Case 1
- What do you know?
- After a % increase (a price including tax)
- Value you know
- 120
- Percentage
- 20%
100.00
Open with these valuesReverse Percentage Calculator
100.00
Result: 100.00120 after a 20 % increase came from 100, not from 96: you divide by 1.20, you do not take 20 % off. The percentage was measured against the original, and the original is larger than the figure you are holding. Pick the situation, then enter your value and the percentage.
Worked examples
Case 2
- What do you know?
- After a % decrease (a sale price)
- Value you know
- 120
- Percentage
- 20%
150.00
Open with these valuesCase 3
- What do you know?
- A % of an unknown number
- Value you know
- 30
- Percentage
- 25%
120.00
Open with these valuesHow it's calculated
increase: V ÷ (1 + p) · decrease: V ÷ (1 − p) · of: V ÷ p
- StepPick the situation: after an increase, after a decrease, or a share of an unknown whole.
- StepEnter the value you already have and the percentage involved.
- StepThe calculator divides by the multiplier — 1.20 after a 20 % rise, 0.80 after a 20 % cut.
- ResultA 100 % decrease and a 0 % share have no original value, so the result stays empty.
Reference table
| What you know | Divide by | Original value |
|---|---|---|
| 80 after a 20 % decrease | 0.80 | 100 |
| 120 after a 20 % increase | 1.20 | 100 |
| 30 is 25 % of a number | 0.25 | 120 |
| 120 after a 20 % decrease | 0.80 | 150 |
| 220 after a 10 % increase | 1.10 | 200 |
Questions
What is a reverse percentage?
It works backwards from a value that already contains a percentage change to the amount you started with. A jacket costing 120 in a 20 % off sale was originally 150. You have the result and want the starting number.
Why can I not just add the percentage back?
Because the percentage was taken from the original, not from the reduced figure. Adding 20 % to a sale price of 120 gives 144, while the correct answer is 150: the discount was 20 % of 150, which is 30, and not 20 % of 120, which is 24. Reversing always means dividing by the multiplier.
How do I find the price before a discount?
Divide the sale price by 1 minus the discount as a decimal. After a 20 % discount you paid 80 % of the original, so 120 ÷ 0.80 = 150. Use the after a decrease mode.
How do I find the value before an increase?
Divide by 1 plus the increase as a decimal. A price of 120 after a 20 % rise is 120 % of the original, so 120 ÷ 1.20 = 100. This is also how you strip a tax that was added on top of a net amount.
How do I work out that a value is a given percentage of what number?
Divide the value by the percentage written as a decimal. If 30 is 25 % of a number, that number is 30 ÷ 0.25 = 120. Use the percent of an unknown number mode, which is handy for finding total sales from a commission.
Sources and last check
Information, not professional advice.