How Stacked Discounts Work: Why 20% Off Plus 15% Off Is Not 35% Off
To calculate stacked discounts, multiply, do not add. Each discount takes a percent off a price that is already lower, so final price = original price × (1 - a) × (1 - b), where a and b are the discounts written as decimals, and the total discount is a + b - a × b. That makes 20% off plus 15% off equal to 32% off, not 35%.
On a $100 item, 20% off leaves $80, and 15% off $80 is $12, not $15, so you pay $68. Below you will find a lookup table of common combinations, the cases where order changes the price, BOGO deals as percentages, and where sales tax and card cash back fit. It is timely: federal law sets Thanksgiving as the fourth Thursday in November (5 U.S.C. 6103), so Black Friday 2026 is November 27 and Cyber Monday is November 30. To check your own numbers, open the Discount Calculator and choose its Two discounts tab.
How to Calculate Stacked Discounts, Step by Step
- Turn each discount into the share of the price you still pay: 1 minus the percent as a decimal. 20% off is 0.80, 10% off is 0.90 and 5% off is 0.95.
- Multiply the original price by each share, one after another.
- Subtract that result from the original price to get your savings, or subtract the multiplied shares from 1 to get the total percent off.
Take a $200 item with 20% off, then an extra 10% off:
$200.00 × 0.80 = $160.00 (20% off)
$160.00 × 0.90 = $144.00 (extra 10%)
Saved $56.00, which is 28% of $200
Adding the percents would claim 30% off and a $140 price, $4 less than you will really pay, and that gap grows as the discounts get bigger. With three layers, 20% then 10% then 5% off, 0.80 × 0.90 × 0.95 = 0.684, so you pay 68.4% of the price and save 31.6%, not 35%. On $200 that is $136.80.
You can also work backward. If you already have 20% off and want 40% off in total, the second discount has to be 1 - (0.60 ÷ 0.80) = 25%, not 20%. Check: 0.80 × 0.75 = 0.60, which is 40% off.
Stacked Discount Lookup Table
This table shows the real percent off for common pairs of discounts. Order does not matter for percent-off discounts, so 10% then 15% equals 15% then 10%. The last column is what you pay on a $100 item, so scale it to your own price. For two discounts, the gap between adding and multiplying is always a × b: 4 points for 20% + 20%, 25 points for 50% + 50%.
| Discounts | Total off | Adding would say | You pay on $100 |
|---|---|---|---|
| 15% + 10% | 23.5% | 25% | $76.50 |
| 20% + 10% | 28% | 30% | $72.00 |
| 20% + 15% | 32% | 35% | $68.00 |
| 20% + 20% | 36% | 40% | $64.00 |
| 25% + 10% | 32.5% | 35% | $67.50 |
| 25% + 20% | 40% | 45% | $60.00 |
| 30% + 10% | 37% | 40% | $63.00 |
| 30% + 20% | 44% | 50% | $56.00 |
| 30% + 30% | 51% | 60% | $49.00 |
| 40% + 10% | 46% | 50% | $54.00 |
| 40% + 20% | 52% | 60% | $48.00 |
| 40% + 40% | 64% | 80% | $36.00 |
| 50% + 20% | 60% | 70% | $40.00 |
| 50% + 30% | 65% | 80% | $35.00 |
| 50% + 50% | 75% | 100% | $25.00 |
| 60% + 20% | 68% | 80% | $32.00 |
| 60% + 40% | 76% | 100% | $24.00 |
| 70% + 30% | 79% | 100% | $21.00 |
| 20% + 10% + 5% | 31.6% | 35% | $68.40 |
Does the Order of Discounts Matter?
Not for two percent-off discounts. Multiplication gives the same answer in either order, so 20% then 15% and 15% then 20% both end at 32% off. The only wrinkle is rounding: a store that rounds after each discount turns $10.02 at 20% off, then 15% off, into $6.82, while the unrounded math gives $6.81. The Discount Calculator also rounds each step, so it can differ from a one-step calculation by a penny.
