How to stack discounts: why 30% off then 20% off is not 50%

You spot a rack marked 30 percent off, then a sign promising an extra 20 percent off at the register. It is tempting to add those up and walk away thinking you are getting 50 percent off. You are not. Stacked discounts, sometimes called double discounts or sale-on-sale, never add together the way our brains want them to. The real total in that example is 44 percent off, and the reason is simple once you see it: the second discount is taken off the already-reduced price, not the original sticker. This guide shows exactly how stacked discounts work, why the percentages multiply instead of add, and how to find the true total off for any combination.

Why the percentages multiply and do not add

Every percent-off discount can be flipped into the fraction of the price you still pay. If something is 30 percent off, you pay the remaining 70 percent, so you multiply by 0.70. If it is 20 percent off, you pay 80 percent, so you multiply by 0.80. When two discounts stack, you apply both of those multipliers one after the other:

you pay = original × 0.70 × 0.80 = original × 0.56

That 0.56 means you pay 56 percent of the original price, which is 44 percent off, not 50. Adding the discounts would only be correct if the second one came off the full original price, but it never does. The first cut shrinks the base that the second cut works on, so a slice of a smaller number is worth less than a slice of the full number. Two stacked discounts are always worth less than their sum.

A worked example on a real price

Say a winter coat is listed at 200 dollars. It is 30 percent off, and you also have a members coupon for an extra 20 percent off. Here is the full walkthrough, one cut at a time:

• Start: 200 dollars.
• After 30 percent off: 200 × 0.70 = 140 dollars.
• After the extra 20 percent off the 140: 140 × 0.80 = 112 dollars.
• Total saved: 88 dollars, which is 44 percent off, not 50 percent.

Or skip the middle step entirely and chain the multipliers in one line:

200 × 0.70 × 0.80 = 112 dollars

You pay 112 dollars and save 88. Notice the saving (88) and the price you pay (112) still add back up to the original 200, which is a quick way to sanity-check any discount, stacked or not.

Stacked combos and their true total off

The table below lines up several popular stacks. The first column is the number people wrongly reach for by adding the two rates together. The second column is the honest total, found by multiplying the fractions you actually pay.

To read any row yourself, turn each percent into the fraction you pay and multiply. For 30 then 30, that is 0.70 × 0.70 = 0.49, so you pay 49 percent and save 51. For 50 then 50, it is 0.50 × 0.50 = 0.25, so you pay a quarter and save three quarters, which is 75 percent off.

Does the order of the discounts matter?

For the final price, no. Because you are just multiplying, the order of the multipliers cannot change the answer. Taking 30 percent off first and then 20 percent gives 200 × 0.70 × 0.80 = 112. Taking 20 percent off first and then 30 percent gives 200 × 0.80 × 0.70 = 112. Same 112 dollars either way. Multiplication does not care which number comes first, so you never have to worry about which coupon to scan at the till to get the best price.

The one place order can matter is when a single discount is capped in dollars, for example "20 percent off, up to 15 dollars." A cap breaks the clean multiplication, so if a promotion has one, work through the cuts in the exact sequence the store states and apply the limit where it lands.

How store coupons and sale-on-sale actually stack

In the real world, most stacking looks like a percent-off sale followed by a percent-off coupon, and it behaves exactly like the math above: the coupon applies to the marked-down price. A few practical wrinkles are worth knowing before you get to the register:

• A percent-off coupon on top of a percent-off sale multiplies, so it is always worth less than the two rates added.
• A fixed-dollar coupon, like 10 dollars off, is subtracted after the sale price is set, so its value does not shrink the way a percentage does.
• The order of a percent coupon and a percent sale does not change the total, but a fixed-dollar coupon combined with a percent one can, so check both ways if a store lets you.
• Some coupons exclude already-reduced items entirely, in which case there is no stack to calculate.

A fixed-dollar coupon is the exception to the multiply rule. If a 200 dollar coat is 30 percent off, that is 140 dollars, and a flat 25 dollar coupon simply brings it to 115. Percentages scale with the price, but a dollar is always a dollar, which is why a big fixed coupon on an already cheap item can be the better deal.

Frequently asked questions

How do stacked discounts work?

Each discount comes off the price left after the one before it, so the percentages never simply add. Turn every percent off into the fraction you pay and multiply those fractions together. For 30 percent off then an extra 20 percent off, you pay 0.70 × 0.80 = 0.56, which is 56 percent of the original, or 44 percent off in total.

Is 30 percent off then 20 percent off the same as 50 percent off?

No. Stacking 30 percent and 20 percent gives 44 percent off, not 50. The 20 percent coupon applies to the already-reduced price, not the original, so a 100 dollar item goes to 70 and then to 56, a total saving of 44 dollars. Two stacked discounts are always worth less than their sum.

Does the order of two discounts change the price?

For two percent-off discounts, no. You are multiplying, so 0.70 × 0.80 and 0.80 × 0.70 both equal 0.56 and the final price is identical. Order only starts to matter when a discount has a dollar cap or when you mix a percent-off coupon with a fixed-dollar coupon.

How do I calculate multiple discounts quickly?

Multiply the original price by the remaining fraction for each discount in turn. For 40 percent off then 10 percent off a 50 dollar item, that is 50 × 0.60 × 0.90 = 27 dollars, a total of 46 percent off. To get the total percent off, multiply the fractions and subtract from one: 1 minus 0.54 is 0.46.