Stacked Discounts Explained: Why 30% + 20% Off Isn't 50% Off
The key idea: "30% off, plus an extra 20% off!" sounds like 50% off, but it's actually 44% off. Discounts stack multiplicatively, not additively.
Why retailers love stacked discounts
"50% off + extra 20% off at checkout!" makes shoppers feel like they're getting 70% off. They aren't. Stacked discounts apply to the running price, not the original, so each layer affects a smaller dollar base than the one before.
This framing isn't dishonest — it's mathematically how percentage discounts work — but most shoppers don't run the actual math, so they overestimate their savings.
The correct formula
where each dₙ is a discount as a decimal
For a $100 item with 30% off then 20% off:
- $100 × (1 − 0.30) = $100 × 0.70 = $70
- $70 × (1 − 0.20) = $70 × 0.80 = $56
You paid $56. Out of $100 original, you saved $44 — that's a 44% effective discount, not 50%.
Worked example: a $80 shirt with two stacked discounts
Imagine a $80 shirt that's already 25% off, with an extra 15%-off coupon at checkout:
- First discount (25% off): $80 × 0.75 = $60
- Second discount (15% off): $60 × 0.85 = $51
- You pay: $51
- You saved: $80 − $51 = $29, which is 36.25% off the original
Notice the gap: the advertised "25% + 15% = 40% off" sounds nicer than the actual 36.25%. Not a scam, just stacked math.
The general rule, simplified
To get the combined discount percentage from any two stacked discounts, use:
Some common stacking pairs:
| Advertised stack | Sounds like | Actually is |
|---|---|---|
| 10% + 10% | 20% | 19% |
| 20% + 10% | 30% | 28% |
| 20% + 20% | 40% | 36% |
| 25% + 15% | 40% | 36.25% |
| 30% + 20% | 50% | 44% |
| 50% + 20% | 70% | 60% |
| 50% + 50% | 100% | 75% |
The discrepancy grows with bigger percentages. "50% + 50% off" sounds like a free item, but it's just 75% off.
Three stacked discounts — and beyond
The same multiplicative principle works for any number of layers. A clearance item with 50% off, an extra 30% promo, and a 10% loyalty coupon:
- $100 × 0.50 × 0.70 × 0.90 = $100 × 0.315 = $31.50
- Effective discount: 68.5% (not the 50+30+10 = 90% it sounds like)
Where stacking gets even more confusing: tax
Tax usually applies after all discounts. So the math becomes:
- $100 with two stacked 20% discounts: $100 × 0.80 × 0.80 = $64
- Then 8% sales tax: $64 × 1.08 = $69.12 final
Tax doesn't compound with the discounts (it's a separate calculation), but it does base on the discounted price, which means stacking discounts also slightly reduces your tax bill.
The "buy one get one free" framing
BOGO offers are mathematically stacked discounts on a multi-item bundle. "Buy one, get one 50% off" for two $80 items:
- Item 1: $80 (full price)
- Item 2: $80 × 0.50 = $40
- Bundle: $120 for two items, or $60 each on average
- Effective discount: 25% per item — half what the framing suggests
For more on this specific trap, see our 50% off post.
Quick mental shortcuts
For rough field math without a calculator:
- Two equal discounts: Square the "keep" rate. Two 20%-offs = 0.8² = 0.64 = 36% off total.
- Adding ~5%: For small additional discounts (under 10%), the stacking gap is small. "30% + 5% extra" is very close to 33.5%, which most people would round to "about a third off."
- Order doesn't matter: 30% off then 20% off equals 20% off then 30% off. Multiplication is commutative, so feel free to apply discounts in whichever order is easier to compute.
Frequently asked questions
Are stacked discounts ever applied differently in stores?
Some retailers apply both discounts to the original price (additive stacking) at checkout, especially when the second discount is a fixed-dollar coupon ("$10 off any purchase"). Read the fine print or watch the running total at checkout — the actual application varies by store and promotion.
Why do retailers stack discounts instead of just advertising the real number?
Behavioral economics: shoppers respond more strongly to "30% off plus an extra 20%!" than to "44% off." The framing also makes the second discount feel like a bonus you earned (by signing up, using a coupon, etc.), increasing engagement and email signups.
How do I figure out the final price if I see "30% + 20% off"?
Multiply the original by 0.70 × 0.80 = 0.56. For a $100 item, that's $56. The 0.56 means you're paying 56%, so you're saving 44%. Or use the discount calculator with the effective percentage.
What about "free shipping if you buy more"?
Free shipping is a fixed-dollar discount, not a percentage. Just add the shipping you'd otherwise pay to your savings calculation. If shipping is $10 and you buy $80 worth of items at 30% off, your effective discount vs. the no-stack baseline is ($24 + $10) / $80 = 42.5%.
Calculate any stacked discount in seconds
The discount calculator handles one discount at a time, but you can chain it — calculate the first discount, then put the result back in as the new "original" for the second discount. Or simply remember the formula: multiply (1 − d) for each layer. Need to factor in tax? Use the sales tax calculator on the final discounted price.