Know the value after a percentage was applied? Enter it with the percentage to recover the original — for discounts, tax and increases.
The backwards question
Ordinary percentage tools go forwards: start with a number, apply a change. This one goes backwards: you know the result — a sale price, a total including tax — and need the original. The trap is dividing instead of multiplying: a price after 25% off is recovered by dividing by 0.75, not by adding 25% back, and the difference is real money.
How to use it
- Enter the final value you can see.
- Enter the percentage that was applied.
- Say whether it was a decrease (a discount) or an increase (tax, a markup).
The formula
after a decrease: original = final ÷ (1 − %)
after an increase: original = final ÷ (1 + %)
A worked example
A jacket costs 60 after 25% off. The original was 60 ÷ 0.75 = 80 — you saved 20. The intuitive-but-wrong route, adding 25% back onto 60, gives 75 and quietly loses 5. The same division logic recovers a pre-tax price: a 108 total at 8% tax was 108 ÷ 1.08 = 100 before tax.
Common questions
Why can’t I just add the percentage back?
Because the percentage was taken of the original, which is bigger than the final. Adding 25% of the smaller sale price back under-shoots — division by (1 − %) is the exact inverse.
What about “100% off”?
The original is unrecoverable — anything times zero is zero, so division by (1 − 1) is undefined, and the calculator says so.
Does this work for stacked discounts?
Divide once per layer: after 20% then 10% off, original = final ÷ 0.8 ÷ 0.9. Stacked percentages never simply add.