When and how to use reverse percentage
When to use it
A reverse percentage calculation is needed whenever you know the final amount after a percentage was applied, but need to find the original value. The most common scenario is seeing a sale price and wanting to know the price before the discount, or receiving a VAT-inclusive amount and needing to extract the pre-tax figure.
The two formulas
If the percentage was added (markup, VAT), the original value is: result divided by (1 + rate / 100). If the percentage was subtracted (discount, reduction), the original value is: result divided by (1 - rate / 100). The most common mistake is simply adding or subtracting the percentage from the result, which yields an incorrect answer.
Worked example
An item costs 84 EUR after à 30% discount. To find the original price, divide 84 by (1 - 30 / 100) = 84 / 0.70 = 120 EUR. Verification: 120 EUR minus 30% gives 120 x 0.70 = 84 EUR. Had you simply added 30% to 84, you would have gotten 109.20 EUR, which is wrong.