What is a backwards percentage?
Sometimes you know the end result of a percentage change but not the starting number. A shop shows a price with tax included, a salary after a raise, or a sale price after a discount. Working backwards finds the original amount.
Reverse percentage formula
For an increase: original = final ÷ (1 + percent ÷ 100)
For a decrease: original = final ÷ (1 − percent ÷ 100)
To find the whole from a part: whole = part ÷ (percent ÷ 100)
Step-by-step example
A price is 120 after a 20% increase. What was it before?
| Step | Calculation | Result |
|---|---|---|
| 1. Build the multiplier | 1 + 20 ÷ 100 | 1.20 |
| 2. Divide the final value | 120 ÷ 1.20 | 100 |
The original price was 100, and the increase was 20.
Common mistakes
- Subtracting the percentage from the final value instead of dividing.
- Using the wrong direction. A decrease uses 1 minus the percentage, an increase uses 1 plus.
- Entering a decrease of 100% or more, which has no valid original value.
How to use this calculator
- Enter your values. Work backwards from a final value to the original number before a percentage was added or taken off.
- Check units and assumptions. Make sure the inputs use the same scale and that any optional settings match your situation.
- Calculate and review. Compare the output with the formula below and note any limitations stated on the page.
Formula and calculation method
Use the relevant percentage relationship shown on this page. For a change between two values, compare the difference with the correct reference value; for reverse calculations, rearrange the equation to solve for the missing starting value.
Worked example
For example, if a price changes from $60 to $80, the difference is $20. Dividing $20 by the starting value of $60 and multiplying by 100 gives a 33.33% increase. Always use the original value as the denominator for percentage increase.
Search and practical tips
People commonly search for a backwards percentage calculator – reverse %, how to calculate the result step by step, which formula to use, and how to check the answer manually. Use the formula above as a transparent starting point, and consult the relevant institution, agency, or qualified professional when an official rule or personal circumstances affect the result.
Frequently asked questions
What is a reverse percentage?
A reverse percentage finds the original amount when you only know the result after a percentage change, for example the price before tax or before a discount.
How do I find the price before a 20% increase?
Divide the final price by 1.20. If the price after the increase is 120, the original price was 120 ÷ 1.20 = 100.
How do I find the price before a 20% discount?
Divide the sale price by 0.80. If the sale price is 80, the original price was 80 ÷ 0.80 = 100.
Why can't I just subtract 20% from the final value?
Because the 20% was calculated on the original amount, not on the final one. Subtracting 20% of 120 gives 96, not 100.
What does 'X is p% of what number' mean?
It asks for the whole when you know a part and its percentage. Divide the part by the percentage as a decimal: 30 is 15% of 30 ÷ 0.15 = 200.