Reverse Percentage Calculator
A reverse percentage calculator finds the original value before a percentage increase or decrease was applied — the opposite direction from a normal percentage calculation. If you know the final price after a discount and want the price before it, or the final price after tax and want the pre-tax price, this is the tool. If instead you already have both the original and new values and want the percentage between them, use the Percentage Change Calculator.
Formula: Original = Final ÷ (1 ± Rate ÷ 100)
Calculate the original value
Original value
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The three reverse percentage formulas
Which formula you need depends on what happened to the number:
| Scenario | Formula |
|---|---|
| Decrease (discount, sale) | Original = Final ÷ (1 − Rate ÷ 100) |
| Increase (tax, markup) | Original = Final ÷ (1 + Rate ÷ 100) |
| Proportion (X% of Y = Z) | Original = Part ÷ (Rate ÷ 100) |
Worked examples
Retail discount
Shoes cost $80 after a 20% discount. What was the original price?
Original = 80 ÷ (1 − 0.20) = 80 ÷ 0.80 = $100
Sales tax
A gadget costs $240 including 20% tax. What's the pre-tax price?
Original = 240 ÷ (1 + 0.20) = 240 ÷ 1.20 = $200
Gross pay before deductions
You take home $1,600 after 20% is deducted for tax. What was your gross pay?
Original = 1,600 ÷ (1 − 0.20) = 1,600 ÷ 0.80 = $2,000
Part-of-total (proportion)
20% of a number is 40. What's the number?
Original = 40 ÷ 0.20 = 200
Common mistakes
- Using subtraction instead of division. A common wrong approach is subtracting the percentage directly from the final value (e.g., "$80 minus 20% is $64"). Reverse percentage always requires dividing, not subtracting.
- Mixing up increase and decrease. Dividing by (1 + rate) when the number actually decreased — or vice versa — gives a wrong original value. Confirm which direction happened first.
- Forgetting to convert the percentage to a decimal. 20% is 0.20, not 20, when it goes into the formula.
Frequently asked questions
What is a reverse percentage?
A reverse percentage problem gives you a final value and a percentage, and asks for the original value — the opposite direction from a normal percentage calculation, where you'd start with the original value.
What's the difference between reverse percentage and percentage change?
Percentage change starts with two known values (an old one and a new one) and calculates the percentage between them. Reverse percentage starts with one known value and a percentage, and calculates the other, unknown value. They're solving opposite problems.
Is reverse percentage the same as percent error?
No. Percent error measures how far an experimental or estimated value is from a true or accepted value. Reverse percentage finds an original value from a known result and a percentage rate — it isn't measuring accuracy at all.
Does this work for percentages over 100%?
Yes. If a population of 300 represents 150% of the original, the same proportion formula applies: 300 ÷ 1.5 = 200.
Why divide instead of just adding or subtracting the percentage back?
Because the percentage was originally applied to the unknown original value, not to the final value. Adding or subtracting the percentage from the final value applies it to the wrong number and gives an incorrect result — division undoes the original multiplication correctly.
Comparing this to percentage change or difference
Reverse percentage, percentage change, and percentage difference all involve percentages between two numbers, but they answer different questions. If you have both an old and a new value and want the percentage between them, use the Percentage Change Calculator. If neither number is a clear "before" value, use the Percentage Difference Calculator Percentage of a Number Calculator.
Read the full breakdown: percentage change vs. percentage difference vs. percentage points →
Sources
Related calculators and guides
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This calculator is provided for general informational purposes and is not financial, tax, or professional advice. Verify important decisions with a qualified professional.
Cedrick Reese, Founder
I'm Cedrick Reese, a retired veteran and web developer who built PercentageChangeCalculators.com as part of Ready Utilities, my collection of free, user-friendly online tools. My journey began in the early 2000s with affiliate marketing and niche site development, which grew into a passion for creating practical digital utilities and calculators. After retiring, I earned a Computer Systems Technician certificate from UEI College, completed Electro-Mechanical Technologies at Tulsa Welding School, and finished the Carpentry program at Florida State College at Jacksonville. Today, I combine my technical background and craftsmanship by building furniture using traditional woodworking methods, gardening, and developing helpful online tools for users worldwide.