Understanding stacked discounts
The table below illustrates how two discounts combine. The effective discount is always less than the sum of the two individual discount percentages.
| Discount 1 | Discount 2 | Sum (incorrect) | Effective discount (correct) |
|---|---|---|---|
| 10% | 10% | 20% | 19% |
| 25% | 10% | 35% | 32.5% |
| 30% | 20% | 50% | 44% |
| 50% | 50% | 100% | 75% |
- The order in which two percentage discounts are applied does not affect the final price: (1 − d1)(1 − d2) = (1 − d2)(1 − d1). The final price and effective discount are the same regardless of which discount is applied first.
- Sales tax, if applicable, is calculated on the final discounted price in most jurisdictions, not the original price. This calculator does not include tax.
- The effective discount percentage is a useful comparison metric when evaluating competing promotions. A single 35% discount is more valuable than a stacked 20% + 20% discount (which is only 36%, but in this case actually better — always compute to be sure).
What is a percent-off calculator?
A percent-off calculator determines the price of an item after one or more percentage discounts are applied. A single discount reduces the original price by the stated percentage. When retailers apply a second discount (a 'stacked' discount), it applies to the already-discounted price, not the original price — so the two discounts combine multiplicatively, not additively.
Stacked discounts are common in retail promotions: a store might offer 25% off all items, plus an additional 10% off at checkout. These are not equivalent to 35% off the original price. Instead: a $100 item becomes $75 after the 25% discount, then 10% of $75 = $7.50 is removed, leaving a final price of $67.50 — a 32.5% effective discount, not 35%.
The effective discount percentage represents the true overall reduction from the original price to the final price, regardless of how many intermediate steps were taken. This is the figure most relevant for comparing different promotional offers.
How to use this percent-off calculator
- Enter the original listed price of the item.
- Enter the first discount percentage.
- If a second discount applies (e.g., a coupon or additional sale), enter it in the 'Additional discount' field. Leave it at 0 if not applicable.
- Read the final price, total savings, and effective discount percentage.
How stacked discounts work
A single discount of d1 reduces the price to price × (1 − d1). A second discount of d2 is then applied to that reduced price, producing: price × (1 − d1) × (1 − d2). The effective overall discount percentage is derived by comparing this final price to the original price.
자주 묻는 질문
Do two discounts add or multiply?
Two sequential discounts multiply, not add. A 20% discount followed by a 10% discount produces an effective discount of 1 − (0.80 × 0.90) = 1 − 0.72 = 28%, not 30%. The second discount applies to the already-reduced price, not the original.
Does the order of stacked discounts matter?
No. Because multiplication is commutative, (1 − d1) × (1 − d2) = (1 − d2) × (1 − d1). The final price and effective discount are identical regardless of which discount is applied first.
How do I find the original price if I know the discounted price and the discount rate?
Divide the discounted price by (1 − discount rate). For example, if an item costs $60 after a 25% discount, the original price was $60 / (1 − 0.25) = $60 / 0.75 = $80.
Is a 50% off sale plus an extra 50% off free?
No. Applying 50% off gives you half the original price. Applying another 50% to that reduced price gives you half of half, which is one quarter (25%) of the original price. The effective discount is 75%, not 100%.
참고 자료
- Consumer Financial Protection Bureau (CFPB). Understanding sale pricing and discounts. consumerfinance.gov.
- Brealey RA, Myers SC, Allen F. Principles of Corporate Finance (13th ed.). McGraw-Hill, 2020. Appendix A: Mathematics of Finance.