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
Change any value to update the result.
100.00
Original value: 100.00Examples
How the result moves
Percentage (%) → Original valueYour current valid inputs, with one value varied across the range.
How the result moves
Held fixed: What do you know? After a % increase (a price including tax), Value you know 120.00.
| Percentage (%) | Original value |
|---|---|
| 0.00 | 120.00 |
| 10.00 | 109.09 |
| 20.00Your value | 100.00 |
| 30.00 | 92.31 |
| 40.00 | 85.71 |
Find the original by dividing the known value by its multiplier. After an increase use 1 + percentage/100; after a discount use 1 − percentage/100. For a known percentage share, divide by percentage/100. Choose the matching mode; subtracting the same percentage gives the wrong original.
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.Value you know=120·Percentage=20%
- 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.Value you know=120→100.00
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.