Order does matter when one discount is a dollar amount and the other is a percent. Say a $50 item has a $10 coupon and 20% off:
| Order | Math | You pay |
|---|---|---|
| Coupon first, then 20% off | ($50 - $10) × 0.80 | $32.00 |
| 20% off first, then the coupon | $50 × 0.80 - $10 | $30.00 |
Taking the percent first is better for you, because the coupon then removes a full $10 instead of being shrunk by the percent. The store sets the order in its terms, so read them and check the cart. Wording matters too: "an extra 20% off the sale price" multiplies, "20% off the original price" is measured against the original, and "save 50% in total" is already the combined figure.
BOGO and Multi-Buy Deals as Percent Off
When the items cost the same, any "buy some, get some" offer is just a percent off. That lets you compare it with other deals and stack it with a coupon.
| Deal | What you pay for | Percent off |
|---|---|---|
| Buy one, get one free | 1 of 2 items | 50% |
| Buy one, get one 50% off | 1.5 of 2 items | 25% |
| Buy 2, get 1 free | 2 of 3 items | 33.3% |
| Buy 2, get 1 half off | 2.5 of 3 items | 16.7% |
| Buy 3, get 1 free | 3 of 4 items | 25% |
| "2 for $30" when each costs $20 | $30 of $40 | 25% |
Stacking works the same way. Buy one, get one free plus an extra 20% off the order leaves 0.50 × 0.80 = 0.40 of the price, so it is 60% off, not 70%. Unequal prices change the math: if you buy a $60 shirt and a $40 shirt and the offer takes 50% off the cheaper one, you pay $60 + $20 = $80 for $100 of shirts, which is 20% off, not 25%. Read which item the offer discounts. Headline percents need the same care: "up to 60% off" names the biggest discount in the sale, not the typical one, so check the tag on your item.
The FTC's pricing guides (16 CFR 233.4) say the terms of a "Buy One, Get One Free" offer should be clear at the outset and that a seller should not raise the regular price of the item you must buy, so compare the unit price with what the item normally costs.
Where Sales Tax Fits
Sales tax is normally figured last, on the discounted price. Here is a $120 jacket with 30% off, an extra 20% off, and 8.25% sales tax, which is the maximum combined state and local rate in Texas:
| Step | Math | Amount |
|---|---|---|
| Starting price | List price of the jacket | $120.00 |
| After 30% off | $120.00 × 0.70 | $84.00 |
| After extra 20% off | $84.00 × 0.80 | $67.20 |
| Sales tax at 8.25% | $67.20 × 0.0825 = $5.544, rounded | $5.54 |
| Total at checkout | $67.20 + $5.54 | $72.74 |
You saved $52.80, or 44%, before tax, and the tax is charged on $67.20, not $120. To rerun it, get the discounted price from the Discount Calculator, then enter it as the price before tax, along with your rate, in the Sales Tax Calculator.
Not every price cut lowers the taxable price, and the rules vary by state, so check your own state's revenue department. Two examples:
- Texas: the Comptroller treats a coupon as a cash discount, so the store subtracts its value from the item's price and collects tax on the lower amount. An instant manufacturer rebate taken at checkout works the same way, but a mail-in manufacturer rebate does not lower the price. On a $250 item with a $50 mail-in rebate, tax is charged on $250.
- California: under CDTFA Publication 113, a retailer's own coupons are excluded from its taxable sales, but amounts a manufacturer reimburses for its coupons are included, so the coupon's value can stay in the taxed price.
Here is what the difference is worth on a $50 item with a $10 manufacturer coupon, using the same 8.25% rate for both rules. If the coupon lowers the taxable price, as in Texas, tax on $40 is $3.30, for $43.30 in total. If the coupon's value stays in the taxed price, tax on the full $50 is $4.13, for $44.13 in total, 83 cents more.
Is It Really a Deal? Check the "Was" Price
A big percent off a made-up starting price is not a deal. The FTC's Guides Against Deceptive Pricing say a legitimate former price is "the actual, bona fide price at which the article was offered to the public on a regular basis," held "for a reasonably substantial period of time." A price inflated only so a large reduction can be advertised does not qualify (16 CFR 233.1).
