A jacket is priced at 1,000. The store takes 20% off for a sale, then applies an extra 10% off at checkout for signing up to a newsletter. Add those together and it feels like 30% off — a final price of 700. The actual final price is 720. That's not a rounding quirk; stacked discounts don't add, they multiply against a shrinking base, and the gap between "feels like" and "actually is" grows every time another discount gets stacked on top.
Why You Can't Add Percentages Off the Same Base
The first discount applies to the full price. The second discount applies to what's left — not the original price. Once the base shrinks, 10% of it is a smaller number than 10% of the original, so the two discounts never sum cleanly to the number they'd suggest if you just added the percentages.
1,000 × (1 − 20/100) = 800 ← after first discount
800 × (1 − 10/100) = 720 ← after second discount, on the new base
Treating it as "30% off the original 1,000" gives 700 — a price that's lower than the real final price, because it assumes the second discount also applies to the full original amount, which it doesn't.
The Formula
For any number of stacked percentage discounts:
Final Price = Base Price × (1 − d₁/100) × (1 − d₂/100) × ... × (1 − dₙ/100)
Each discount multiplies the result of the previous step, never the original base. The order doesn't change the final price (multiplication is commutative), but it does mean you can never shortcut the calculation by summing the percentages first.
Worked Example: Three Stacked Discounts
A 2,000 item gets a 25% seasonal discount, an additional 10% loyalty discount, and a final 5% coupon at checkout:
| Step | Calculation | Running Price |
|---|---|---|
| Start | — | 2,000.00 |
| 25% off | 2,000 × 0.75 | 1,500.00 |
| 10% off | 1,500 × 0.90 | 1,350.00 |
| 5% off | 1,350 × 0.95 | 1,282.50 |
Naively adding 25 + 10 + 5 = 40% off would suggest a final price of 1,200. The real final price is 1,282.50 — the effective combined discount is only about 35.9%, not 40%. The more discounts get stacked, the wider this gap grows, because every additional percentage is being taken from an already-reduced number.
The Effective Discount Percentage
To express stacked discounts as a single equivalent percentage, don't sum them — compute what's left, then subtract from 100:
Effective Discount % = 100 − [(1−d₁/100) × (1−d₂/100) × ... × 100]
For the example above: (0.75 × 0.90 × 0.95) = 0.64125, so the effective discount is 100 − 64.125 = 35.875% — not 40%.
Where This Actually Costs Money or Misleads
Comparing two "better" deals. "40% off" at one store versus "25% off + 15% off" at another sounds like the second one wins by a smaller margin than it actually does. Run the multiplication: 0.75 × 0.85 = 0.6375, an effective 36.25% off — worse than the flat 40%, even though 25 + 15 = 40 makes them look identical on paper.
Advertised vs actual checkout price. Retailers that stack a site-wide sale with a coupon code are, correctly, not being deceptive when the final price is higher than "sale % + coupon %" suggests — that's just how the math works. The mistake is on the shopper's side, expecting simple addition.
Reversing to find the original price. If a receipt only shows the final price after multiple stacked discounts, you can't divide by a summed percentage to recover the original — you'd need to divide by each (1 − d/100) factor individually, in reverse order, or use the effective-discount percentage computed above.
Quick FAQ
Does the order of stacking discounts change the final price? No — multiplication is commutative, so 25% then 10% gives the same final price as 10% then 25%. Only the intermediate "running price" at each step differs.
Is a flat discount always better than an equal-sounding stack? Yes, when the numbers are equal on paper — a single 30% discount always beats any combination of stacked discounts that sum to 30%, because stacking always produces a smaller effective percentage than the sum.
How do stores calculate discount plus tax together? Discount is applied first, to get the taxable amount, then tax is calculated on that discounted price — never the other way around. See how GST/tax is calculated on a discounted price for the full breakdown.
What if a discount is a flat amount, not a percentage (like "500 off")? Flat-amount discounts do subtract directly, in any order, without this multiplicative effect — the compounding issue only applies when two or more discounts are both expressed as percentages of a price.
Skip the Manual Multiplication
Rather than chaining × 0.75 × 0.90 × 0.95 by hand across multiple discounts, the Discount Calculator computes the final price and total savings instantly — useful for checking whether a stacked deal actually beats a flat one before you buy.
Related Free Tools
- Discount Calculator — final price and savings after one or more discounts
- Percentage Calculator — percentage increase, decrease, and ratios
- GST / Tax Calculator — calculate tax on the discounted price, inclusive or exclusive
- Loan Calculator — EMI, total interest, and full amortization schedule