Reverse Percentage Calculator
Enter the value after a percentage increase or decrease, and the percentage, to find the original value. The check formula is shown too.
How to find the original value
- After an increase: original value = new value ÷ (1 + percent increase ÷ 100)
- After a decrease: original value = new value ÷ (1 − percent decrease ÷ 100)
For example, if a value went up by 20% and is now 120, call the original x. Then x × 1.2 = 120, so x = 120 ÷ 1.2 = 100.
The calculation uses exact fractions and rounds once at the end to the number of decimal places you choose. Below the result, a check formula applies the percentage to the original value again.
Which tool should I use?
- Reverse Percentage Calculator (this page): you know the value after a percentage change and the percentage, and want the original value.
- Percentage Calculator: you know the original value and the percentage, and want the result, such as "increase 200 by 8.5%".
- Percentage Change Calculator: you know two values and want the percentage change between them.
Examples
- Up 20% to 120: the original is 120 ÷ 1.2 = 100 (a change of 20).
- Down 20% to 80: the original is 80 ÷ 0.8 = 100 (a change of −20).
- Up 10% to 1,100: the original is 1,000.
- Up 50% to −50: the original is about −33.33 (negative values work).
A 20% increase followed by a 20% decrease does not get you back
Increase 100 by 20% and you get 120. Decrease 120 by 20% and you get 96, not 100. The second percentage is taken of the larger number, not of the original.
To get back from 120 to 100 you need a decrease of about 16.67% (20 ÷ 120). Always check what a percentage is a percentage of.
Notes
- A percent increase can be up to 100,000%. A percent decrease must be less than 100%: with a 100% decrease the new value is always 0, so the original value cannot be determined.
- The value after the change can have up to 12 digits before the decimal point, and the percentage up to 6 digits. Both allow up to 6 decimal places.
- For a discount, choose "Decreased". For a price that went up, choose "Increased".
Frequently asked questions
Can I find the original price before a 30% discount?
Yes. Choose "Decreased" and enter 30. If the price is now 70, the original price is 70 ÷ 0.7 = 100.
Does it work with decimal percentages?
Yes. If a value went up by 2.5% to 102.5, the original value was 100.
What if the original value does not divide evenly?
It is rounded to the number of decimal places you choose (2 by default). Inside, the calculation is exact, so there is no rounding error before the final rounding.
Why can't I use a 100% decrease?
After a 100% decrease the value is always 0, whatever the original was. So the original value cannot be recovered from it.