$80.00
$68.00
$61.20
$38.80
38.80%
$80.00
$68.00
$61.20
$38.80
38.80%
The Triple Discount Calculator extends stacked discount analysis to three sequential percentage reductions — the most complex scenario commonly encountered in retail and commercial pricing. Triple discounts occur during mega-sale events where a category promotion, a loyalty membership discount, and a limited-time coupon code all apply to the same item; in B2B wholesale pricing with trade discounts, volume discounts, and promotional rebates stacked; and in clearance phases where items are progressively marked down over time.
The mathematical principle compounds: each successive discount applies not to the original price but to the most recently discounted price. Three discounts of 10%, 10%, and 10% do not produce a 30% combined discount — they produce a 27.1% effective discount (0.9 × 0.9 × 0.9 = 0.729). The divergence between the sum of discounts and the effective combined discount grows larger as the individual discount percentages increase.
This calculator makes all intermediate steps visible: you can see the price after each successive reduction, the final net price, total dollar savings, and most importantly the true effective discount — the single percentage that describes the overall reduction from original to final price. This complete transparency helps both consumers and pricing managers understand the real economic impact of layered promotional structures.
Triple discounts are applied as three successive multiplications:
$$\text{After 1st} = P \times \left(1 - \frac{d_1}{100}\right)$$
$$\text{After 2nd} = P \times \left(1 - \frac{d_1}{100}\right)\left(1 - \frac{d_2}{100}\right)$$
$$\text{Final Price} = P \times \left(1 - \frac{d_1}{100}\right)\left(1 - \frac{d_2}{100}\right)\left(1 - \frac{d_3}{100}\right)$$
$$\text{Effective Discount} = \left[1 - \left(1 - \frac{d_1}{100}\right)\left(1 - \frac{d_2}{100}\right)\left(1 - \frac{d_3}{100}\right)\right] \times 100$$
For $100 with discounts of 20%, 15%, 10%:
$$\text{After 1st} = 100 \times 0.80 = \$80$$
$$\text{After 2nd} = 80 \times 0.85 = \$68$$
$$\text{Final} = 68 \times 0.90 = \$61.20$$
$$\text{Effective Discount} = (1 - 0.80 \times 0.85 \times 0.90) \times 100 = (1 - 0.612) \times 100 = 38.8\%$$
Note: the sum of individual discounts was 45%, but the effective combined discount is only 38.8%.
The three intermediate price outputs show exactly how the price progresses through each discount stage, making it easy to verify the calculation at any point. The effective discount is the single most important summary metric — it answers: 'If this were a single-percentage sale, what would the percentage be?'
For any set of three discounts, the effective rate is always less than the arithmetic sum of the three percentages. The bigger each discount, the larger the gap between the sum and the effective rate. This is why savvy shoppers and pricing analysts always calculate the effective combined discount rather than summing individual percentages.
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Results
$500 item through three discounts of 30%+20%+10% reaches $252. Effective discount is 49.6%, not the 60% naive sum.
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Results
$200 at 15%+10%+5% stacked yields $145.35. Effective discount is 27.3%, not 30%.
For three equal discounts of d% each, the effective combined discount is: 1 - (1 - d/100)^3. For example, three 10% discounts: 1 - (0.9)^3 = 1 - 0.729 = 27.1% effective. Three 20% discounts: 1 - (0.8)^3 = 1 - 0.512 = 48.8% effective (not 60%). Three 25% discounts: 1 - (0.75)^3 = 1 - 0.422 = 57.8% effective. The effective rate grows non-linearly and always lags behind the arithmetic sum of the three percentages.
This calculator handles exactly three discounts. For four or more sequential discounts, extend the formula: multiply an additional factor (1 - d_n/100) for each additional discount. Alternatively, apply this calculator iteratively: compute the final price for three discounts, then use that final price as the 'original price' input in this (or the double discount) calculator for any remaining discounts. The math chains indefinitely using the same multiplicative principle.
A trade discount chain like '20/10/5' (also written 20-10-5) means three sequential discounts of 20%, then 10%, then 5% applied to the list price. This notation is common in wholesale, manufacturing, and B2B distribution. Using this calculator with 20%, 10%, and 5%: the effective discount is 31.6%, not 35%. Trade discounts are always applied sequentially, never additively, which is why understanding the effective combined rate matters for accurate cost accounting and margin analysis.
Reverse the formula: Original = Final / [(1 - d1/100)(1 - d2/100)(1 - d3/100)]. For example, if the final price is $61.20 after 20%, 15%, 10% discounts: Original = 61.20 / (0.80 × 0.85 × 0.90) = 61.20 / 0.612 = $100. This reverse calculation is useful in retail when a clearance tag shows only the final price and each markdown percentage applied, but you want to recover the original retail price.
No — as with double discounts, the order of application does not affect the final price. Since we're multiplying three factors (1 - d1/100), (1 - d2/100), (1 - d3/100), and multiplication is commutative and associative, any ordering of the three discounts produces the same final price. You can verify this by swapping d1 and d3 — the product of the three factors is unchanged. There is no mathematical advantage to any particular ordering.
The triple discount's effective discount percentage IS the single equivalent discount. If three sequential discounts of 20%, 15%, and 10% produce an effective discount of 38.8%, then a single discount of 38.8% on the same original price would yield the exact same final price. This equivalence is useful for communicating the true value of a stacked promotion to customers or management in a single, comprehensible number rather than a chain of percentages.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
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