How to Find the Original Price After a Discount

A receipt shows a final price of $80 after a "20% off" discount. What was the item's original price? The instinctive move is to add 20% of $80 back — giving $96 — but that's incorrect. The real original price is $100. The gap between $96 and $100 is small here, but it grows fast with bigger discounts, and it's one of the most frequent percentage mistakes people make.

Why adding the percentage back fails

The 20% discount was calculated as 20% of the original price, not 20% of the sale price. Once the item is discounted, 20% of the new, smaller sale price is a smaller dollar amount than the original discount was — so adding it back doesn't get you all the way home.

Concretely: $100 discounted by 20% becomes $80 (a $20 reduction). But 20% of $80 is only $16, not $20. Add $16 back to $80 and you get $96 — still $4 short of the real original price of $100.

The remaining-percentage method

The correct approach uses division, not addition. If a discount removes a certain percentage, the sale price represents the remaining percentage of the original. To reverse it, divide by that remaining share rather than adding the discount percentage back:

Original Price = Sale Price ÷ (1 − Discount Percentage ÷ 100)

A 20% discount leaves 80% of the price remaining, so you divide the sale price by 0.80 (not by 1.20, and not by adding 20% back). You can run this calculation directly in our reverse percentage calculator, which has a dedicated mode for reversing a discount.

A 20% discount example

Sale price: $80. Discount: 20%.

Original Price = 80 ÷ (1 − 0.20) = 80 ÷ 0.80 = $100

A 25% discount example

Sale price: $90. Discount: 25%.

Original Price = 90 ÷ (1 − 0.25) = 90 ÷ 0.75 = $120

A 10% discount example

Sale price: $90. Discount: 10%.

Original Price = 90 ÷ (1 − 0.10) = 90 ÷ 0.90 = $100

Notice the same sale price ($90) produces two very different original prices (\$120 vs. \$100) depending on the discount percentage — which is exactly why the discount rate has to be known, not guessed, to reverse a sale price accurately.

Reversing a percentage increase

The same logic applies in reverse to an increase, just with addition instead of subtraction in the denominator:

Original Value = Final Value ÷ (1 + Increase Percentage ÷ 100)

If a price rose 20% to reach $120, the original price was 120 ÷ 1.20 = $100. For more on why this division-based approach is necessary instead of simply subtracting the percentage back, see why a 20% increase and decrease don't cancel out.

Where this comes up

This calculation is useful any time you know a final number and a percentage change but need to work backward: reconstructing an original price from a discounted receipt, checking whether an advertised "you saved $X" figure adds up, undoing a tax or fee that was already included in a total, or verifying a reported growth percentage by working back to the prior period's value. Anywhere a percentage was applied to a number you no longer have, reverse percentage calculation gets you back to it.