How Discounts Stack: Why Two Sales in a Row Do Not Simply Add Up

“Twenty percent off, plus an extra 10 percent off at the register? That makes it 30 percent off!” A shopper says it to a friend while holding up a $100 coat. The friend nods. It sounds right, and it is a very common way to think about a sale.

Yet stacking discounts works a little differently. The second discount usually comes off the already lower price, so it takes off fewer dollars than it would on the full price. In this made-up example, the coat ends up costing $72, which is 28 percent off. That is close to 30 percent, but the gap grows as the numbers get bigger.

This guide shares general information about how stacked discounts work, with step by step math and made-up prices. It is not advice or instructions about what to buy, and every store sets its own rules for how deals combine. Go one step at a time, and try each example with a pencil if that feels helpful.

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See why the second discount takes off fewer dollars

A discount is a part of the price taken away. When a second discount follows the first, it usually applies to the new, lower price. That is the heart of the whole idea.

Let’s walk through the made-up $100 coat. First, 20 percent off. Twenty percent of $100 is $20, so the price drops to $80. Next, an extra 10 percent off. Ten percent of $80 is $8, so the price drops to $72.

The first discount took off $20. The second took off $8, not $10, because it worked on $80 instead of $100. Together they took off $28, which is 28 percent of the original $100.

Work through the $100 coat example on paper, one discount at a time.

Multiply the parts you still pay

There is a quicker way to get the same answer. After a 20 percent discount, you pay 80 percent of the price. After a 10 percent discount, you pay 90 percent of what is left.

Write those as decimals and multiply them. Eighty percent is 0.8, and ninety percent is 0.9. Then 0.8 times 0.9 is 0.72. So you pay 72 percent of the original price. On the made-up $100 coat, that is $72.

This one step works for any number of discounts in a row. Turn each discount into the part you pay, multiply them together, and then multiply by the starting price. For related reading, see deciding whether a sale is a good deal.

Turn two made-up discounts into decimals of what you pay and multiply them together.

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Notice that the order of percent discounts does not change the result

Some people wonder if it matters which percent comes first. When both discounts are percents, the order gives the same final price.

Try the made-up coat the other way around. Ten percent off $100 gives $90. Then 20 percent off $90 is $18 off, which gives $72. That matches the first way exactly.

This happens because multiplying works the same in either order. Whether you do 0.8 times 0.9 or 0.9 times 0.8, the answer is 0.72. Things change when a dollar-off coupon joins the mix, which a later section covers.

Run one made-up pair of discounts in both orders and check that the final prices match.

“The second sale works on what is left, so let the math finish before the excitement does.”

Use a quick shortcut to find the combined percent

If you want the total percent off in one go, here is a handy shortcut. Add the two discounts. Then multiply them together, divide by 100, and subtract that from the sum.

For 20 percent and 10 percent, the sum is 30. Twenty times ten is 200, and 200 divided by 100 is 2. Then 30 minus 2 is 28. So the combined discount is 28 percent, which matches the coat example.

Try it on 25 percent and 15 percent. The sum is 40. Twenty-five times fifteen is 375, and divided by 100 that is 3.75. Then 40 minus 3.75 is 36.25. So the two discounts together take off 36.25 percent, a bit less than 40.

Use the shortcut on one made-up pair of discounts and check it by working the prices step by step.

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Watch the gap grow with bigger discounts

With small discounts, the gap between the simple sum and the real result is small. With big discounts, the gap gets much wider.

Picture a made-up $50 item marked 50 percent off, with another 50 percent off at the register. Simply adding them would suggest 100 percent off, which would make the item free. Instead, the first discount brings it to $25. The second takes half of $25, bringing it to $12.50. The total discount is 75 percent.

Here is another made-up case with a $120 coat. It is 25 percent off, then an extra 15 percent off. The first step brings it to $90. Fifteen percent of $90 is $13.50, so the price lands at $76.50. Adding the percents would have suggested 40 percent off, or $72. The real price is $4.50 higher.

Pick two large made-up discounts and compare the simple sum with the real result.

Follow three discounts in a row, step by step

Some sales stack three discounts. The same idea still holds. Each one comes off the price left by the one before.

In a made-up example, a $200 rug is 30 percent off, then 20 percent off, then 10 percent off. Thirty percent off $200 leaves $140. Twenty percent off $140 is $28 off, which leaves $112. Ten percent off $112 is $11.20 off, which leaves $100.80.

Adding 30, 20, and 10 would suggest 60 percent off, or $80. The real price is $100.80, which is $99.20 off. That works out to 49.6 percent off, a good deal in this made-up case, and still well short of 60 percent. Another place to look is saving on groceries without extreme couponing.

Write out a three-step made-up discount, one line per step, and check the final price.

Know that dollar-off coupons can change with order

A dollar-off coupon takes away a set amount, like $10. When a coupon like that mixes with a percent discount, the order can change the final price.

Here is a made-up example with a $50 pair of shoes, 20 percent off, and a $10 coupon. If the percent comes first, $50 drops to $40, and the coupon brings it to $30. If the coupon comes first, $50 drops to $40, and 20 percent off $40 is $8 off, which leaves $32.

That is a $2 difference from the same two deals. Each store decides the order and whether deals can be combined at all, and those rules vary. The store’s own terms or a quick question at the counter can tell you how a deal works. You may also like back-to-school shopping hacks for frugal families.

Try one made-up percent discount and one dollar-off coupon in both orders and compare.

Ask a few questions about how a stacked deal works

Stacked deals often come with fine print. A reader might notice words like “extra,” “additional,” or “off the lowest marked price.” These hint at how the store applies the second discount.

A few questions can make it clear. Does the extra discount come off the sale price or the original price? Are some items left out? Can a coupon be used along with the sale? Rules vary from store to store, and asking is always an option.

Some people also compare the final price with what similar items cost in other places. A big stack of discounts can sound exciting, and the final dollar amount is the number that lands on the receipt.

Before your next stacked sale, write down one question to ask about how the discounts combine.

Keep your own plan in the picture

A deep discount is still a cost. In a made-up case, a $200 rug at $100.80 saves $99.20 compared with the original price. It also spends $100.80 that might have had another job in your plan.

Some people pause and ask, “Would I buy this at the final price if there were no sale sign at all?” Others set a spending limit before shopping and stick to items on a list. These are just ideas, and what fits your life is up to you.

Sales come and go, and many return in a similar form later. Taking a moment to do the math can turn a rushed choice into a calm one. For related reading, see strategies to stop impulse spending.

Next time you see a stacked deal, find the final price and compare it with your plan before deciding.

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