Reverse percentage calculator.
Work back from a number that already includes a percentage: the price before tax, the list price before a sale, or a salary before a raise. The working shows why you divide instead of subtract.
To undo a percentage, divide, don’t subtract. The original before a 15% increase is the new value ÷ 1.15, so 115 ÷ 1.15 = 100. The original before a 20% discount is the sale price ÷ 0.80, so 72 ÷ 0.80 = 90. Enter your numbers above.
See also: Discount calculator · GST, VAT and customs guide · Percentage increase calculator
How to reverse a percentage
A reverse percentage works back from a number that already includes a percentage change to the number before it. The key fact: after a P% increase, the new value is (100 + P)% of the original. So you divide by that multiplier.
original = new value ÷ (1 + P ÷ 100) after an increase
original = sale price ÷ (1 − P ÷ 100) after a discountWhy subtracting the percentage gives the wrong answer
A price rose 15% to 115. Taking 15% off 115 gives 115 − 17.25 = 97.75, not 100. The 15% was 15% of the original 100, which is 15. Taking 15% of 115 uses the wrong base, so the result comes out too low. The same mistake on a discount comes out too low as well: adding 20% back onto a sale price of 72 gives 86.40, but the list price was 72 ÷ 0.80 = 90.
Removing tax from a price that includes it
Many countries quote prices with tax included: VAT in the UK and EU, GST in India and Australia. To find the price before tax, divide by 1 plus the rate. A ₹1,180 bill that includes 18% GST is ₹1,180 ÷ 1.18 = ₹1,000 before tax, and the tax is ₹180. A £120 price including 20% VAT is £120 ÷ 1.20 = £100 before VAT.
This tool takes the rate you type and keeps no tax tables, so check the rate for your product and country with the tax authority. The GST, VAT and customs guide links to the official rate pages.
Two worked examples
A salary after a raise. Your salary is 61,800 after a 3% raise. Before the raise it was 61,800 ÷ 1.03 = 60,000, so the raise was worth 1,800.
A sale price. A jacket costs 63 at 30% off. The full price was 63 ÷ 0.70 = 90, so you save 27.
Reverse percentage in Excel or Google Sheets
With the final value in A2 and the percentage in B2, the original before an increase is =A2/(1+B2/100), and before a discount it is =A2/(1-B2/100). If B2 is already formatted as a percentage, drop the /100.
When to use this vs the other calculators
Use this tool when you know the result and need the starting number. If you know the starting number and the percentage, use the percentage increase calculator or the discount calculator instead.
Sources
About this tool.
Divide the new price by 1 plus the percentage as a decimal. After a 15% increase to 115, the original is 115 ÷ 1.15 = 100.
Divide the sale price by 1 minus the discount as a decimal. A sale price of 72 after 20% off was 72 ÷ 0.80 = 90 before the discount.
Because the percentage was taken from the original number, not the new one. 15% of 115 is 17.25, but the increase was 15% of 100, which is 15. Subtracting gives 97.75 instead of 100.
Divide the price that includes GST by 1.18. ₹1,180 including 18% GST is ₹1,000 before tax, and the GST is ₹180.
Divide by 1.20. A price of £120 including 20% VAT is £100 before VAT; the VAT is £20. Dividing by 1.2 is not the same as taking 20% off, which would give £96.