To calculate percentage change, subtract the old value from the new value, divide the result by the old value, and multiply by 100. So the formula is: (new value − old value) ÷ old value × 100. A positive answer means a percentage increase; a negative answer means a percentage decrease.
That’s the whole method in one sentence, and honestly it’s one of those bits of maths that pays for itself many times over. Whether you’re working out a pay rise, a sale discount, a house price movement or a GCSE maths question, the process is identical. Let’s walk through it properly so it sticks.
The percentage change formula, step by step
Take it in three moves:
- Find the difference. Subtract the original (old) number from the new number: new − old.
- Divide by the original. Take that difference and divide it by the old number — always the starting value, never the new one.
- Multiply by 100. This converts the decimal into a percentage.
Example: your £40,000 salary rises to £43,000. The difference is £3,000. Divide £3,000 by £40,000 to get 0.075. Multiply by 100 and you get a 7.5% increase. Done in under a minute.
Now try a decrease: a jacket reduced from £80 to £60. Difference: £20. Divide £20 by £80 to get 0.25. Multiply by 100 — that’s a 25% decrease. Notice the formula handles both directions; you just describe the result as an increase or decrease depending on whether the new value is bigger or smaller.
Percentage increase vs percentage decrease
The maths is the same, but it’s worth pausing on the language because exam questions love to test it. A percentage increase means the new value is larger — prices going up, marks improving, populations growing. A percentage decrease means the new value is smaller — discounts, pay cuts, falling temperatures.
One handy shortcut: if a quantity increases by 20%, the new value is 120% of the old (multiply the old value by 1.2). If it decreases by 20%, the new value is 80% of the old (multiply by 0.8). This “multiplier” approach is a favourite in GCSE papers and is worth practising alongside the standard formula.
Common mistakes to avoid
Most errors with percentage change come from the same handful of slips:
- Dividing by the new value instead of the old. The starting point is always your reference. A rise from £50 to £60 is a 20% increase (£10 ÷ £50), not 16.7% (£10 ÷ £60).
- Forgetting to multiply by 100. Leaving your answer as 0.25 instead of 25% is the classic lost mark.
- Mixing up percentage points and percentages. If interest rates rise from 4% to 5%, that’s a rise of 1 percentage point — but a 25% percentage increase (1 ÷ 4 × 100). Journalists and politicians blur this constantly; mathematicians shouldn’t.
- Assuming increases and decreases cancel out. A 50% increase followed by a 50% decrease does not return you to the start: £100 → £150 → £75. Each change is calculated from a different base.
- Rounding too early. Keep the full decimal through the division step and round only the final percentage — rounding midway through a multi-step question can easily cost you a mark.
If percentages in general still feel shaky, start with the basics in our guide to how to find a number as a percentage before tackling change over time.
Real-world examples you’ll actually use
House prices: a flat bought for £220,000 sells for £253,000. (£253,000 − £220,000) ÷ £220,000 × 100 = a 15% increase.
Exam results: you scored 56% on a mock and 70% on the real thing. (70 − 56) ÷ 56 × 100 = a 25% improvement. (That’s 14 percentage points, for the purists.)
Energy bills: your direct debit rises from £145 to £174 a month. (£174 − £145) ÷ £145 × 100 = a 20% increase — worth knowing before you ring your supplier.
Pay vs inflation: a 4% pay rise when inflation is running at 6% is actually a real-terms cut of roughly 2%. Percentage change cuts through the nominal figures and shows what’s really happening to your money.
Working backwards: finding the original value
Sometimes you know the percentage change and the new value, but need the original. A TV is £360 after a 10% discount — what was it before? Divide by the multiplier: a 10% discount means you paid 90%, so £360 ÷ 0.9 = £400. The same trick works for increases: if a £2,875 bonus followed a 15% rise, the original was £2,875 ÷ 1.15 = £2,500. GCSE papers love this “reverse percentage” question, so practise it until the multiplier step feels automatic.
The BBC Bitesize maths section has interactive practice questions on exactly this topic if you want to drill it, and statistics-minded readers may also enjoy how to find degrees of freedom.
Quick-fire FAQs
What is the formula for percentage change?
(New value − old value) ÷ old value × 100. Positive result = increase, negative result = decrease.
How do you calculate percentage increase only?
Use the same formula — if the new value is larger, the answer is automatically positive, which is your percentage increase. Example: 50 to 65 is (65 − 50) ÷ 50 × 100 = 30%.
How do you work out percentage decrease?
Same formula again. Example: 80 to 60 is (60 − 80) ÷ 80 × 100 = −25%, i.e. a 25% decrease. Many people just calculate (old − new) ÷ old × 100 to keep the number positive.
What is the difference between percent change and percentage points?
Percent change is relative to the starting value; percentage points are the simple arithmetic difference between two percentages. Going from 20% to 25% is a 5-percentage-point rise but a 25% increase.
Can percentage change be more than 100%?
Yes. If something doubles, that’s a 100% increase; if it triples, it’s a 200% increase. Percentage decreases, though, can never go below −100% (that would mean going below zero).
