How Do You Calculate a Discount?
Multiply the original price by the discount percentage expressed as a decimal, then subtract that amount from the original price. Or use the shortcut formula: Sale Price = Original Price × (1 − Discount Rate). Both methods give the same answer.
Leah Novak at Rise & Shine Bakery in Pinewood Falls runs a 15% discount on day-old pastries. A croissant that normally costs $4.50 becomes $4.50 × (1 − 0.15) = $4.50 × 0.85 = $3.83. She programs this into her point-of-sale system so the discount applies automatically at closing time.
The Three Discount Formulas
There are three discount calculations, each solving for a different unknown. This calculator handles all three with the tab selector above.
| Find | Formula | Example |
|---|---|---|
| Sale Price | Original × (1 − Discount %) | $80 × 0.75 = $60 |
| Discount % | (Original − Sale) / Original × 100 | ($80 − $60) / $80 = 25% |
| Original Price | Sale Price / (1 − Discount %) | $60 / 0.75 = $80 |
The third formula is especially useful during sales when stores show only the sale price and discount percentage. For example, a lamp marked "$45 after 40% off" had an original price of $45 / (1 - 0.40) = $45 / 0.60 = $75.
Common Discount Calculations
The table below shows final prices for common discount percentages applied to a $100 item. Use it as a quick reference for mental math while shopping.
| Discount | You Pay | You Save | Mental Math Shortcut |
|---|---|---|---|
| 5% | $95.00 | $5.00 | Subtract 1/20 of price |
| 10% | $90.00 | $10.00 | Move decimal one left |
| 15% | $85.00 | $15.00 | 10% + half of 10% |
| 20% | $80.00 | $20.00 | Divide by 5 |
| 25% | $75.00 | $25.00 | Divide by 4 |
| 33% | $67.00 | $33.00 | Divide by 3 |
| 40% | $60.00 | $40.00 | Take 3/5 of price |
| 50% | $50.00 | $50.00 | Divide by 2 |
| 75% | $25.00 | $75.00 | Divide by 4 |
Stacked Discounts Explained
Many stores offer stacked discounts: "20% off sale + additional 15% with coupon." This is not 35% off. The second discount applies to the already-reduced price.
Example on a $200 jacket: First, 20% off = $200 × 0.80 = $160. Then, 15% off the $160 = $160 × 0.85 = $136. The combined discount is $64, which is 32% — not 35%.
Maya Singh discovered this in her consumer math class at Pinewood Falls High. Her teacher showed that two 50% discounts stacked together equal 75% off (not 100% — or free). The formula for combined discount rate is: 1 − (1 − d1) × (1 − d2). For 50% + 50%: 1 − (0.50 × 0.50) = 1 − 0.25 = 75%.
The order of stacked discounts does not matter mathematically. Whether you apply 20% first then 15%, or 15% first then 20%, the final price is the same. This is because multiplication is commutative: 0.80 × 0.85 = 0.85 × 0.80 = 0.68.
Smart Shopping Tips
Compare Dollar Savings, Not Percentages
A 60% discount sounds better than 20%, but what matters is the actual price you pay. A $30 item at 60% off costs $12. A $15 item at 20% off costs $12. Same final price, completely different percentages. Always compare the final price, not the headline discount.
Calculate Price Per Unit
"Buy 2, Get 1 Free" is equivalent to roughly 33% off - but only if you actually need three items. If you only need one, you are spending more money total. A case discount on restaurant supplies only saves money if the ingredients get used before they expire.
Factor in Sales Tax
Sales tax is calculated on the discounted price, not the original. A $100 item at 25% off with 8% sales tax costs ($75 × 1.08) = $81, not ($100 × 1.08 × 0.75) = $81. The final price is the same because multiplication is commutative, but understanding this helps you verify receipts. Use our sales tax calculator to find the exact after-tax total on any purchase.
For business owners setting discount strategies, check how discounts affect your profit margins and break-even point. Use the percentage calculator for quick percentage conversions.
This calculator provides general estimates for informational purposes. Actual prices may vary due to rounding, tax rates, and store-specific policies.