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Why a 20% Off Sale Plus a 30% Off Coupon Doesn't Equal 50% Off
You've done the mental math a hundred times at checkout: "20% off, plus my coupon is 30% off, so that's half price, right?" Not quite — and the gap between what shoppers expect and what actually gets charged is one of the most common sources of receipt confusion. Here's the real math, plus how to check a sale price, a discount rate, or an original price in seconds.
Short answerA discounted price is the original price multiplied by (1 − discount rate ÷ 100): Discounted price = Price × (1 − Rate ÷ 100). A $500 item with a 15% discount comes to 500 × 0.85 = $425, a savings of $75.
That's the easy part, and it's the case most shoppers picture when they hear "20% off." The trouble starts when a second discount — a coupon, a loyalty discount, an extra "take an additional X% off" promotion — gets layered on top of the first one.
Why stacked discounts multiply instead of add
Short answerA 20% discount followed by a 30% discount, applied sequentially, doesn't total 50% — it equals 1 − (1−0.20)×(1−0.30) = 1 − 0.80×0.70 = 44% off. Order doesn't matter: 20% then 30% gives the same result as 30% then 20%.
The reason is simple once you see it: the second discount isn't applied to the original price, it's applied to the price that's already been reduced by the first discount. Each step only takes a cut of whatever is left, so the combined effect is always a little smaller than simple addition would suggest.
💡 Example (illustrative, not a real receipt): Say a jacket is tagged at $200. A first sale takes 20% off, dropping it to $160. A coupon then takes 30% off that $160, not the original $200 — so it drops another $48, landing at $112. That $112 is 44% below the original $200, not 50%.
Example: stacking a 20% sale with a second discount, on a $200 item
Second discount
Combined equivalent
Final price
+10% off
28%
$144
+20% off
36%
$128
+30% off
44%
$112
+40% off
52%
$96
This is exactly the calculation behind the "Stacked Discount" mode on the discount calculator — you list the discounts in the order they're applied, and it works out both the final price and the single equivalent discount rate.
Finding the original price from a sale price
Short answerOriginal price = Sale price ÷ (1 − Discount rate ÷ 100). An item on sale for $750 at 25% off had an original price of 750 ÷ 0.75 = $1,000.
This "reverse" direction is handy for checking whether an advertised discount is actually as large as it sounds, or for figuring out what a wholesale/pre-markup price must have been. If you instead know both the old and new price and want the rate that was applied, the formula flips: Rate (%) = ((Old price − New price) ÷ Old price) × 100 — an $800 item that drops to $600 was discounted (800−600)÷800×100 = 25%.
Tax-included prices: most US price tags already include sales tax where it applies, so a discount is normally applied straight to that tax-inclusive number. To back out the pre-tax amount, divide by (1 + tax rate ÷ 100) — a $240 tax-inclusive price with 20% tax included works out to a pre-tax equivalent of $200.
Cart totals and "buy X, pay for Y" deals
Short answerFor a cart, calculate each item's discounted price separately, then add them up for the cart total. The cart's effective discount rate is total savings divided by total normal price — it can differ from a simple average if items carry different discount rates.
Promotions phrased as "buy 3, pay for 2" or "second item 50% off" are really just discount rates in disguise. A "buy X, pay for Y" deal works out to (1 − Quantity paid ÷ Quantity bought) × 100 percent off — "buy 3, pay for 2" is about 33.3% off, "buy 2, pay for 1" is 50% off. A "second item X% off" deal on two equally priced items is worth half of X off the whole purchase, since the discount only touches one of the two items.
Skip the mental math — enter your own price and discounts.
What do a 20% and a 30% discount add up to when stacked?
A 20% discount followed by a 30% discount, applied sequentially, doesn't total 50% — it equals 1 − (1−0.20)×(1−0.30) = 1 − 0.80×0.70 = 44%. Order doesn't change the result: applying 20% then 30% gives the same 44% equivalent as applying 30% then 20%.
How do you calculate a discounted (sale) price?
A discounted price is found by multiplying the original price by (1 − discount rate ÷ 100): Discounted price = Price × (1 − Rate ÷ 100). For example, a $500 item with a 15% discount costs 500 × 0.85 = $425, a savings of $75.
How do you find the original price from a sale price?
If you know the sale price and the discount rate that was applied, the original price is: Original price = Sale price ÷ (1 − Discount rate ÷ 100). For example, an item on sale for $750 at 25% off had an original price of 750 ÷ 0.75 = $1,000.
How do you calculate the total discount on a cart with multiple items?
Calculate each item's discounted price separately, then add all the discounted prices together for the cart total. The cart's average (effective) discount rate is the total savings divided by the total normal price — if items have different discount rates, this can differ from a simple average of the individual rates.
What's the real discount rate on a "buy X, pay for Y" deal?
The real discount rate on a "buy X, pay for Y" deal is (1 − Quantity paid ÷ Quantity bought) × 100. For example, "buy 3, pay for 2" equals (1 − 2/3) × 100 ≈ 33.3% off, and "buy 2, pay for 1" equals 50% off.
🧮 Methodology: All figures on this page use standard discount arithmetic — Discounted price = Price × (1 − Rate ÷ 100), applied sequentially for stacked discounts. The jacket example above is illustrative and assumes round, hypothetical numbers, not a real transaction. This guide is for general informational purposes only; confirm exact promotion terms, sales tax rates, and return policies with the seller.