Reverse Percentage Calculator
Find the original value before a percentage was applied.
A value after a percentage change — what was it before?
One signed transformation: −20% applied to the starting value.
You divide by 1 − 0.2 instead of adding the percent back — adding it back to 80 would overshoot.
Formula
Build the divisor: 1 + (-20 ÷ 100) = 0.8
Divide, don't subtract: 80 ÷ 0.8 = 100
Verify
100 − 20 = 80Check it forwards: applying the same change to the original returns the value you have now.
80 after a −20% change means the original value was 100. You divide by 1 − 0.2 instead of adding the percent back — adding it back to 80 would overshoot.
Instant answer
How do you find the original value before a percentage was applied?
A price of 120 after 20% off was 150 before the discount.
Divide, don't subtract: Original = Final ÷ (1 + rate). A price of 120 after 20% off was 150 before the discount.
- Formula
- Original = Final Value ÷ (1 + (Percentage ÷ 100))
- Definition
- A reverse percentage recovers the value a percentage was applied to, given only the result and the rate.
- Build the divisor:1 + (-20 ÷ 100) = 0.8
- Divide, don't subtract:120 ÷ 0.8 = 150
How to use
- 01Enter the final value — The value after the percentage was applied.
- 02Enter the percentage — The percentage that was added (e.g. 20%).
- 03Get the original — The original value before the change is shown.
Tab to move between fields · Results update instantly as you typeResults update instantly as you type
How to Reverse a Percentage
Sometimes you know the final price after a percentage was added (like tax or a markup) and need to work backwards to find the original amount. This is called a reverse percentage calculation. Instead of multiplying, you divide — undoing the percentage that was applied.
The Formula: Original = Final Value ÷ (1 + Percentage ÷ 100)
For decreases, use a negative percentage. If a price dropped 25% to land at $75, enter 75 and −25 to find the original was $100.
Real-World Uses
- Tax-inclusive pricing: A receipt shows $59.99 including 8% sales tax. The pre-tax price is $59.99 ÷ 1.08 = $55.55. For VAT-specific calculations, use our VAT Calculator.
- Salary after raise: Your new salary is $68,000 after a 6% raise. Your previous salary: $68,000 ÷ 1.06 = $64,150.94.
- Investment returns: A portfolio is now worth $13,200 after a 10% gain. The starting value: $13,200 ÷ 1.10 = $12,000.
- Deflated prices: A house is listed at $380,000 after a 5% decline. Original value: $380,000 ÷ 0.95 = $400,000.
Why Simple Subtraction Doesn't Work
A common mistake is subtracting the percentage from the final value directly. If $120 includes a 20% increase, subtracting 20% of $120 ($24) gives $96 — not the correct $100. The percentage was applied to the original value, not the final one. This calculator handles the math correctly every time.
To calculate the forward direction — applying a percentage increase — use our Percentage Increase Calculator. For a broader foundation, read How to Calculate a Percentage.
Common Reverse Percentage Examples
Working backwards from a known final value. Click any row to load the values in the calculator.
| Final value & % | Math | Original | |
|---|---|---|---|
| $120 with 20% added | $120 ÷ 1.20 | $100.00 | Open |
| $108 with 8% tax | $108 ÷ 1.08 | $100.00 | Open |
| $240 with 20% VAT | $240 ÷ 1.20 | $200.00 | Open |
| $80 after 20% discount | $80 ÷ 0.80 | $100.00 | Open |
| $75 after 25% discount | $75 ÷ 0.75 | $100.00 | Open |
| $150 after 50% off | $150 ÷ 0.50 | $300.00 | Open |
| $53,000 after 6% raise | $53,000 ÷ 1.06 | $50,000.00 | Open |
Reverse percentage — worked examples
| Question | Calculation | Answer | Open |
|---|---|---|---|
| 120 after -20% | 120 ÷ 0.8 | 150 | Prefilled |
| 126 after +5% | 126 ÷ 1.05 | 120 | Prefilled |
| 150 after +20% | 150 ÷ 1.2 | 125 | Prefilled |
| 60 after -25% | 60 ÷ 0.75 | 80 | Prefilled |
| 575 after +15% | 575 ÷ 1.15 | ≈ 500 | Prefilled |
| 90 after -10% | 90 ÷ 0.9 | 100 | Prefilled |
| 240 after +20% | 240 ÷ 1.2 | 200 | Prefilled |
Every figure above is produced by the same calculation engine that powers the calculator on this page.
Calculation method and limitations
Method: The rate is converted to a multiplier (1 + rate ÷ 100) and the final value is divided by it. Use a negative rate for a discount or decrease.
Limitations
- Subtracting the percentage from the final value gives the wrong answer — the base has changed.
- A rate of −100% is undefined, because the multiplier becomes 0.
- Stacked changes must be reversed one at a time, in reverse order.
Method and examples last reviewed by the Snap Percent Calc editorial team. All calculations run locally in your browser.
Frequently Asked Questions
Learn more about percentages
Discount Percentages Explained: Sales, Stacking and Fake Deals
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Read guidePercentage Word Problems: A Method That Always Works
A four-step method for turning any percentage word problem into an equation, plus 12 graded problems with step-by-step solutions.
Read guideHow to Calculate Percentage: The Complete Guide
Every percentage formula in one guide: percentage of a number, increase, decrease, difference, reverse, discount, VAT and markup, with worked examples.
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