Reverse Percentage Calculator
Work backwards from a final value to the number before a percentage was added or taken off.
Multiplier = 1 + 20 ÷ 100 = 1.2Original = 90 ÷ 1.2 = 75Check: 75 × 1.2 = 90
How reverse percentages work
A percentage increase multiplies the original value by (1 + p ÷ 100); a decrease multiplies it by (1 − p ÷ 100). To undo it, divide by the same multiplier. Do not apply the percentage to the final value: it was calculated on the original.
Examples
| Situation | Working | Original |
|---|---|---|
| Price after a 20% rise is 90 | 90 ÷ 1.20 | 75 |
| Paid 60 after 25% off | 60 ÷ 0.75 | 80 |
| 54 including 8% sales tax | 54 ÷ 1.08 | 50 |
Related
To find the percentage itself when you know both numbers, use the percent increase or percent decrease calculator.
Frequently asked questions
How do I find the original value before a percentage increase?
Divide the final value by (1 + percentage ÷ 100). If a price rose 20% to 90, the original was 90 ÷ 1.2 = 75.
How do I find the original price before a discount?
Divide the price you paid by (1 − discount ÷ 100). If you paid 60 after a 25% discount, the original price was 60 ÷ 0.75 = 80.
How do I remove tax from a price?
Divide the price including tax by (1 + tax rate ÷ 100). A total of 54 including 8% tax is 54 ÷ 1.08 = 50 before tax.
Why can't I just subtract the percentage?
Because the percentage was applied to the original value, not the final one. Taking 20% off 90 gives 72, but 72 increased by 20% is 86.40, not 90.