How to Find the Original Price After a Discount
You see a jacket for 80 after 20% off and wonder what it cost before the sale. This is a reverse percentage, and the usual mistake is adding 20% back onto 80.
Why adding the percentage back is wrong
A 20% discount is taken from the original price, not from the sale price. So 20% of 80 is not the amount that was removed. If you add 16 to 80 you get 96, which is lower than the true original.
The correct method
The sale price is what remains after the discount, so it equals the original price multiplied by (1 − discount). To go backwards, divide.
Original = Sale price ÷ (1 − discount as a decimal)
Worked example
- Sale price is 80 and the discount is 20%, which is 0.20.
- Calculate 1 − 0.20 = 0.80.
- Divide 80 ÷ 0.80 = 100.
The original price was 100. Check it: 20% of 100 is 20, and 100 − 20 = 80.
The same idea for price increases
If a price rose by 15% and is now 230, divide by 1.15 instead. 230 ÷ 1.15 = 200, so the old price was 200.
When this helps
- Checking whether a shop really cut the price by the amount it claims.
- Working out a supplier's list price from a discounted invoice.
- Removing tax from a total, which is the same calculation with a rate above 1.
Quick tip
When the discount is 25%, the sale price is three quarters of the original, so multiply the sale price by 4 and divide by 3. When it is 50%, simply double it.
Can I check a price tag this way?
Yes. If a tag says 60 after 25% off, divide 60 by 0.75 and you get 80. Compare that with the shelf price you remember. If the old price was never actually charged, the discount is only on paper. Doing this takes ten seconds and protects you from inflated sale claims, especially during big shopping seasons when many prices change at once.
Try it yourself
Use our free percentage calculator to check your numbers instantly.