Percentage Increase and Decrease, Explained with Examples
Maths guide · Updated June 2026
Prices go up, audiences grow, energy bills jump, sale tags promise "30% off." All of these are the same idea — a percentage increase or decrease — and once you can calculate one, you can calculate them all. The arithmetic takes ten seconds. What trips people up is what happens when changes stack, or when you need to run one backwards. This guide covers the basic formula and then the two situations where intuition fails most people. To check any figure as you go, the percentage change calculator handles increases and decreases in one place.
The one formula behind both
Increase and decrease are not two formulas — they are one. Take the difference between the new and old values, divide by the old value, and multiply by 100. A positive answer is an increase, a negative one a decrease.
Increase example. A subscription rises from £50 to £65.
- Difference: £65 − £50 = £15
- £15 ÷ £50 = 0.30 = a 30% increase
Decrease example. A coat drops from £80 to £60.
- Difference: £60 − £80 = −£20
- −£20 ÷ £80 = −0.25 = a 25% decrease
The only thing to be careful about is the denominator: you always divide by the figure you started from. If you want each direction on its own, the percentage increase calculator and percentage decrease calculator do exactly that.
Applying a change directly
Often you don't want the percentage — you want the result. To apply a change in one step, use a multiplier: for an increase multiply by (1 + rate); for a decrease multiply by (1 − rate).
So £200 increased by 15% is £200 × 1.15 = £230, and £200 reduced by 15% is £200 × 0.85 = £170. A "30% off" tag is just a 30% decrease — multiply the price by 0.70. That's the engine inside the percent-off calculator and the discount calculator you reach for at the till.
Trap 1: changes don't add up
Stack two percentage changes and you cannot simply add them, because the second change is applied to the new, larger (or smaller) amount — not the original.
Example. A £100 bill rises 10%, then rises another 10%.
- After the first rise: £100 × 1.10 = £110
- After the second: £110 × 1.10 = £121
- Overall change: 21%, not 20%
That extra 1% is the second rise acting on the first rise's £10. The effect grows with bigger numbers and more steps — it's the same compounding that makes savings and inflation snowball over time, explored in the compound interest calculator.
A rise and a fall don't cancel either. Put £100 up 25% to £125, then down 25%, and you land on £93.75 — not £100. Because the 25% fall is taken from the bigger £125, it removes more than the rise added. Equal-looking percentages in opposite directions always leave you below where you began.
Trap 2: running a change backwards
When you know the result and want the starting point — the price before a discount, the figure before a markup — you must divide, not add the percentage back.
Example. A jacket costs £90 after 25% off. What was the original price?
- £90 is 75% of the original (100% − 25%)
- Original: £90 ÷ 0.75 = £120
Adding 25% back to £90 would give £112.50 — wrong, because the discount was calculated on the higher original, not the sale price. This "work backwards" job is common enough to have its own tool: the reverse percentage calculator.
Quick reference
| You want to… | Do this |
|---|---|
| Find the % change between two numbers | (New − Old) ÷ Old × 100 |
| Increase a number by a % | × (1 + rate) |
| Decrease a number by a % | × (1 − rate) |
| Find the original before a change | Result ÷ (1 ± rate) |
The takeaway
One formula covers both increase and decrease — difference over the original, times 100. To apply a change, multiply by (1 ± rate). Remember that stacked changes multiply rather than add, that a matching rise and fall never cancel, and that going backwards means dividing. Keep the percentage change calculator to hand for the everyday cases and you've got every version covered.
Frequently asked questions
What's the formula for a percentage increase?
Subtract the old value from the new value, divide by the old value, and multiply by 100. From 50 to 65 is (65 − 50) ÷ 50 × 100 = a 30% increase. A percentage decrease uses the same formula; the result simply comes out negative.
Do two percentage changes add together?
No. A 10% rise followed by another 10% rise is not a 21% gain because the second rise applies to the already-larger amount. £100 becomes £110, then £121 — a 21% increase overall, not 20%. Successive percentages multiply, they don't add.
If a price rises 25% then falls 25%, am I back where I started?
No, you end up lower. £100 rising 25% is £125; £125 falling 25% is £93.75. Each percentage is taken from a different base, so an equal rise and fall never cancel — you finish below the original every time.
How do I find the original price after a discount?
Divide, don't add. If an item is £90 after 25% off, that £90 is 75% of the original, so the original was £90 ÷ 0.75 = £120. Adding 25% back on would give the wrong answer because the discount was taken from the higher original price.
Is '20% off' the same as a 20% decrease?
Yes — they're identical calculations. '20% off' is just retail language for a 20% decrease on the original price. Multiply the price by 0.80 (or 1 minus the discount) to get the sale price.