present your final answer clearly. Work through the examples, then practise with randomly generated questions so you can build speed and accuracy.
How to Calculate Percentage Change: Step by Step
Percentage change tells you how much a value has grown or shrunk relative to its original size. Follow these four steps:
- Find the difference. Subtract the original value from the new value: \( \text{new} - \text{original} \). Take the size (absolute value) of this number.
- Divide by the original value. Always divide by the value you started with, not the new value.
- Multiply by 100. This converts the decimal into a percentage.
- State the direction. If the new value is larger, it is a percentage increase. If smaller, it is a percentage decrease.
Quick example: if a price rises from \(£200\) to \(£230\), the difference is \(£30\). Dividing by the original gives \( 30 \div 200 = 0.15 \), and multiplying by 100 gives a \(15\%\) increase.
Worked Examples
💡 Example 1: Percentage Increase
A bike's price rises from \( £260 \) to \( £299 \). Find the percentage increase.
\( \text{difference} = 299 - 260 \)
\( = 39 \)
What's happening?
Find the difference between the new price and the original price.
\( \dfrac{39}{260} = 0.15 \)
What's happening?
Divide by the original value (\(£260\)), not the new one.
\( 0.15 \times 100\% = 15\% \)
Answer: \(15\%\) increase.
What's happening?
Multiply by 100 to convert to a percentage. The new price is higher, so it is an increase.
💡 Example 2: Percentage Decrease
A school's energy use drops from \( 12{,}000 \) kWh to \( 9{,}600 \) kWh. Find the percentage decrease.
\( \text{difference} = 12{,}000 - 9{,}600 \)
\( = 2{,}400 \)
What's happening?
Find the size of the drop.
\( \dfrac{2{,}400}{12{,}000} = 0.2 \)
What's happening?
Divide by the original value (\(12{,}000\) kWh).
\( 0.2 \times 100\% = 20\% \)
Answer: \(20\%\) decrease.
What's happening?
The new value is lower, so it is a decrease.
💡 Example 3: Rounding the Answer
A phone's price rises from \( £349 \) to \( £419 \). Find the percentage increase to 1 decimal place.
\( \text{difference} = 419 - 349 \)
\( = 70 \)
What's happening?
Find the size of the rise.
\( \dfrac{70}{349} = 0.200573\ldots \)
What's happening?
Divide by the original. Keep the full decimal for now.
\( 0.200573\ldots \times 100\% = 20.0573\ldots\% \)
\( \approx 20.1\% \) (to 1 d.p.)
Answer: \(20.1\%\) increase.
What's happening?
Multiply by 100, then round. Rounding earlier would lose accuracy.
💡 Example 4: Large Decrease
A library's stock falls from \( 1{,}840 \) books to \( 1{,}564 \) books. Find the percentage decrease.
\( \text{difference} = 1{,}840 - 1{,}564 \)
\( = 276 \)
What's happening?
Find the size of the drop.
\( \dfrac{276}{1{,}840} = 0.15 \)
What's happening?
Divide by the original value, \(1{,}840\). A common mistake is to divide by the new value (\(1{,}564\)) which would give the wrong answer.
\( 0.15 \times 100\% = 15\% \)
Answer: \(15\%\) decrease.
What's happening?
The new value is smaller, so it is a decrease.
🔑 Key Points
- Formula: \( \dfrac{\text{new} - \text{original}}{\text{original}} \times 100\% \).
- Always divide by the original value, never the new one.
- Use the absolute size of the difference, then decide the direction from the signs of the values.
- Round only at the very end, to the accuracy the question asks for.
- Include the \(\%\) symbol and state whether it is an increase or decrease.
⚠️ Common Pitfalls
- Dividing by the new value instead of the original. This is the most common error.
- Forgetting to multiply by 100, giving an answer like \(0.15\) when \(15\%\) was wanted.
- Rounding mid-calculation and losing accuracy in the final answer.
- Omitting the direction. "It changed by \(15\%\)" is ambiguous: say "increase" or "decrease".
- Confusing percentage change with percentage of. \(15\%\) of \(£200\) is \(£30\); that is a different calculation.