Successive discounts: why 20% + 10% is not 30%
Calculate stacked discounts in sequence and convert them into one equivalent effective discount.
“20% off, plus an extra 10%” does not mean 30% off. Each discount applies to the price left by the previous one.
Formula for stacked discounts
Convert each percentage into the fraction of the price that remains:
final price = original price x (1 - d1 / 100) x (1 - d2 / 100)Add another multiplier for every additional discount.
For a $1,000 item discounted first by 20% and then 10%:
1000 x 0.80 = 800
800 x 0.90 = 720The final price is $720, so the saving is $280.
Equivalent effective discount
effective discount = 1 - (final price / original price)
1 - (720 / 1000) = 0.28 = 28%A single 28% discount produces the same result as successive discounts of 20% and 10%.
Common combinations
| Original price | Successive discounts | Final price | Effective discount |
|---|---|---|---|
| $500 | 10% + 10% | $405 | 19% |
| $1,000 | 20% + 10% | $720 | 28% |
| $2,000 | 30% + 20% | $1,120 | 44% |
| $800 | 50% + 10% | $360 | 55% |
With positive discounts, the effective rate is lower than their simple sum. For example, 30% plus 20% leaves 0.70 x 0.80 = 0.56 of the original price, for an effective discount of 44%.
Compare promotions carefully
Check whether a coupon applies before or after another markdown, whether it has a maximum value and whether taxes, shipping or financing are excluded. The amount finally payable is more informative than the promotional wording.
For one markdown, see how to calculate a discount. In the percentage calculator, subtract each percentage in sequence using the previous result as the next base.
Frequently asked questions
Why are 20% and 10% not 30% together?
Because the second 10% is taken from 80% of the original price, not from the original price itself.
Is one 30% discount better than 20% plus 10%?
Yes. On $1,000, 30% leaves $700; 20% followed by 10% leaves $720.