Double (Stacked) Discount Calculator
From an original price and two sequential discounts, compute the final price, total saved and the equivalent single discount rate.
輸入資料
計算結果
重點速覽：Sequential discount: after first = price x (1 - d1); final = x (1 - d2). Total saved = original - final; equivalent discount = (1 - final/original) x 100%. Because the second discount is on the reduced price, the equivalent is ALWAYS less than d1 + d2. Example: 100, 20% then 10% → final 72, saved 28, equivalent 28% (not 30%). Order doesn't matter (× commutes). WARNING: Whether discounts stack and on what base follows store terms — some exclude already-discounted items. Education, not advice.
計算公式
第一次折後價 = 原價 × (1 − 第一次折扣%)。
最終價格 = 第一次折後價 × (1 − 第二次折扣%)。
等效折扣率 = (1 − 最終價 ÷ 原價) × 100%。
$$第一次折後價：$P_1 = Price\times(1-d_1)$$$$$最終價格：$Final = P_1\times(1-d_2)$$$$$等效折扣率：$d_{eff}=\left(1-\dfrac{Final}{Price}\right)\times100\%$$$使用說明
- Enter the original price and two discount percentages.
- View the final price, amount saved and equivalent single discount.
原價 100 下不同雙重折扣組合的最終價與等效折扣
| 原價 (HK$) | 第一折 | 第二折 | 最終價 (HK$) | 等效折扣 |
|---|---|---|---|---|
| 100 | 20% | 10% | 72 | 28% (非 30%) |
| 1,000 | 30% | 20% | 560 | 44% (非 50%) |
| 500 | 50% | 50% | 125 | 75% (非 100%) |
理財情境案例
案例一：減 20% 再減 10%，等於減多少？
某商品原價 HK$100，商店標示『減 20%,結帳再減 10%』。很多人以為總共減 30%,實付 HK$70——這是錯的。
第一次折後價 = 100 × (1 − 20%) = HK$80；最終價格 = 80 × (1 − 10%) = HK$72；總節省 = 100 − 72 = HK$28；等效折扣率 = (1 − 72/100) × 100% = 28%。
解讀：實際只減了 28%,不是 30%。原因是第二次的 10% 折扣，是針對已經打折後的 HK$80 來計算 (只減 8 元),而不是原價 100。所以雙重折扣的等效折扣率永遠『小於』兩個折扣直接相加。看到『再減 X%』的宣傳，別急著把兩個百分比加起來。
案例二：兩個 50% 折扣不會讓商品免費
有人以為『半價再半價』(減 50% 再減 50%) 就等於減 100%、免費拿走——這是嚴重誤解。以原價 HK$500 為例。
第一次折後價 = 500 × (1 − 50%) = HK$250；最終價格 = 250 × (1 − 50%) = HK$125；總節省 = 500 − 125 = HK$375；等效折扣率 = (1 − 125/500) × 100% = 75%。
解讀：兩次五折後，實付 HK$125，等效折扣只有 75% off，絕不是免費。因為第二個 50% 是對已經半價的 HK$250 再打對折 (減 125),而非對原價。事實上，無論打幾次折，只要每次折扣小於 100%,價格永遠趨近於零但不會真正變成零或負數。另外值得一提：兩次折扣『先後次序不影響最終價』(先 20 後 10 與先 10 後 20 結果相同，因為乘法可交換),但商店有時會用次序來製造心理錯覺。⚠️ 實際優惠是否可疊加、以哪個為基數，須以商店條款為準，本計算器示範的是標準的『逐次折扣』算法。
常見問題
Why is the equivalent discount less than the two added?
Because the second discount applies to the ALREADY discounted price, not the original. With original 100, 20% then 10%: after first 80, second takes 10% of 80 = only 8 off, total 28 off → equivalent 28%, not 30%. The second percentage acts on a smaller base, so it contributes less. Always compute sequentially, never just add.
Does the order of the two discounts matter?
No — multiplication commutes. 20% then 10% and 10% then 20% both give final = original x 0.8 x 0.9 = 0.72. The order does not change the result, though shops may sequence them to create a psychological illusion. The final price is identical either way.
Is two 50% off the same as 100% off (free)?
No — a common and serious misconception. 500, 50% then 50% → after first 250, then 50% of 250 = 125; final 125, equivalent 75% off. You still pay 125, never free. Because the second 50% is on the already-halved price. And as long as each discount is below 100%, the price approaches (never reaches) zero no matter how many times discounted.
Does the order really not matter, and is 50% off twice = free?
Order: genuinely does not matter for the final price, because both discounts are multipliers on the price and multiplication commutes (0.8×0.9 = 0.9×0.8). Shops may sequence them for a psychological 'first big cut' effect, but the math is identical. '50% off twice = free' is FALSE — it is 75% off, you pay 25%. Why people confuse it: they mentally add 50%+50%=100%, forgetting the second 50% is on the halved price (only 125 off a 500 base). Remember the equivalent is always less than the sum, and as long as each discount < 100%, price never reaches zero or negative.
What should I watch when an online store shows stacked discounts?
Three points. (1) Confirm whether they truly stack — some promos exclude already-discounted items, or 'second discount' applies only to part (e.g. clearance). Read the terms; our tool assumes standard sequential stacking. (2) Watch the base — is the second discount on the post-first price or on the original (rare but possible; if on original, the two do add)? The tool uses the standard 'on reduced price' convention. (3) Beware urgency/illusion — a 'extra 10% off' sounds like 10% more saving but only 10% of the reduced price. Compute the equivalent discount with this tool to see the real cut, then compare with the usual price to decide. Don't let 'double discount' framing rush you into overspending.
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參考資料
內容審核：香港計算器財經團隊。計算邏輯與公式參考香港金融管理局（HKMA）及投資者及理財教育委員會（IFEC）之個人理財計算指引，結果僅供參考，實際以相關機構公佈為準。