Discount calculator
Stacked discounts multiply rather than add: 20% off then 10% off is 28% off, not 30%. Shops know this and shoppers often do not.
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%
Price after both discounts
86.40
- Total saved
- 33.60
- Effective discount
- 28.000 %
- What adding the percentages would suggest
- 30.00 %
- How much that overstates it
- 2.000 %
- Price after the first discount only
- 96.00
- Original price behind that sale price
- 108.00
Show the working
- Original price = 120
- First discount = 20
- Second discount = 10
- Or a sale price to work back from = 86.4
- Price after the first discount only = 120 * (1 - 20/100) = 96
- Price after both discounts = 96 * (1 - 10/100) = 86.4
- Total saved = 120 - 86.4 = 33.6
- Effective discount = 120 > 0 ? 33.6 / 120 * 100 : 0 = 28
- What adding the percentages would suggest = 20 + 10 = 30
- Original price behind that sale price = 20 < 100 ? 86.4 / (1 - 20/100) : 0 = 108
- How much that overstates it = 30 - 28 = 2
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- final = price x (1 - d1) x (1 - d2)
- effective discount = 1 - (1 - d1)(1 - d2)
A "50% off, then an extra 20% off" sale is 60% off, not 70%.