Reverse percentage calculator
Know the final value and the percentage applied? Work backwards to the original amount.
Find the original value
Example: $120 after a 20% increase → original $100
How reverse percentages work
To undo a percentage change you divide by the growth factor — you never just subtract the percentage from the final value, because the percentage was applied to the original, smaller (or larger) number.
After an increase
$120 after a 20% increase → 120 ÷ 1.20 = $100
After a decrease
$56 after a 30% discount → 56 ÷ 0.70 = $80
Examples
The classic mistake
A price of $120 after a 20% increase did not start at $96 (120 minus 20%). The 20% was charged on the original $100, not on $120 — so 20% of the final value is too much to subtract. Whenever you need to undo a percentage, divide by the factor instead of subtracting the percentage.
Frequently asked questions
How do I find the original price before VAT?
Divide the gross price by (1 + rate ÷ 100). For 20% VAT divide by 1.20 — or use the VAT calculator in remove mode.
How do I find the price before a discount?
Divide the sale price by (1 − discount ÷ 100). $56 after 30% off → 56 ÷ 0.70 = $80.
Why can’t I just subtract the percentage from the final value?
Because the percentage was calculated on the original value, not the final one. Subtracting it from the final value uses the wrong base and gives an answer that is too low (after increases) or too high (after decreases).
What happens with a 100% decrease?
The original cannot be recovered — a 100% decrease sends every value to zero, so the calculation is undefined.
Does this work for successive changes?
Undo them one at a time in reverse order. After +10% then +20%, divide by 1.20 first, then by 1.10.