Triple Discount Calculator
From the original price and three sequential discounts, compute the price after each step, the final price, the total saved and the single equivalent discount rate.
Input Data
Results
At a glance:Three discounts stack on the falling price. After each d%: price = price × (1 − d ÷ 100). Final price follows all three; total saved = original − final; equivalent single discount = 1 − final ÷ original (as a percent). The combined effect is less than the sum of the three percents.
Formula
After each discount: price = price × (1 − discount% ÷ 100).
Total saved = original − final price.
Equivalent discount = (1 − final ÷ original) × 100.
$$P_{\text{final}} = P_0 \times (1 - d_1)(1 - d_2)(1 - d_3)$$$$\text{Effective \%} = \left(1 - \dfrac{P_{\text{final}}}{P_0}\right) \times 100\%$$How to Use
- Enter the original price.
- Enter the three discount percents in order.
- Read each step's price, the final price, the saving and the equivalent discount.
FAQ
If I take 30%, 20% and 10% off in turn, is that the same as 60% off?
No. Each discount applies to the previous discounted price, and the base shrinks each time. From HK$100 the price steps down to 70, 56, then 50.4; the equivalent discount is only 49.6%, far less than a straight 60% off. The more and larger the stacked discounts, the bigger this gap becomes.
Does the order of the three discounts matter?
No. Because it is a chain of multiplications (1 − d1) × (1 − d2) × (1 − d3), multiplication is commutative, so whichever discount you apply first gives the same final price. Some shops, however, prescribe the order or forbid stacking, so the store's terms ultimately prevail.
Can I use this for only two discounts?
Yes—enter 0 for one of the discounts, e.g. set the third discount to 0 to make it a double discount, or just use the double-discount calculator. For more than three, first compute the final price after the first three, then feed that as a new 'original price' to stack the next discount.
What is the 'equivalent discount rate' and why is it lower than simply adding the discounts?
The 'equivalent discount rate' is the key to seeing the true benefit of chained discounts, and this calculator works it out for you. It means: if I take several discounts in a row, what single discount percentage would produce the same final result? It answers 'I was discounted three times in a row—if I had to summarise it as one number, how much did I actually save?' The formula is direct: equivalent discount = (1 − final price ÷ original price) × 100%. For example, HK$100 chained down to HK$50.4 gives (1 − 50.4 ÷ 100) × 100% = 49.6%. That 49.6% is the real reduction once the triple discount is 'compressed' into a single discount. Why is it 'lower' than adding the percentages (30% + 20% + 10% = 60%)? Because each discount acts on the 'already-reduced, smaller' price, not on the original. The first 30% off is taken on the full HK$100, cutting HK$30—the most 'generous' cut since the base (100) is largest. The second 20% is taken on the reduced HK$70, cutting only HK$14, not the HK$20 you might imagine. The third 10% is taken on the even smaller HK$56, cutting just HK$5.6. The same percentages cut less actual money each time because the base shrinks, so the total really saved (30 + 14 + 5.6 = 49.6) is far below the 60 you might imagine from adding them. That is why the equivalent discount is always below the sum, and the gap widens with more and bigger discounts. Understanding the equivalent discount is the best tool to see through a shop's 'pile of big-looking discounts creating a bargain illusion'—don't be fooled by '30% then 20% then 10%'; the real deal is the equivalent rate. Our percentage-discount calculator can be used alongside this.
Does discount order really not matter, and can I use fewer or more than three?
These are two common questions, answered together. First, order: it does NOT matter for the math—whatever order you apply the same discounts, the final price is identical, because chained discounts are a multiplication: final = original × (1 − d1) × (1 − d2) × (1 − d3). Multiplication is commutative, so 0.7 × 0.8 × 0.9 equals 0.9 × 0.8 × 0.7, both 0.504, meaning applying 30% first or 10% first both end at 50.4% of the original. This is handy: when a shop says 'discount A then discount B', you need not worry about the sequence. One real-world caveat: some shops prescribe the order, forbid stacking certain offers, or apply some discounts 'pre-tax' and others 'post-tax'—those commercial rules change the result from the pure math, so the store's terms prevail. Second, fewer or more than three: absolutely. With only two discounts, set one field to 0 (e.g. third discount = 0 means 'take 0% more, i.e. no change'), and the calculator effectively does a double discount. With more than three (four, five…), use a stepping technique: compute the final price after the first three with this tool, then enter that result as a new 'original price' and apply the remaining discounts, repeating as needed. Treating an intermediate result as a new original works for any multi-discount scenario. Our percent-off and markdown calculators handle single discounts alongside this.
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References
Content review: Calculatorism Finance Team. Results are for reference only; please refer to the relevant authorities for the official figures.