The second discount applies to a new price
If an item starts at 1,000 and receives 20% off, its price becomes 800. A further 10% discount is 10% of 800, or 80, not 10% of 1,000. The final price is 720. Total savings are 280, or 28% of the original price—not 30%.
Here d1 and d2 are decimal discount rates. Example: 1,000 × 0.80 × 0.90 = 720.
The two-discount shortcut
In decimals: 0.20 + 0.10 − 0.20 × 0.10 = 0.28, or 28%. The subtracted product corrects the overlap counted when rates are simply added.
| Method | Calculation | Final price | Effective discount |
|---|---|---|---|
| 20% then 10% | 1,000 × 0.80 × 0.90 | 720 | 28% |
| 10% then 20% | 1,000 × 0.90 × 0.80 | 720 | 28% |
| Incorrect 30% addition | 1,000 × 0.70 | 700 | 30% |
Does order change the result?
The order of two percentage discounts on the same base does not change the final price because multiplication is commutative: 0.80 × 0.90 = 0.90 × 0.80. Store terms can still change the base: a fixed-value coupon, discount cap, excluded products, or shipping conditions may require a different calculation.
Discounts, tax, and shipping are separate items
If tax applies to the discounted price, calculate discounts first and then tax under local rules; add shipping if due. Do not assume a universal order when the offer or law specifies another. Also distinguish “saved 280” from “paid 720” so savings and final price remain clear.
Three-discount example
An 800 price with 10%, 20%, and 5% discounts is not 800 × 0.90 × 0.80 × 0.45: the retention factor for 5% off is 0.95. The correct calculation is 800 × 0.90 × 0.80 × 0.95 = 547.20. Effective discount = (800 − 547.20) ÷ 800 = 31.6%, not 35%.
Common mistakes
- Adding 20% and 10% directly.
- Applying both percentages to the original price in a stacked offer.
- Using 0.10 as the remaining-price factor after 10% off; it is 0.90.
- Treating a fixed coupon as a percentage.
- Ignoring exclusions, caps, tax, and shipping.
Frequently asked questions
Does 50% off then another 50% off make the item free?
No. One quarter remains: 0.50 × 0.50 = 0.25, so the effective discount is 75%.
How do I find the effective discount quickly?
Divide savings by original price and multiply by 100, or calculate one minus the product of remaining-price factors.
Can adding rates ever be correct?
Only when the offer defines a single combined discount whose components all apply to the original price, rather than successive discounts.
Sources and references
- OpenStax — Prealgebra 2e: Solve Sales Tax, Commission, and Discount Applications: educational reference for the discount and sale-price model. Reviewed 2026-11-06.
- The formulas are direct applications of percentages and repeated multiplication. Examples assume no tax, fees, or retailer-specific conditions.
- Check offer terms for each discount's base, eligible products, caps, and the order of coupons, tax, and shipping.