Reverse Percentage Calculator
A reverse percentage recovers the original value from a final amount that already had a percentage added or removed. If a total includes a markup, you divide by 1 plus the rate to get the pre-markup value; if a price reflects a discount, you divide by 1 minus the rate to get the pre-discount value. This calculator does both directions and shows the original amount and the size of the adjustment, which is exactly what you need to strip a markup out of a total or find the list price behind a sale price.
Reverse percentage formula
Increase: original = final / (1 + rate/100)
Discount: original = final / (1 - rate/100)
adjustment = |final - original|
Example markup: 120 / 1.20 = 100, adjustment 20
The factor (1 plus or minus the rate) is what was multiplied to produce the final amount, so dividing by it reverses the operation exactly.
Reverse percentage context
- Use increase mode to strip a markup or tax already baked into a total.
- Use discount mode to find the list price behind a sale price.
- Multiplying the final amount by the rate gives the wrong base; you must divide by the factor.
- A 100 percent discount makes the factor zero and the result undefined.
- The adjustment amount is the dollar value added or taken off the original.
Reverse percentage: frequently asked questions
What is a reverse percentage?
A reverse percentage works backwards from a final amount to the original amount before a percentage was added or removed. If a price already includes a 20 percent increase, dividing by 1.20 recovers the original price.
How do I remove a percentage increase from a total?
Divide the final amount by 1 plus the percentage as a decimal. For a total of 120 that includes a 20 percent markup, the original is 120 divided by 1.20, which is 100. The added amount is 120 minus 100, or 20.
How do I find the price before a discount?
If a sale price reflects a discount, divide by 1 minus the discount as a decimal. A $80 item after a 20 percent discount had an original price of 80 divided by 0.80, which is 100.
Why not just multiply the final amount by the percentage?
Because the percentage was applied to the original, not the final amount. Multiplying the final by the rate gives the wrong base. You must divide by the growth or discount factor to undo the operation correctly.
What if the discount is 100 percent or more?
A 100 percent discount makes the factor zero, so the division is undefined and the calculator shows n/a. Discounts of 100 percent or more cannot be reversed because no original price maps to the result.
Official sources
- NIST Digital Library of Mathematical Functions: DLMF home.
- NIST: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.