Reverse Percentage Calculator
Enter the final amount and the percentage that was added or taken off. You get the original amount and how much the change was worth.
Do not take the percentage off the final amount. The percentage was applied to the original, so you divide instead.
Worked examples
A sale price
£60 after 25% off
Original £80
£60 ÷ 0.75 = £80. The discount was £20.
Taking VAT off
£120 after 20% added
Original £100
£120 ÷ 1.2 = £100.
About Reverse Percentage Calculator
A reverse percentage problem gives you the amount after a percentage change and asks for the amount before it. The usual mistake is to take the percentage off the new figure. If a coat is £60 in a sale with 25% off, the original price is not £60 plus 25% of £60, which would be £75. The sale price is 75% of the original, so the original is £60 divided by 0.75, which is £80.
The method never changes: turn the change into a multiplier and divide by it. An increase of 20% has a multiplier of 1.2, a decrease of 25% has a multiplier of 0.75, and a value that is 40% of the original has a multiplier of 0.4. Choose what happened, enter the amount you have now and the percentage, and the page gives the original, the size of the change and a check that multiplying back gets you to your starting amount.
How to use Reverse Percentage Calculator
- Choose whether the original was increased, reduced, or whether your amount is a percentage of it.
- Enter the amount you have now.
- Enter the percentage.
- Read the original amount, the amount added or taken off, and the check.
Common uses
- Finding the full price before a sale discount
- Taking VAT off a price that includes it
- Working out a salary before a pay rise
- Exam questions on reverse percentages
Frequently asked questions
How do I find the price before 20% VAT was added?
Choose increased by a percentage, enter the total and 20. The original is the total divided by 1.2, so £120 becomes £100 before VAT.
Why can I not just take the percentage off the new price?
The percentage was worked out on the original amount, not on the new one. Taking 25% off £60 gives £45, but the original was £80, as 25% of £80 is £20 and £80 - £20 is £60.
What if the discount is 100%?
Nothing would be left, so the original cannot be found. The page shows a message in that case.
What does the third option do?
It is for when your amount is a stated percentage of the original, for example £45 is 30% of the original. Divide by 0.3 to get £150.
Can I use it for a percentage fall in a population or value?
Yes. Any quantity that has gone down by a percentage can be reversed the same way, using the reduced by a percentage option.