Why stacked discounts do not add
Retail promotions are often written to make two discounts feel like one large number: “40% off, then take an extra 20% off at checkout.” Adding those numbers suggests a 60% saving, but the actual saving is 52%. The first discount leaves 60% of the original price. The second discount removes 20% of that smaller amount, leaving 80% of 60%, or 48% of the original price.
The easiest way to see the difference is with a $100 item:
- The first 40% discount removes $40 and leaves $60.
- The extra 20% discount removes $12, because 20% of $60 is $12.
- The final price is $48.
- The total saving is $52, so the equivalent single discount is 52%.
The advertised percentages describe separate operations with separate starting amounts. Only the first one uses the original price as its base.
The stacked discount formula
For each discount, convert the rate into a remaining-price multiplier. A 20% discount leaves 80%, so its multiplier is 0.80. A 35% discount leaves 65%, so its multiplier is 0.65.
For two discounts:
Final price = Original price × (1 − discount 1) × (1 − discount 2)
The discounts are written as decimals in the formula. A 25% discount becomes 0.25, and the amount remaining becomes 0.75.
To find the equivalent single discount:
Equivalent discount = 1 − [(1 − discount 1) × (1 − discount 2) × ...]
Multiply by 100 to express the answer as a percentage. For successive discounts of 25%, 10% and 5%, the remaining proportion is:
0.75 × 0.90 × 0.95 = 0.64125
That means 64.125% of the original price remains. The equivalent single discount is therefore 35.875%, usually rounded to 35.88%.
A useful two-discount shortcut
For exactly two discounts, there is a compact formula:
Combined discount = A + B − (A × B ÷ 100)
If the discounts are 30% and 20%:
30 + 20 − (30 × 20 ÷ 100) = 50 − 6 = 44%
The product term is the overlap created by applying the second discount to a price that has already fallen. It is also exactly how much simple addition overstates the result. Adding 30% and 20% gives 50%, which is 6 percentage points too high; 30% of 20% is 6%.
This shortcut becomes awkward with three or four discounts, which is why multiplying the remaining proportions is the more reliable general method.
Does the order of discounts matter?
For pure percentage discounts, no. A price multiplied by 0.80 and then by 0.70 ends at the same number as a price multiplied by 0.70 and then by 0.80. This follows from the fact that multiplication can be performed in either order.
The individual line-by-line savings will look different, however. On a $100 item, 20% then 30% saves $20 in the first step and $24 in the second. Reversing them saves $30 first and $14 second. Both routes end at $56 and both save $44 overall.
Order begins to matter as soon as the promotion includes anything that is not a simple percentage:
- A fixed $10 coupon combined with 20% off.
- A percentage coupon capped at a maximum dollar saving.
- A minimum-spend offer that stops applying after another coupon reduces the basket.
- Shipping added before or after a storewide promotion.
- Tax calculated on a legally defined taxable price.
- A discount that excludes one product but applies to the rest of the basket.
In those cases, follow the seller’s stated order and calculate each stage separately.
Worked examples
Clearance price plus an extra coupon
A jacket was $240, is marked 50% off, and has an extra 20% member coupon.
- After 50% off: $240 × 0.50 = $120.
- After another 20% off: $120 × 0.80 = $96.
- Total saved: $240 − $96 = $144.
- Equivalent discount: $144 ÷ $240 = 60%.
The promotion is not 70% off. The extra 20% removes $24, which is 10% of the original $240 price.
Three supplier trade discounts
A wholesaler lists equipment at $5,000 with successive trade discounts of 15%, 10% and 5%.
- $5,000 × 0.85 = $4,250.
- $4,250 × 0.90 = $3,825.
- $3,825 × 0.95 = $3,633.75.
The buyer saves $1,366.25. The equivalent discount is 27.325%, not the 30% suggested by adding 15 + 10 + 5.
Comparing two promotions
Store A offers 35% off. Store B offers 20% off plus an extra 20% off. Store B’s promotion sounds like 40%, but it leaves 0.80 × 0.80 = 64% of the original price, making the effective discount 36%. Store B is one percentage point better before shipping, tax, loyalty rewards and other conditions are considered.
This is where the equivalent single discount is most useful: it puts a complicated promotion and a simple promotion on the same basis.
Fixed coupons are different
A fixed-value coupon is subtraction, not multiplication. Suppose a $100 item is 20% off and you also have a $10 coupon.
If the percentage applies first, the result is $100 × 0.80 − $10 = $70. If the $10 coupon applies first, the result is ($100 − $10) × 0.80 = $72. The two-dollar difference appears because the percentage is being measured from a different base.
This calculator accepts percentage reductions only. To include a fixed coupon, calculate the percentage stack, subtract the coupon at the stage specified by the retailer, and then check any minimum-price or minimum-spend restriction.
Discounts and sales tax
The checkout total may still differ from the calculator because tax rules decide which discounts reduce the taxable price. A retailer-funded markdown normally reduces the selling price before tax. Manufacturer-funded coupons can be handled differently because the retailer may be reimbursed for the coupon value. Rules vary by jurisdiction and by the exact structure of the promotion.
For planning a purchase, first use this page to find the price after successive percentage discounts. Then use the Sales Tax Calculator with the taxable amount and the combined rate for the sale location. For bookkeeping or invoicing, follow the tax authority’s rule instead of assuming that every coupon reduces tax.
Rounding and one-cent differences
The calculator carries the full precision through the entire stack and rounds the displayed currency values to two decimal places. A cash register may round after each discount step instead. On a long chain of discounts, those two methods can differ by a cent.
For example, a discount can produce a price containing a fraction of a cent. Rounding that intermediate price changes the base used for the next discount. Neither approach changes the percentage logic, but the seller’s system determines the actual amount charged. The receipt is authoritative for a completed transaction.
Common mistakes
Adding the rates. This is the main error. Multiple positive percentage discounts always produce a smaller saving than their sum, unless all but one are zero.
Taking every discount from the original price. That is another way of adding the rates. Each successive discount uses the price left by the previous step.
Calling 20% off twice a 40% discount. Two 20% discounts leave 0.80 × 0.80 = 64%, so they equal 36% off.
Mixing “percent off” with “percent of.” A final price that is 40% of the original means the discount was 60% off the original.
Ignoring the offer conditions. Product exclusions, coupon caps, loyalty requirements, minimum baskets and expiration dates can matter more than a one-point difference in the effective discount.
What this calculator includes and leaves out
It applies up to four percentage discounts successively, shows the price after every step, and converts the complete chain into one equivalent percentage. The currency choice changes formatting only; the mathematics is identical for dollars, pounds, euros, rupees and other currencies.
It does not decide whether discounts can legally or contractually be combined. It does not apply fixed coupons, tax, delivery charges, cashback received later, points with a non-cash value, quantity discounts that change at thresholds, or a maximum saving cap. Those terms must be checked against the promotion itself.
For a clean comparison, use the same starting price and include only discounts that are actually available to you. A promotion with a slightly better percentage can still cost more if its starting price is higher.