To calculate stacked discounts, multiply the remaining percentages instead of adding the discounts together. A 20% discount leaves you paying 80% of the price, and a 30% discount leaves 70%, so 0.80 × 0.70 = 0.56. You pay 56% of the original price, which is a 44% total discount, not 50%.
Stores know most shoppers add the numbers. “Extra 30% off already reduced items” reads like half price when it hangs next to a 20% markdown, and the sign is doing exactly what it was designed to do. If you want the real figure without doing math in the aisle, the free discount calculator on CalcRange stacks the percentages for you.
Here is why the shortcut fails, and the formula that fixes it.
Why adding the percentages goes wrong
The second discount never touches the original price. It only applies to whatever is left after the first cut.
Take a $100 pair of sneakers at 20% off. You are down to $80. Now the store offers an extra 30% off sale items, the classic extra discount on an already discounted price. That 30% comes off $80, which is $24, not $30. Final price: $56. Total saved: $44, so 44% off.
The missing $6 is the slice of the second discount that would have applied to money you already saved. Percentages compound downward the same way interest compounds upward, which is also why a 50% loss needs a 100% gain to recover. Same math, opposite direction. Our guide to percentage increase and decrease covers that side of it.
The successive discount formula
Two versions, same answer. Learn either one and you know how to calculate stacked discounts for any pair of percentages.
The multiplier method: final price = original price × (1 – first discount) × (1 – second discount), with the discounts written as decimals. For 20% and 30% that is 0.80 × 0.70 = 0.56, meaning you pay 56% of the tag.
The shortcut, which anyone who prepped for an aptitude exam in India or Pakistan can probably recite in their sleep: combined discount = x + y – (xy ÷ 100). Plug in 20 and 30 and you get 20 + 30 – 6 = 44%. That xy ÷ 100 term is exactly the overlap you lose, the chunk of the second discount that lands on money the first discount already removed.
This double discount formula extends to longer chains too. Keep multiplying: three successive 10% discounts give 0.9 × 0.9 × 0.9 = 0.729, a combined 27.1% off, never 30%. If single discounts still feel wobbly, start with how to calculate a discount and come back.
A worked example with a coupon on top
Say a jacket lists at $150. It sits on the clearance rack at 40% off, and you have a 20% coupon that works on top of the sale price. (The currency changes nothing, by the way. A Rs 5,000 kurta behaves exactly the same.)
Step 1: apply the first discount. 40% of $150 is $60, so the sale price is $90.
Step 2: apply the coupon to the sale price, not the tag. 20% of $90 is $18. You now owe $72.
Step 3: find the combined discount percentage. You saved $78 on a $150 jacket. 78 ÷ 150 = 0.52, so 52% off.
Check it against the formula: 40 + 20 – (40 × 20 ÷ 100) = 60 – 8 = 52. Matches.
The signs said 40% and 20%, and plenty of people leave the store believing they got 60% off. They got 52%. Still a solid deal, honestly, just not the one on the sign.
Combined discount table for common stacks
Bookmark this if you shop clearance events. The gap between the “feels like” number and the real one widens as the discounts grow.
| Advertised stack | Feels like | Actual discount | You pay (per $100) |
|---|---|---|---|
| 10% + 10% | 20% off | 19% off | $81 |
| 20% + 10% | 30% off | 28% off | $72 |
| 20% + 20% | 40% off | 36% off | $64 |
| 20% + 30% | 50% off | 44% off | $56 |
| 30% + 30% | 60% off | 51% off | $49 |
| 40% + 20% | 60% off | 52% off | $48 |
| 50% + 20% | 70% off | 60% off | $40 |
| 50% + 30% | 80% off | 65% off | $35 |
| 70% + 20% | 90% off | 76% off | $24 |
Look at the 50% + 30% row. Adding promises 80% off, reality delivers 65%. That is a $15 difference on every $100, which gets painful quickly on a full cart.
Do discounts stack, and does order matter?
Whether discounts stack at all is a store policy question, not a math question. Retail pricing has dozens of named markdown types (the Wikipedia entry on discounts and allowances is a surprisingly long read) and most stores only let you combine a couple of them. Read the coupon’s fine print. “Excludes clearance” is everywhere.
When both discounts are percentages, order changes nothing. 0.70 × 0.80 equals 0.80 × 0.70. The receipt looks different line by line, but the total is identical.
Mixing a dollar coupon with a percentage is a different animal. Take $100, a $10 coupon, and 20% off. Percentage first: $80 minus $10 leaves $70. Coupon first: $90 × 0.80 = $72. The percentage-first order saves you $2 here, and the register, not you, usually decides which order runs.
One more caution. A huge advertised stack sometimes leans on an inflated original price, so the “before” number was never real. We covered that pattern in how to spot fake discounts.
Frequently asked questions
Is 30% off plus 20% off the same as 50% off?
No, 30% off plus 20% off equals 44% off, not 50% off. The second discount applies to the already reduced price, so it removes fewer dollars than it would from the original. On a $100 item you pay $70 after the first cut and $56 after the second.
How do you calculate an extra 20% off an already discounted item?
Multiply the sale price by 0.80 to take an extra 20% off an already discounted item. If a $60 sweater was marked down from $100, the extra 20% comes off the $60, so you pay $48. That is a 52% total discount from the original price.
What is the formula for two successive discounts?
The formula for two successive discounts is x + y – (xy ÷ 100), where x and y are the two percentages. For 20% and 30% that gives 20 + 30 – 6 = 44% combined. You can also multiply the price multipliers: 0.80 × 0.70 = 0.56, which means 44% off.
Does the order of stacked discounts matter?
Order does not matter when both discounts are percentages, because multiplication gives the same result either way. 0.80 × 0.70 equals 0.70 × 0.80. Order does matter when a fixed dollar coupon mixes with a percentage discount, and applying the percentage first usually leaves you paying less.
Can you stack coupons with sale prices?
Many retailers let you use a coupon on top of a sale price, but the coupon applies to the reduced price, not the original. Check the exclusions first, since clearance items are often left out. When stacking is allowed, multiply the multipliers to find your real total discount.
What does ‘extra 40% off at checkout’ really mean?
An extra 40% off at checkout applies to the current sale price, not the original tag. A $200 coat already at 50% off costs $100, and the extra 40% brings it to $60. Your total discount is 70%, which sounds close to 90% but is a long way from it.
Next time a banner promises an extra 40% off at checkout, multiply instead of adding. Or skip the mental math and let the CalcRange discount calculator stack the numbers before you tap pay. It shows the final price and the real combined percentage in seconds.