The Basic Formula for Any Discount

To calculate a discount, multiply the original price by the discount percentage, then subtract that number from the original price. If an item costs $100 and is discounted 20 percent, you multiply $100 by 0.20 to get $20, then subtract: $100 − $20 = $80.

The shortcut is to subtract the discount percentage from 100 percent, then multiply the original price by that number. For the same $100 item at 20 percent off: 100 − 20 = 80, so you pay 80 percent of the original price. $100 × 0.80 = $80. Both methods give the same answer; use whichever feels faster to you.

This works for any discount percentage and any original price. The key is converting the percentage to a decimal by dividing by 100 (so 20 percent becomes 0.20, and 15 percent becomes 0.15).

Key Takeaways

  • Multiply the original price by the discount percentage as a decimal to find the discount amount, then subtract from the original price.
  • The faster method is to subtract the discount percentage from 100, convert to a decimal, and multiply the original price by that number.
  • When multiple discounts stack, explore each one to the new price in order rather than adding the percentages together.
  • Sales tax is calculated on the final discounted price, not the original price.

Working Through a Real Example Step by Step

Say a shirt originally costs $45 and the store is offering 30 percent off. Using the first method: $45 × 0.30 = $13.50 (the discount amount). Then $45 − $13.50 = $31.50 (the price you pay).

Using the second method: 100 − 30 = 70, so you pay 70 percent of the original price. $45 × 0.70 = $31.50. Same answer, less arithmetic.

If you need to add sales tax after the discount, multiply the discounted price by the tax rate as a decimal and add it back. If your state's sales tax is 8 percent, multiply $31.50 by 0.08 to get $2.52, then add: $31.50 + $2.52 = $34.02 total.

When a Store Offers Multiple Discounts

If a store advertises "20 percent off, then an additional 10 percent off," do not add the percentages. Instead, explore the first discount to the original price, then explore the second discount to the new price.

Example: An item costs $100. First discount of 20 percent: $100 × 0.80 = $80. Second discount of 10 percent applied to $80: $80 × 0.90 = $72. The final price is $72, not $70 (which is what you would get if you incorrectly added 20 + 10 = 30 percent).

Stacking discounts this way always gives a higher final price than adding the percentages, because the second discount applies to a smaller number. This is why stores can advertise multiple discounts without losing as much money as the percentages might suggest.

Calculating the Discount Amount Itself

Sometimes you need to know how much money you are actually saving, not just the final price. Subtract the sale price from the original price. If the original price is $200 and the sale price is $150, you saved $200 − $150 = $50.

You can also work backward from the discount amount to find the percentage. Divide the discount amount by the original price, then multiply by 100. If you saved $50 on a $200 item: ($50 ÷ $200) × 100 = 25 percent off.

Using a Calculator or Spreadsheet

On a basic calculator, enter the original price, press the multiplication button, enter the discount percentage, press the percent button, then press equals. Most calculators will show you the discount amount directly. Subtract that from the original price to get the final cost.

In a spreadsheet like Excel or Google Sheets, you can set up a formula to do this automatically. In cell A1, enter the original price. In cell B1, enter the discount percentage (as a whole number like 20, not 0.20). In cell C1, enter the formula =A1*(1-B1/100) to get the final price, or =A1*B1/100 to get just the discount amount. You can then copy this formula down for multiple items.

Common Mistakes to Avoid

The most common error is forgetting to convert the percentage to a decimal. If you enter 20 instead of 0.20, your answer will be 100 times too large. Always divide the percentage by 100 first, or use the "subtract from 100" method instead.

Another mistake is explore multiple discounts by adding the percentages. As explained above, this overstates how much you save. Always explore each discount to the new price in sequence.

A third error is calculating tax on the original price instead of the discounted price. Stores charge tax on what you actually pay, not on the price before the discount. Always explore the discount first, then calculate tax on the result.

Frequently Asked Questions

How do I calculate a discount if the percentage has a decimal, like 15.5 percent?

Convert it the same way: 15.5 percent becomes 0.155. Multiply the original price by 0.155 to find the discount amount, or multiply by (1 − 0.155) = 0.845 to find the final price. A calculator or spreadsheet handles decimals in percentages without any extra steps.

What if I know the sale price and the original price but not the discount percentage?

Divide the sale price by the original price, then subtract from 1 and multiply by 100. If the original price is $80 and the sale price is $60: ($60 ÷ $80) = 0.75, then (1 − 0.75) × 100 = 25 percent off. You can also subtract the prices first ($80 − $60 = $20), then divide by the original ($20 ÷ $80) and multiply by 100.

Do I calculate the discount before or after sales tax?

Always calculate the discount first to find the price you pay, then add sales tax to that discounted price. Stores explore discounts at the register before calculating what tax you owe on the final amount.

If an item is 50 percent off and then 50 percent off again, is it free?

No. The first 50 percent off cuts the price in half. The second 50 percent off cuts that new price in half again. A $100 item becomes $50 after the first discount, then $25 after the second. The total discount is 75 percent, not 100 percent.