A reverse percentage calculation finds the original number before a percentage was added, removed, or applied. The key is to treat the final amount as a percentage of the original—not simply add or subtract the same percentage again.
Reverse percentage formula
Original value = Final value ÷ Percentage multiplier
After a percentage increase, the multiplier is 1 plus the rate as a decimal. After a decrease, it is 1 minus the rate.
Find the original value after an increase
If a price is $120 after a 20% increase, the final price equals 120% of the original. Convert 120% to 1.20, then calculate 120 ÷ 1.20. The original price was $100.
The general formula is: Original = Final ÷ (1 + rate ÷ 100).
Find the original value after a decrease
If a jacket costs $72 after a 20% discount, the sale price is 80% of the original. Calculate 72 ÷ 0.80 to get an original price of $90.
The general formula is: Original = Final ÷ (1 − rate ÷ 100).
Why adding the percentage back does not work
A 20% discount on $90 is $18, producing $72. Adding 20% of $72 gives $86.40, not $90, because the two percentages use different base values. Division by the remaining percentage correctly restores the original base.
When one number is a percentage of another
If 45 is 15% of an unknown number, divide 45 by 0.15. The original number is 300. In general: Whole = Part ÷ (percentage ÷ 100).
More examples
| Final value | Change | Calculation | Original |
|---|---|---|---|
| 230 | 15% increase | 230 ÷ 1.15 | 200 |
| 170 | 15% decrease | 170 ÷ 0.85 | 200 |
| 84 | 30% of original | 84 ÷ 0.30 | 280 |
Common mistakes
- Adding a discount percentage to the discounted price.
- Using 20 instead of 0.20 in the multiplier.
- Using 0.20 rather than 0.80 for a value remaining after a 20% decrease.
- Rounding the multiplier or intermediate result too early.
Frequently asked questions
How do I reverse a 25% increase?
Divide the final number by 1.25.
How do I reverse a 25% discount?
Divide the sale value by 0.75 because 75% remains.
Can I reverse a 100% decrease?
No. A 100% decrease turns every starting value into zero, so the original cannot be recovered from the final value alone.
Use the percentage calculator to check the percentage steps in your calculation.