How to find the original price before a discount
Updated on June 30, 2026 · by Rafael Rossi
A reverse percentage means finding the value before an increase or a discount, knowing only the final figure. There is one rule, and one mistake: you divide, you never subtract the percentage.
The two formulas
After a discount: original = final ÷ (1 − discount/100)
After an increase: original = final ÷ (1 + increase/100)
Worked example
You paid $80 for an item marked 20% off. What was the ticket price?
- 1 − 0.20 = 0.80
- 80 ÷ 0.80 = $100
The common error is 80 × 1.20 = $96. It looks reasonable and it is wrong, because the 20% was calculated on the original $100, not on the $80 you paid. The base of a discount is always the larger figure.
Why intuition gets it wrong
Taking 20% off and then adding 20% back does not return you to the start — the same trap as percentages that do not add. Look at the size of the gap:
| Discount applied | Increase that undoes it |
|---|---|
| 10% | 11.1% |
| 20% | 25% |
| 30% | 42.9% |
| 50% | 100% |
The larger the discount, the further division drifts from naive subtraction.
Backing sales tax out of a total
This is the everyday case. A receipt shows $108.75 including 8.75% sales tax. What was the pre-tax subtotal?
subtotal = 108.75 ÷ 1.0875 = $100.00
Subtracting 8.75% of $108.75 would give $99.23 — off by $0.77 on a $100 purchase, and off by more on larger ones. The tax was computed on the subtotal, so the subtotal is what you divide back to.
The same applies to a tip already added to a bill: a $220 restaurant total including 10% service came from 220 ÷ 1.10 = $200 of food and drink.
Other frequent uses
- Salary before the raise. You now earn $4,320 after an 8% increase. Before: 4,320 ÷ 1.08 = $4,000.
- Gross from net. If 11% comes out of a payment and $4,000 lands in the account, the gross was 4,000 ÷ 0.89 = $4,494.38.
- Original price after two markdowns. A final price of $56 after 30% and then a further 20%: 56 ÷ (0.70 × 0.80) = $100.
Margin and markup: the same error with another name
Applying a 40% markup to cost does not deliver a 40% margin. An item costing $60 with a 40% markup sells for $84, and the margin on the selling price is (84 − 60) ÷ 84 = 28.6%.
To get a 40% margin on a $60 cost, you must sell at 60 ÷ 0.60 = $100 — a markup of 66.7%. Markup takes cost as its base; margin takes the selling price. It is a reverse percentage again, and confusing the two is one of the most common causes of underpricing.
The five-second check
One verification prevents nearly every reverse-percentage error: the original must be larger than the final after a discount, and smaller after an increase.
If you calculated a "price before the discount" and got a number smaller than what you paid, you multiplied where you should have divided. It is the same kind of check that catches unit errors in physics, and it takes the same amount of time: look at the answer and ask whether it makes sense in the right direction.
The second check, whenever in doubt, is to run it forwards: take the original you found, apply the percentage, and see whether it lands on the known final. $100 with 20% off gives $80 — confirmed.
Frequently asked questions
How do I find the percentage when I know both values? change = (final ÷ original − 1) × 100. From $100 to $80: 0.80 − 1 = −20%.
Does it work for an increase above 100%? It does. A value that tripled rose by 200%, so the original is the final divided by 3 (1 + 2.00).
What if I only know the discount amount, not the percentage? Then it is simpler: add the discount back. Reverse percentages are only needed when the percentage, rather than the amount, is what you know.
Why divide rather than subtract? Because applying a percentage is a multiplication by a factor (0.80, 1.08, 1.40). Every operation is undone by its inverse, and the inverse of multiplication is division — never subtraction.