So test the claim. If a tag says "Was $150, now $90, 40% off" but you have seen the same item at $100 for weeks, the real saving is $10, or 10%. In the Percentage Calculator, choose the % change button, enter 100 as the old value and 90 as the new value, and it shows a 10% decrease.
Compare final prices, not percentages. Store A lists a jacket at $150 and offers 30% and 10% off, so $150 × 0.70 × 0.90 = $94.50. Store B lists it at $90 with 5% off, which is $85.50. The smaller discount wins because it starts lower.
Cash Back and Card Rewards: A Third Layer
Card cash back is paid after the purchase and is earned on the discounted price, not the $120 tag. Back to the jacket, leaving tax aside: 5% back on $67.20 is $3.36, a net cost of $63.84. That is 46.8% below the $120 starting price, because 0.70 × 0.80 × 0.95 = 0.532. It does not change your checkout total, so it never shows on the receipt.
Each card defines which purchases earn rewards, so check whether sales tax and shipping count. Navy Federal, for example, counts "purchases for goods and services, minus returns and other credits." If your card counts the tax-inclusive charge, 5% of the $72.74 total is $3.64 instead of $3.36.
A Note for Sellers
If an item costs you $60 and sells for $100, a 30% code plus a 20% member discount is 44% off and a $56.00 price, $4 below your cost. Test combinations in the Profit Margin Calculator before you let codes stack, and see margin vs markup for how a price relates to your cost.
Frequently Asked Questions
Is 50% off plus 50% off free?
No. The second 50% comes off a price that is already halved, so you pay 25% of the original, which is 75% off in total. On a $200 item, 50% off leaves $100 and another 50% off leaves $50. Two percent-off discounts make an item free only if one is 100% off.
Can you stack coupons on Black Friday?
Only if the retailer's terms allow it, and terms differ by store and by offer. Look for wording such as one code per order, cannot be combined with other offers, or excludes sale items and doorbusters. The cart summary shows which discounts the store actually applied, so check it before you pay.
Is 20% off then 10% off the same as 30% off?
No, it is 28% off. You pay 0.80 × 0.90 = 0.72 of the price. On a $200 item that is $144, not the $140 a flat 30% off gives. The gap grows fast: 40% off plus 40% off is 64% off, not 80%.
Do you pay sales tax before or after a coupon?
Usually after a store discount or coupon, so tax is figured on the lower price. Some price cuts are treated differently. Texas treats coupons as cash discounts but does not lower the taxed price for a mail-in manufacturer rebate, and California includes the value of manufacturer coupons in the retailer's taxable sales. Check your state revenue department.
Why does my receipt show a different total?
The usual causes are rounding to the cent at each step, a dollar coupon applied before or after a percent discount, an item excluded from the promotion, a percent taken off the original price instead of the sale price, tax figured before a manufacturer coupon, and shipping or fees added after the discounts. Compare the receipt line by line with your own math and ask the store about any line that differs.
Check your own stack
Open the Discount Calculator, choose the Two discounts tab, and type the original price, the first discount and the extra discount. It shows the final price, the total saved and the effective discount.
Open the Discount CalculatorSources
Figures and rules in this guide were checked against these primary references.
- FTC Guides Against Deceptive Pricing, 16 CFR Part 233 (eCFR): former price comparisons (233.1) and bargain offers (233.4)
- 5 U.S.C. 6103, federal holidays: Thanksgiving is the fourth Thursday in November
- Texas Comptroller, Grocery and Convenience Stores (publication 96-280, March 2024): coupons, instant and mail-in rebates, tax on the discounted price
- Texas Comptroller, Sales and Use Tax: 6.25 percent state rate, 8.25 percent maximum combined rate
- California CDTFA, Coupons, Discounts, and Rebates (Publication 113, revised September 2018): retailer and manufacturer coupons
- Navy Federal Credit Union, Redeem Rewards: how one card defines eligible purchases