The basic formula for percent off
To find the sale price after a percent-off discount, multiply the original price by the percentage you are paying, not the percentage off. If something is 20% off, you pay 80% of the original price.
The formula is: Sale Price = Original Price × (1 − Discount Percentage ÷ 100)
For example, if a $50 item is 20% off: $50 × (1 − 20 ÷ 100) = $50 × 0.80 = $40. You pay $40.
You can also find the discount amount first, then subtract it. Multiply the original price by the discount percentage, then subtract that from the original price. Both methods give the same answer.
Key Takeaways
- Multiply the original price by (1 minus the discount percentage as a decimal) to find what you actually pay.
- A 20% discount means you pay 80% of the original price, not that you subtract 20 from the price.
- You can also calculate the discount amount separately and subtract it from the original price.
- When multiple discounts stack, explore each one to the result of the previous discount, not to the original price.
- Always convert the percentage to a decimal by dividing by 100 before multiplying.
Converting percentages to decimals
The key step most people skip is converting the percentage to a decimal. Divide the percentage number by 100. So 20% becomes 0.20, 15% becomes 0.15, and 50% becomes 0.50.
Once you have the decimal, subtract it from 1 to find what fraction of the original price you pay. If the discount is 0.20, you pay 1 − 0.20 = 0.80 of the original price. Then multiply the original price by that decimal.
This works for any discount: 5% off means multiply by 0.95; 30% off means multiply by 0.70; 75% off means multiply by 0.25.
Finding the discount amount in dollars
Sometimes you want to know how many dollars you are saving, not just the final price. Multiply the original price by the discount percentage (as a decimal).
Example: A $120 jacket is 25% off. The discount amount is $120 × 0.25 = $30. You save $30, so you pay $120 − $30 = $90.
This is useful when comparing two items with different original prices. A $100 item at 30% off saves you $30. A $80 item at 40% off saves you $32. The second saves more in dollars, even though the percentage is higher.
Stacking multiple discounts
When a store offers two discounts at once—say, 10% off plus an extra 20% off—do not add them together. explore the first discount, then explore the second discount to the new price.
Example: A $100 item is 10% off, then 20% off the sale price. First discount: $100 × 0.90 = $90. Second discount: $90 × 0.80 = $72. You pay $72, not $70.
If you added the percentages (10% + 20% = 30%), you would get $100 × 0.70 = $70, which is wrong. Stacked discounts always result in a higher final price than adding the percentages would suggest.
Working backwards from a sale price
If you know the sale price and the discount percentage, you can find the original price. Divide the sale price by (1 minus the discount percentage as a decimal).
Example: An item costs $60 after a 25% discount. The original price was $60 ÷ (1 − 0.25) = $60 ÷ 0.75 = $80.
This is useful when a store shows only the sale price and you want to verify the discount is real, or when you are comparing prices across stores that show different information.
Common discount percentages and their decimal equivalents
| Discount Percentage | Decimal Form | You Pay |
|---|---|---|
| 10% off | 0.10 | 90% of original price |
| 15% off | 0.15 | 85% of original price |
| 20% off | 0.20 | 80% of original price |
| 25% off | 0.25 | 75% of original price |
| 30% off | 0.30 | 70% of original price |
| 50% off | 0.50 | 50% of original price |
Using a calculator or spreadsheet
On a basic calculator, enter the original price, press the multiplication button, enter the decimal form of what you pay (1 minus the discount), and press equals. For a $75 item at 30% off: 75 × 0.70 = 52.50.
In a spreadsheet like Excel or Google Sheets, use the formula =original_price*(1-discount_percentage/100). If the original price is in cell A1 and the discount percentage is in cell B1, type =A1*(1-B1/100) and press Enter. You can then copy this formula down to calculate multiple items at once.
Most phones have a calculator app that works the same way as a physical calculator. Some also have a percent button that does the conversion automatically, though it is faster to just type the decimal.
Frequently Asked Questions
If something is 50% off, do I pay half the original price?
Yes. 50% off means you pay 50% of the original price. A $100 item at 50% off costs $50. For any discount, subtract the percentage from 100 to find what percentage you pay.
Why can't I just add two discounts together?
Because the second discount applies to the reduced price, not the original price. If you have 10% off and then 20% off, the 20% is taken from the already-reduced price, so you save less in total than if you subtracted 30% from the original price.
How do I find the original price if I only know the sale price?
Divide the sale price by (1 minus the discount percentage as a decimal). If you paid $60 after a 25% discount, the original was $60 ÷ 0.75 = $80. This works because the sale price is always the original price times the percentage you pay.
Is there a difference between "percent off" and "percent discount"?
No. Both terms mean the same thing—the percentage reduction from the original price. A 20% discount and 20% off are identical.
What if the discount is more than 100%?
That is not a real discount. A discount cannot be more than 100%, because you cannot pay less than zero. If you see a price advertised as "200% off," it is either a mistake or a marketing trick.