Reverse Percentage Calculator

Use this reverse percentage calculator to find an original amount when you know the final amount and the percentage increase or decrease. For example, a price of $80 after a 20% discount means the original price was $100.

What this calculator does

The tool works backward through one percentage change. Choose whether the amount increased or decreased, enter the final amount, and supply the known rate. The result shows the original amount, the size of the change and the multiplier linking the two values.

Use it for an original sale price, a bill before a stated increase, or another nonnegative quantity changed by a known percentage. Amounts are unitless: if you enter dollars, every amount in the result represents dollars. No exchange rate or tax rule is selected.

How to reverse a percentage

1. Choose After a decrease for a discount or reduction, or After an increase for a rise.
2. Enter the amount remaining after that change.
3. Enter the percentage as a number: use 20 for 20%, rather than 0.20.
4. Read the original amount and check the multiplier in the breakdown.

Let F be the final amount and r the percentage rate. The formulas are:

• After an increase: original = F ÷ (1 + r ÷ 100).
• After a decrease: original = F ÷ (1 − r ÷ 100).

A decrease leaves 100 − r percent of the original; an increase leaves 100 + r percent. Dividing by that multiplier recovers the starting value. The York St John University percentages factsheet explains both inverse methods. The algebra applies to quantities in any consistent unit.

Example: original price before a discount

Suppose shoes cost $80 after a 20% discount. You paid 80% of the original price, so:

• Remaining multiplier = 1 − 20 ÷ 100 = 0.8.
• Original price = $80 ÷ 0.8 = $100.
• Discount amount = $100 − $80 = $20.

Adding 20% to $80 would give $96. That does not reverse the discount because the $16 addition is based on $80, while the original $20 discount was based on $100.

Example: amount before an increase

A ticket costs $72 after a 20% increase. The final amount is 120% of the original. Divide $72 by 1.2 to get $60. The increase was $12, which is 20% of $60.

Check and interpret the result

Multiply the calculated original amount by the displayed multiplier to check the final amount. Use the original, unrounded inputs for another calculation. If you instead know the starting amount, use Add or Subtract a Percentage. If both amounts are known and the rate is missing, use the Percentage Increase Calculator.

Assumptions and limitations

Only one known change is reversed. Several consecutive discounts or increases require their combined multiplier; adding the rates usually gives the wrong answer. A decrease must be below 100%: a 100% reduction erases the starting value and cannot identify a unique original. Increase rates above 100% are supported.

Amounts must be between 0 and 10^15; rates are limited to 10^6 percent before the decrease rule is applied. Negative values are excluded. These are numerical limits, not economic assumptions. Display normally rounds to two decimal places, with scientific notation for very small or large results. Extremely small changes that exceed reliable numerical precision produce an error.

If the final price or rate was rounded, the calculated original is an inference and may differ from the actual original. This tool does not reconstruct receipt rounding, fees, tax exemptions or official financial terms.

How we explain formulas, assumptions and sources