How to Calculate Discount and Sale Prices
The discount formula is: Sale Price = Original Price x (1 - Discount% / 100). A 30% discount on an $89.99 item gives you $89.99 x 0.70 = $63.00 (rounded). That is the entire concept. The rest of this post covers variations and shortcuts.
The basic discount formula
To find the sale price, multiply the original price by (1 minus the discount as a decimal).
Example 1: 30% off $89.99
$89.99 x (1 - 0.30) = $89.99 x 0.70 = $62.99
Example 2: 25% off $149.95
$149.95 x (1 - 0.25) = $149.95 x 0.75 = $112.46
Example 3: 40% off $64.00
$64.00 x (1 - 0.40) = $64.00 x 0.60 = $38.40
You can also calculate the dollar amount of the discount separately. Multiply the original price by the discount percentage: $89.99 x 0.30 = $27.00. Then subtract: $89.99 - $27.00 = $62.99. Both methods give the same result.
Stacking discounts: why 20% + 10% is not 30%
Stores sometimes offer stacked discounts. “Take 20% off, then an extra 10% off.” This is not the same as 30% off.
Here is why. Start with a $100 item.
- 20% off first: $100 x 0.80 = $80.00
- 10% off the $80: $80 x 0.90 = $72.00
- Final price: $72.00
If it were a straight 30% off: $100 x 0.70 = $70.00. The stacked discount saves you $28, not $30. The second discount applies to the already-reduced price, not the original.
The general formula for stacked discounts is:
Final Price = Original x (1 - First Discount) x (1 - Second Discount)
For 20% + 10%: $100 x 0.80 x 0.90 = $72.00. The combined effective discount is 28%, not 30%.
Finding the original price from a sale price
Sometimes you see a sale price and want to know the original. If a shirt is marked “$45 after 25% off,” what was the full price?
Rearrange the formula: Original Price = Sale Price / (1 - Discount% / 100)
$45 / (1 - 0.25) = $45 / 0.75 = $60.00
A common mistake is to add the discount percentage to the sale price: $45 + 25% of $45 = $45 + $11.25 = $56.25. That is wrong. 25% of $45 is not the same as 25% of the original $60.
Mental math shortcuts for common discounts
You do not need a calculator for most common discount percentages.
10% off: Move the decimal one place left. 10% off $85 means subtract $8.50. Sale price: $76.50.
20% off: Find 10%, then double it. 10% of $85 is $8.50. Double that is $17.00. Sale price: $68.00.
25% off: Divide by 4. $85 / 4 = $21.25 discount. Sale price: $63.75.
33% off: Divide by 3. $85 / 3 = $28.33 discount. Sale price: $56.67.
50% off: Divide by 2. $85 / 2 = $42.50.
75% off: Find 25% (divide by 4) and that is your sale price. 25% of $85 is $21.25. Sale price: $21.25. Or equivalently, subtract 75%: $85 - $63.75 = $21.25.
For odd percentages like 15% off, combine 10% + 5%. 10% of $85 is $8.50. 5% is half of that: $4.25. Total discount: $12.75. Sale price: $72.25.
Don’t forget sales tax
A sale price is the price before tax. If your state has 8% sales tax, an item marked 30% off at $89.99 costs $62.99 + ($62.99 x 0.08) = $62.99 + $5.04 = $68.03 at the register.
When comparing deals, always calculate the final out-of-pocket cost including tax.
Key takeaways
- Sale Price = Original Price x (1 - Discount% / 100)
- Stacked discounts multiply, they do not add. 20% + 10% off is 28% off, not 30%
- To find the original price: divide the sale price by (1 - discount decimal)
- For 10% off, move the decimal left. For 25% off, divide by 4. For 50% off, divide by 2.
- Always account for sales tax when calculating your real out-of-pocket cost
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