Percentage change, explained with examples

By The STEM-Tutor team · Updated October 2026

Percentage change describes how much a quantity has gone up or down compared with where it started. It is used for prices, wages, populations and exam results, and it appears on every GCSE Maths paper.

The formula

percentage change = (change ÷ original) × 100

where change = new value − original value. A positive answer is a percentage increase; a negative answer is a percentage decrease. The most important word is original: always divide by the starting value, never by the new one.

Worked examples

Example 1: a percentage increase

A bike's price rises from £240 to £276. Find the percentage increase.

• Change = 276 − 240 = £36.
• Percentage increase = 36/240 × 100 = 15%.

Example 2: a percentage decrease

A town's population falls from 12,500 to 11,750. Find the percentage decrease.

• Change = 750. Percentage decrease = 750/12,500 × 100 = 6%.

Example 3: profit

A trader buys a phone for £180 and sells it for £225. Find the percentage profit.

• Profit = £45. Percentage profit = 45/180 × 100 = 25%.
• Profit and loss percentages are always calculated using the cost price, the original amount.

Example 4: a loss

A car bought for £8000 is sold for £6800. Find the percentage loss.

• Loss = £1200. Percentage loss = 1200/8000 × 100 = 15%.

Increasing and decreasing by a percentage

To change an amount by a percentage, the quickest method is a multiplier:

• increase by r%: multiply by (1 + r/100), so a 20% increase uses × 1.20;
• decrease by r%: multiply by (1 − r/100), so a 20% decrease uses × 0.80.

Multipliers work in one step and are especially useful on a calculator.

Example 5: using a multiplier

Increase £65 by 12%, and decrease 340 kg by 35%.

• 65 × 1.12 = £72.80.
• 340 × 0.65 = 221 kg.

Reverse percentages

A reverse percentage question gives the value after a change and asks for the original. The common mistake is to take the percentage off the new value. Instead, divide by the multiplier.

Example 6: after an increase

After a 20% pay rise, Amira earns £27,000. What did she earn before?

• New = original × 1.20, so original = 27,000 ÷ 1.20.
• £22,500. Taking 20% off £27,000 would give £21,600, which is wrong, because the 20% was of the smaller original amount.

Example 7: after a decrease

In a 30% off sale, a coat costs £56. What was the original price?

• Multiplier 0.70, so original = 56 ÷ 0.70.
• £80.

Example 8: VAT

A price including 20% VAT is £150. Find the price before VAT.

• 150 ÷ 1.2 = £125.

Successive percentage changes

When one change follows another, multiply the multipliers. Percentages do not simply add, because the second change applies to the new amount.

Example 9: up then down

A price rises by 10% and then falls by 10%. What is the overall change?

• Overall multiplier: 1.10 × 0.90 = 0.99.
• That is a 1% decrease, not zero. The 10% decrease was taken from a larger amount.

Example 10: two increases

A population grows by 5% one year and 8% the next. Find the overall percentage increase.

• 1.05 × 1.08 = 1.134.
• 13.4% increase, slightly more than 5 + 8 = 13.

Choosing the right method

Most percentage questions fall into one of four types. Asking which one you have is the quickest route to the right method:

• Find a percentage of an amount: multiply by the percentage as a decimal.
• Increase or decrease an amount: multiply by the multiplier.
• Find the percentage change: change ÷ original × 100.
• Find the original amount: divide by the multiplier.

Example 11: which deal is better?

A shop offers either 30% off a £20 shirt, or “buy 3 shirts for the price of 2”. Which is cheaper per shirt if you need three?

• 30% off: each shirt costs 20 × 0.7 = £14.
• 3 for 2: three shirts cost £40, so £13.33 each, a saving of 33.3%.
• The 3 for 2 offer is cheaper per shirt. Converting every offer to a price per item makes comparison easy.

Percentages in everyday life

Percentage change is everywhere: inflation figures compare prices with a year ago, sales advertise percentage discounts, and pay rises and tax rates are given as percentages. Being comfortable with multipliers and reverse percentages lets you check whether a deal is as good as it sounds. For example, if prices rise by 5% a year, something that costs £100 today will cost about £128 in five years, because 1.05⁵ ≈ 1.28.

Percent versus percentage points

If an interest rate rises from 4% to 5%, it has risen by one percentage point, but by 25 percent, because the increase of 1 is a quarter of the original 4. News stories sometimes mix these up, which can make changes sound much larger or smaller than they are. In exam answers, be precise about which one you mean, and show the original value you divided by so the examiner can follow your reasoning.

Expressing one quantity as a percentage of another

A related skill is writing one amount as a percentage of another: divide the part by the whole and multiply by 100. For example, 18 out of 24 is 18/24 × 100 = 75%. Make sure both amounts are in the same units first: 45 minutes as a percentage of 2 hours is 45/120 × 100 = 37.5%.

Common mistakes

• Dividing by the new value instead of the original.
• Subtracting the percentage from the new value in reverse percentage questions.
• Adding successive percentages instead of multiplying multipliers.
• Confusing percentage points with percent.
• Forgetting to convert units before writing one quantity as a percentage of another.

Practice questions

Try each one before opening the answer.

Frequently asked questions

Is percentage change on the Foundation paper?

Yes. Percentage change, profit and loss, and multipliers are on both tiers. Reverse percentages and successive changes appear on both, and are very common on Higher.

How do I do percentage change without a calculator?

Simplify the fraction first. For example, 36/240 = 3/20 = 15/100 = 15%. Knowing that 1/4 = 25%, 1/5 = 20% and 1/8 = 12.5% helps a lot.

Key takeaways

• Percentage change = change ÷ original × 100.
• Increase by r%: × (1 + r/100). Decrease: × (1 − r/100).
• Reverse percentages: divide by the multiplier.
• Successive changes: multiply the multipliers.
• A change of one percentage point is not the same as one percent.

Related guides

• Compound interest
• Ratio
• GCSE Maths topics