Why is 20% plus 10% off not 30% off?

Because the second discount applies to the already-discounted price. On $100: 20% off leaves $80, then 10% off that equals $8, so you pay $72. That is $28 saved, a 28% discount. A true 30% off would leave $70, which is why adding discounts overstates the saving.

How do I combine two stacked discounts correctly?

Use the formula 1 minus (1 minus the first discount) times (1 minus the second). For 20% and 10%: 1 - (0.80 x 0.90) = 1 - 0.72 = 0.28, so 28%. Apply the discounts in sequence, never add the percentages together.

Are stacked discounts always applied in sequence?

Usually yes, but retailers sometimes cap the combined total, exclude items, or apply the larger discount first. Read the terms. Whatever order the store uses, the honest result is still less than the simple sum of the advertised percentages.

Stacked Discounts: Why 20% Plus 10% Equals 28%

“Take an extra 10% off our 20% sale” sounds like a combined 30% off, and that is exactly what the store wants you to think. It is also wrong. Stacked discounts do not add; they multiply in sequence. The second cut lands on the reduced price, not the original, so the total saving always sits below the simple sum. Understanding this one quirk keeps a “can’t-miss deal” honest — and tells you precisely how much money is really leaving your wallet.

What “20% Plus 10%” Actually Means

Discounts are steps, not flasks of fluid being poured together. Each percentage shaves the price that exists right before it. Work a $100 purchase with a first discount of 20% off, then a second of 10% off the result:

Step 1: $100 × (1 − 0.20) = $100 × 0.80 = $80
Step 2: $80 × (1 − 0.10) = $80 × 0.90 = $72

Your total saving is $100 − $72 = $28, so the combined discount is 28%. If the store had meant a true 30% off, you would pay $70. That $2 gap between $72 and $70 is the difference between multiplying and adding, and it is where stores quietly earn their margin.

The General Formula for Two Discounts

Rather than babysit both steps, combine them into one expression. The amount you keep paying is the product of the two “remaining” shares, so the saving is:

Combined = 1 − [(1 − first) × (1 − second)]

For 20% and 10%: 1 − (0.80 × 0.90) = 1 − 0.72 = 0.28 = 28%. This is handy because it scales to three discounts too: just keep multiplying the remaining shares. And it proves the rule — with any two positive percentages, the product of the two remaining shares is larger than (1 minus the sum), so stacking always gives you less than the sum promises.

How Retailers Phrase It

Honest signs say “an extra 10% at the register” or “10% off already-reduced prices,” which quietly admits the second cut hits a smaller base. Aggressive signs say “25% off plus an additional 15%,” expecting you to read 40%. Run the real numbers: 1 − (0.75 × 0.85) = 1 − 0.6375 = 36.25%, not 40%. The difference of roughly four points is money you would only recover by doing the math before checkout rather than trusting the headline.

When Stacking Gets Capped

Reality adds one more wrinkle: capped stacking. Many promotions apply a maximum total discount, exclude clearance items, or make the second discount members-only. A $200 order might advertise “20% off, then an extra 10%,” but the terms cap the extra at $30, so the second step stops early and your real saving drops below the 28% the pure math suggests. Always check whether the offer applies to the products in your basket and whether a dollar cap exists. The formula tells you the ideal; the small print tells you the actual.

Stacking is still worth taking — 28% beats a single 20% any day. Just never confuse it with 30%. Run your exact numbers through the DiscountVibe discount calculator with the double-discount mode and see the true total before you commit.