A shop shows a jacket at $63 after 30% off but hides the original price. Many people add 30% back and get $81.90 — which is wrong. Here is the correct way to work backwards from a sale price, and why the quick way fails.
Why adding the percentage back doesn't work
The 30% discount was taken from the original price, not from the sale price. The sale price is therefore 70% of the original. Adding 30% of the smaller number back gives too little.
The reverse percentage formula
Original price = sale price ÷ (1 − discount ÷ 100)
For the jacket: 63 ÷ (1 − 0.30) = 63 ÷ 0.70 = $90.
Check it: 30% of $90 is $27, and $90 − $27 = $63. ✔
More examples:
- $40 after 20% off → 40 ÷ 0.80 = $50
- $75 after 25% off → 75 ÷ 0.75 = $100
- $12.60 after 10% off → 12.60 ÷ 0.90 = $14
How to check it with a calculator
- Open the free Percentage Calculator.
- Choose A is what percent of B?, enter 63 and 90, and you'll get 70% — exactly what's left after 30% off.
- Or open the Discount Calculator, enter $90 and 30%, and confirm the final price is $63.
The same trick works for tax and price rises
Reverse percentages apply whenever a number has already been increased or decreased by a percentage:
- Price before tax: total ÷ (1 + tax rate). $108 including 8% tax → 108 ÷ 1.08 = $100. The VAT Calculator does this for you with "remove VAT".
- Salary before a raise: new salary ÷ (1 + raise). $52,500 after a 5% raise → $50,000.
FAQ
Is a "50% off, then 20% off" deal the same as 70% off? No. It's 60% off: 50% leaves 0.5, a further 20% off leaves 0.5 × 0.8 = 0.4 of the original.
Why do shops show "was" prices? To show the saving. If a "was" price looks inflated, use the formula to check that the numbers add up.
Try it now
Work out any sale with the free Discount Calculator and Percentage Calculator.
Related reading
See How to Calculate a Discount and How to Calculate Percentage Decrease. Browse the full blog for more guides.