Reverse Percentage Calculator
Find the original price before a discount, tax or increase.
Good to know. A 20% discount isn’t undone by a 20% increase. It takes 25%.
How it works
In plain words
Divide the final amount by the multiplier that produced it: 1 minus the percentage after a discount, 1 plus the percentage after a tax or increase.
The formula
after a decrease: original = final ÷ (1 − p ÷ 100) after an increase: original = final ÷ (1 + p ÷ 100)
Worked example
A jacket costs 60 after 25% off. The multiplier was 0.75, so the original price was 60 ÷ 0.75 = 80.
Sources
No outside data or rates: this is plain arithmetic.
7 automated tests check its answers on every change.
About the reverse percentage calculator
Reverse percentages are where most mental math goes wrong. If a jacket costs 60 after a 25% discount, it is tempting to add 25% back on: 60 + 15 = 75. But that is wrong, because the 25% was taken off the original price, not off 60. The right answer is 80.
The reliable method is to remember what happened to the original. A 25% discount left 75% of the price, so the final amount is the original × 0.75. To reverse it, divide by 0.75. The same logic works for taxes. A price including 20% VAT is the net price × 1.2, so divide by 1.2 to remove the VAT.
This is useful for checking whether a "sale" price is honest, for finding the pre-tax cost of something on a receipt, for working out a salary before a raise, or for finding a starting value from a known growth rate.
A decrease of 100% or more cannot be reversed, because nothing (or less than nothing) is left. For adding or removing VAT with more detail, try the VAT calculator.
Questions people ask
How do I find the original price before a discount?
Divide the sale price by (1 − discount). For 60 after 25% off: 60 ÷ 0.75 = 80.
Why can’t I just add the percentage back?
Because the percentage was calculated from the original, bigger number. Adding 25% of 60 gives 75, not the true original of 80.
How do I remove 20% VAT from a price?
Divide the price by 1.2. For 120 including VAT, the price before VAT is 100.
Does this work for sales tax too?
Yes. Choose "increase" and enter the tax rate. For 8% sales tax, the calculator divides by 1.08.