What this tool does and when to use it
To reverse a percentage, divide the final number by what it represents as a decimal. After a 25% discount you paid 75%, so divide by 0.75. After 20% VAT was added you paid 120%, so divide by 1.2. Never just take the percent off the final number: 20% of £120 is £24, which gives £96, the wrong answer.
How to calculate a reverse percentage
- Choose added or taken off. Was the percent added (tax, a raise, a markup) or taken off (a sale, a cut)?
- Turn it into a multiplier. Added 20% means the final is 120%, or 1.2. Taken off 25% means the final is 75%, or 0.75.
- Divide. Divide the final number by the multiplier to get the original.
The reverse percentage formula
Original = final ÷ (1 − percent ÷ 100) when the percent was taken off, and original = final ÷ (1 + percent ÷ 100) when it was added. The trick is to ask what percent of the original the final number is. After a 30% cut, what is left is 70% of the original, so you divide by 0.7. After a 15% raise, the new pay is 115% of the old, so you divide by 1.15.
Original price before a discount
Divide the sale price by what you paid as a decimal:
| Sale price | Discount | Original price |
|---|---|---|
| $45 | 25% off | $60 |
| $56 | 30% off | $80 |
| $60 | 40% off | $100 |
| $35 | 50% off | $70 |
| $68 | 15% off | $80 |
| $72 | 20% off | $90 |
A common slip is to add the percent back on. $45 plus 25% is $56.25, not the original $60, because the 25% was taken off the bigger, original price.
Price before VAT (UK, 20%)
UK standard rate VAT is 20%, so a price including VAT is 120% of the price before VAT. Divide by 1.2 to take VAT off. For the 5% reduced rate, divide by 1.05.
| Price inc. VAT | Price before VAT | VAT in the price |
|---|---|---|
| £12 | £10 | £2 |
| £60 | £50 | £10 |
| £99.99 | £83.33 | £16.66 |
| £120 | £100 | £20 |
| £250 | £208.33 | £41.67 |
| £1,000 | £833.33 | £166.67 |
Quick check: the VAT inside a 20% VAT price is always one sixth of it. £120 ÷ 6 = £20.
Price before US sales tax
Divide the total by 1 plus the tax rate. A $107.25 receipt at 7.25% sales tax was $107.25 ÷ 1.0725 = $100 before tax. Sales tax rates vary by state, county and city, so use the combined rate printed on your receipt.
Reverse percentages in exams (GCSE and SAT)
Exam questions usually give the price after a change and ask for the price before it. Write the final as a percent of the original, turn that into a decimal and divide. Example: after a 12% increase a phone costs £336. 336 ÷ 1.12 = £300. Check by going forward: £300 plus 12% is £336.
Reverse percentage in Excel and Google Sheets
- Before a discount:
=A1/(1-B1)with B1 typed as 25%. - Before VAT or a raise:
=A1/(1+B1)with B1 typed as 20%.
