How to Calculate Percentage Change
Percentage change = change ÷ original × 100
The bottom of the fraction is always the original value — the amount before the change — never the new one. That single choice is what most marks are lost on.
Worked example. A price rises from £80 to £92. The change is £12, so 12 ÷ 80 × 100 = 15% increase. Dividing by 92 instead gives 13.0%, which is the classic wrong answer.
Percentage change tells you how much a value has gone up or down compared with the amount it started at, and it is one of the most heavily examined percentage skills in Edexcel IGCSE Maths. This page covers the three questions the topic asks: writing one amount as a percentage of another, finding the percentage increase or decrease from an old value to a new one, and working out a percentage error. Each method is set out step by step with worked examples, and there are four practice rooms of randomly generated questions below that mark themselves the moment you answer.
How to Calculate Percentage Change: Step by Step
Three exam questions live inside this one topic. They look different on the page but they are the same piece of arithmetic: put one number over another, then multiply by 100. What changes each time is which number goes on the bottom, and getting that right is the whole skill.
The three questions this topic asks, and what goes on the bottom of each
Writing one amount as a percentage of another
- Check the two amounts are in the same units. If they are not, convert one of them first.
- Write the amount you are describing over the amount you are comparing it with.
- Multiply by 100.
On the bottom: the amount named after "as a percentage of".
Finding a percentage increase or decrease
- Work out the change: subtract the smaller value from the larger one.
- Divide the change by the original value, the one the quantity started at.
- Multiply by 100, then say whether it is an increase or a decrease.
On the bottom: where the quantity started, never where it finished.
Finding a percentage error
- Work out the error: the gap between the measured or estimated value and the true value.
- Divide the error by the true value, never by the measurement.
- Multiply by 100.
On the bottom: the value it should have been, not the one that was read off.
Percentage profit and percentage loss are method 2 with the buying price as the original, and percentage error is method 2 with the true value as the original. Once you can name the starting amount, all three are the same three steps.
Which bar goes on the bottom of the fraction
The lower bar is the new value, and it is the original value with the change added on. The fraction is orange over blue: the change divided by the original. The new total, the whole lower bar, never goes on the bottom.
Worked Examples
💡 Example 1: One amount as a percentage of another
A cable 84 cm long is cut from a reel holding 3 m of cable. What percentage of the reel is used?
What's happening?
The units do not match, so the reel is converted to centimetres before anything else. The reel is the amount being compared with, so 300 goes on the bottom.
💡 Example 2: Percentage increase
A bakery's weekly flour order rises from 45 kg to 54 kg. Work out the percentage increase.
What's happening?
The order started at 45 kg, so 45 is the original and goes on the bottom. Dividing by 54 would give 16.67%, which is the classic wrong answer here.
💡 Example 3: Percentage decrease, with rounding
A ferry crossing is shortened from 96 minutes to 71 minutes. Work out the percentage decrease, correct to 2 decimal places.
What's happening?
Keep the full decimal on your calculator and round only at the very end. Rounding 26.0416 to 26.0 and then to 26 loses accuracy the mark scheme will not give back.
💡 Example 4: Percentage error
A tank holds 640 litres. A faulty gauge reads 664 litres. Work out the percentage error in the gauge reading.
What's happening?
640 is what the tank really holds, so it is the true value and goes on the bottom. The 664 is only what the gauge claimed, and it never goes there.
💡 Example 5: Percentage profit and percentage loss
A trader buys a bicycle for £240 and sells it for £306. On the same day she buys a scooter for £180 and sells it for £153. Work out her percentage profit on the bicycle and her percentage loss on the scooter.
What's happening?
Profit and loss are percentage change under another name, and the buying price is always the original. Notice that the two items have different buying prices, so the same cash change would not give the same percentage. That is exactly why the question is worth asking.
Choosing the Bottom of the Fraction
The bottom is never hidden: the question always names it, in one of a small number of ways. Learn to spot the phrase and the fraction writes itself.
| The question asks for | Write this fraction | The words that name the bottom |
|---|---|---|
| x as a percentage of y | \( \dfrac{x}{y} \times 100 \) | Whatever comes straight after "as a percentage of". |
| Percentage increase | \( \dfrac{\text{increase}}{\text{original}} \times 100 \) | "rose from", "increased from", "started at". The from value. |
| Percentage decrease | \( \dfrac{\text{decrease}}{\text{original}} \times 100 \) | "fell from", "reduced from", "was shortened from". Again the from value. |
| Percentage profit or loss | \( \dfrac{\text{profit or loss}}{\text{buying price}} \times 100 \) | "bought for", "paid", "cost price". Never the selling price. |
| Percentage error | \( \dfrac{\text{error}}{\text{true value}} \times 100 \) | "actually", "really", "true value", "should have been". |
Every top is a gap between two amounts, so work it out as the larger minus the smaller and give the answer as a positive percentage, then say in words whether it is an increase, a decrease, a profit or a loss.
🔑 Key Points
- Every question on this page is one fraction multiplied by 100. Only the bottom changes.
- The bottom is always where the quantity started: the original value, the buying price, or the true value.
- Convert to matching units before dividing, not after.
- A percentage increase and a percentage decrease are both reported as a positive number, with the direction stated in words. Writing the change as a signed percentage, such as a fall of 12% being −12%, means the same thing.
- Keep the full calculator value until the final line, then round once.
- A percentage change can be larger than 100%: doubling a value is a 100% increase, and trebling it is a 200% increase.
⚠️ Common Pitfalls
- Dividing by the new value. This is the single most common lost mark on the topic. A rise from 45 to 54 is a 20% increase, not a 16.67% increase.
- Comparing amounts in different units. 84 cm out of 3 m is 28%, not 2800%.
- Forgetting to multiply by 100. An answer of 0.28 is a decimal, not a percentage.
- Rounding too early. Rounding the division before multiplying by 100 can move the final answer by a whole percent.
- Assuming a decrease then an increase of the same percentage returns you to the start. It does not, because the second percentage is taken of a different amount.
- Using the measured value as the true value in a percentage error. The true value is what the quantity actually is, and it is always the bottom.
The Rest of the Percentages Topic
Percentage change is one skill inside a larger topic. These are the other percentage questions the exam asks, each with its own worked examples and its own auto-marked practice rooms.
Percentage increase and decrease — running the change forwards
Percentage change works backwards from two known amounts to find the percentage. Increase and decrease works forwards: you are given a starting amount and a percentage, and you find the new value. The multiplier method does it in one step — a 15% increase is × 1.15, and a 15% decrease is × 0.85.
Percentage increase and decrease →
Reverse percentages — finding the original value
A reverse percentage question gives you the amount after a change and asks what it was before. You divide by the multiplier instead of multiplying by it. If a price is £92 after a 15% increase, the original was 92 ÷ 1.15 = £80. The common mistake is taking 15% off the £92, which gives the wrong answer every time.
Reverse and inverse percentages →
Compound interest — the same change repeated
When a percentage change is applied over and over, each change acts on the new amount rather than the original. You raise the multiplier to a power: £80 growing at 15% a year for 3 years reaches 80 × 1.153. This covers compound interest, depreciation and population growth.
Compound interest and depreciation →
Ratios — the neighbouring topic
Ratio questions share the same underlying skill of comparing two amounts, and exam questions often combine the two.