To increase a number by a percentage, multiply it by 1 plus the percentage as a decimal. To decrease it, multiply by 1 minus the percentage. So adding 10% means multiplying by 1.1, and taking off 10% means multiplying by 0.9. To go backwards, divide by the same multiplier instead.
The multiplier method
The quickest, least error-prone way to handle any percentage change is a single multiplication. Turn the percentage into a decimal (divide by 100), then add it to or subtract it from 1.
| Change | Multiplier |
|---|---|
| Increase by 5% | × 1.05 |
| Increase by 20% | × 1.2 |
| Increase by 50% | × 1.5 |
| Decrease by 10% | × 0.9 |
| Decrease by 25% | × 0.75 |
| Decrease by 50% | × 0.5 |
Worked example: a price of £200 goes up by 10%. The multiplier is 1.1, and £200 × 1.1 = £220. If it came down by 10% instead, £200 × 0.9 = £180. The method is the same as the one in our guide on How to calculate percentages, just with a final step of adding or subtracting.
You can also work out the change first and then add it. Ten per cent of £200 is £20, so the new price is £200 + £20 = £220. Both routes give the same answer; the multiplier is quicker when you are applying a change several times.
Why +10% then −10% does not get you back
This catches many people out. Start with £100, add 10% to get £110, then take off 10%. The second percentage is taken from £110, not from £100, so you lose £11 and end at £99.
The same happens with any pair of equal changes in opposite directions. Increase 50% then decrease 50%: 100 becomes 150, then 75. You finish at 75% of where you began.
The reason is that percentages are always relative to the number they are applied to. A rise makes the base bigger, so the matching fall removes more. To undo a change exactly, the reverse percentage is not the same size:
- After a 10% rise, you need a fall of about 9.09% to get back (1 ÷ 1.1 = 0.909).
- After a 10% fall, you need a rise of about 11.11% (1 ÷ 0.9 = 1.111).
- After a 50% fall, you need a rise of 100%.
The Percentage increase and decrease shows this “change needed to get back” figure for any percentage you enter.
Repeated percentage changes
When the same percentage is applied again and again, such as yearly growth or a repeated discount, the changes compound. Each step applies to the result of the previous one, so you multiply by the multiplier once for each step.
Worked example: £1,000 grows by 5% a year for three years. The overall multiplier is 1.05 × 1.05 × 1.05 = 1.157625, giving £1,157.63 (rounded to the penny). The overall rise is about 15.76%, not 15%, because the later rises are applied to a larger amount.
Never add the percentages together when changes follow each other. Two successive 20% discounts are not a 40% discount: 0.8 × 0.8 = 0.64, so the total reduction is 36%. For more on this, see Percentage change, increases and discounts.
Reverse percentages: finding the original
A reverse percentage question starts from the final figure and asks for the original. The rule is to divide by the multiplier, not to subtract or add the percentage.
- If a percentage was added, original = final ÷ (1 + rate).
- If a percentage was taken off, original = final ÷ (1 − rate).
Worked example: a sale price is £75 after 25% was taken off. The multiplier was 0.75, so the original was £75 ÷ 0.75 = £100. If you wrongly added 25% to £75 you would get £93.75, which is not the original price.
Removing VAT from a VAT-inclusive price
A common reverse percentage is taking VAT out of a price. UK VAT has a standard rate of 20%, a reduced rate of 5% and a zero rate. Check GOV.UK for which rate applies to a particular good or service.
At 20%, a price including VAT is the net price × 1.2. To get back to the net price, divide by 1.2. For a VAT-inclusive price of £120, the net price is £120 ÷ 1.2 = £100, and the VAT is £20.
The tempting shortcut is to take 20% off £120, which gives £96. That is wrong, because the VAT was 20% of the net price, not 20% of the total. Our guide to VAT explained: adding and removing VAT covers adding and removing VAT in more detail, and the Reverse percentage and VAT-inclusive price has 20%, 5% and 0% presets.
Note: This is general information, not financial, tax or accounting advice. Check GOV.UK or a qualified adviser for your own VAT position.
Try the calculator
Use the Percentage increase and decrease to increase or decrease any number and see the multiplier and the step-by-step results. Use the Reverse percentage and VAT-inclusive price to find the original price before VAT or a discount. To compare two known numbers, the Percentage change works out the percentage between them.
Open the free Percentage increase and decrease
Frequently asked questions
How do I increase a number by 15%?
Multiply it by 1.15. For example, 80 × 1.15 = 92. To decrease it by 15%, multiply by 0.85 instead.
Why isn't a 20% rise followed by a 20% fall back to the start?
The fall is taken from the larger, increased number. 100 rises to 120, then falls by 20% of 120, which is 24, leaving 96.
How do I find the original price after a discount?
Divide the sale price by 1 minus the discount as a decimal. If the sale price is £60 after 40% off, divide by 0.6 to get £100.
Can I just subtract 20% to remove VAT?
No. Divide the VAT-inclusive price by 1.2 for the standard rate. Subtracting 20% of the total takes off too much.