Stacked discount calculator

"Take an extra 20 percent off already reduced prices" reads as though a 30 percent rack has become 50 percent off, but that is not how successive discounts work. Each cut applies to the price left after the one before it, so the second 20 percent comes off a price that has already shrunk, and the combined saving is always less than the two rates added together. This calculator does that stacking for you: enter the original price and up to three discounts applied in turn, and it returns the final price, the total saved, and the single effective discount that would produce the same result in one step. The effective figure is the honest headline, and it is the number worth carrying in your head. Work through the classic case. A coat priced at 100 is marked down 30 percent, leaving 70. A checkout coupon then takes a further 20 percent, but off the 70, not the 100, so it removes 14 and leaves 56. You have paid 56, saved 44, and the effective discount is 44 percent, not the 50 percent the two labels seemed to promise. The rule behind it is that discounts multiply rather than add: 30 percent off means you pay 70 percent, and a further 20 percent off means you pay 80 percent of that, so you pay 0.7 times 0.8, which is 0.56, or 56 percent of the original. Chain a third discount and it keeps compounding: 56 percent after another 10 percent off becomes 0.56 times 0.9, which is 0.504, an effective 49.6 percent. The gap between the added rates and the real saving grows as the rates get larger, which is exactly why stores present deals this way. Two 50 percent discounts do not make an item free; they make it 75 percent off, because half of a half is a quarter. One useful consequence is that the order does not change the final price. Applying 30 percent then 20 percent gives the same 56 as 20 percent then 30 percent, since multiplication does not care about order. Where order can matter is in the real world rather than the arithmetic: a store might apply a loyalty discount before a coupon, or tax might be added at a particular stage, and some promotions bar stacking altogether or cap the combined saving. The calculator assumes clean, uncapped, back-to-back percentage cuts, which is the common case for sale-plus-coupon shopping. It is worth separating this from a single discount, which many people reach for by habit and which quietly gets the wrong answer when two offers combine. It also differs from adding a tax or a surcharge, where percentages are applied to a base and can genuinely add up. Here every step is a reduction of the running total, so the effect always tapers. People use this when a sale sign and a coupon overlap, when a members' discount sits on top of a seasonal markdown, when comparing a straight 40 percent off against a 30-plus-15 stack to see which really wins, and when a "buy more, save more" tier applies a second cut at the till. Reading the effective discount lets you compare offers on the same basis instead of being swayed by the bigger-sounding pair of numbers. A 45 percent single discount beats a 30 percent then 20 percent stack, even though 30 plus 20 looks like the larger deal, because the stack is only worth 44 percent. Keep two cautions in mind. First, confirm the offers actually stack: plenty of promotions exclude sale items or say a coupon cannot be combined with other discounts, in which case only one applies. Second, the final price is what matters, so use it rather than the effective percentage when deciding whether something is worth buying, because a large discount on an inflated original is not the same as a fair price. The tool gives you both the money figure and the true rate so you can judge on either.

How it works

1. Enter the original price before any reduction.
2. Enter the first discount as a percentage.
3. Add a second and, if needed, a third discount, each applied to the price left after the previous one.
4. The calculator multiplies the price down through each cut to get the final price.
5. It reports the total saved and the single effective discount that would give the same final price in one step.

What a stack is really worth

Key facts

• Successive discounts multiply, so the combined saving is always less than the rates added together.
• 30 percent then 20 percent off is an effective 44 percent, not 50 percent.
• The order of the discounts does not change the final price.
• The effective discount is the fair way to compare a stack against a single offer.

Tips

• Compare offers by their effective discount, not by adding the rates on the signs.
• Check the terms first, since many promotions bar stacking on already reduced items.
• Judge the deal on the final price, because a big discount on an inflated original is not a bargain.
• A single discount elsewhere can beat a bigger-looking stack; work out both before buying.

Frequently asked questions

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