A single discount is easy: multiply the price by one minus the percentage. Stacked discounts are where intuition fails. Taking 30% off and then a further 10% off does not give 40% off, because the second discount applies to the already-reduced price. The true combined saving is 37%, and the gap widens as the individual discounts get larger.
The correct method is to multiply the surviving fractions. Thirty percent off leaves 0.70 of the price; ten percent off leaves 0.90 of that. Multiplying gives 0.63, so 63% of the original price remains and 37% has been saved. The order of the two discounts makes no difference to the result, which surprises people who assume the larger one should go first.
On the defaults, $249.00 less 30% is $174.30, and a further 10% off that is $156.87. The real saving is $92.13, or 37.0% — not the 40% the two numbers suggest. With 7.5% sales tax the amount payable is $168.64.
The formula
price- Original list price
d<sub>1</sub>- First discount as a decimal
d<sub>2</sub>- Second discount applied to the reduced price
effective- True combined percentage off
How to use this calculator
- Enter the original price before any reduction.
- Enter the first discount percentage.
- Enter a second discount if one stacks on top, or leave it at zero.
- Enter the sales tax rate; the gauge shows the final price after discounts.
Worked examples
30% then 10% off $249.00
$249.00 × 0.70 = $174.30. Then $174.30 × 0.90 = $156.87. The surviving fraction is 0.63, so the true discount is 37.0% — $7.47 less saving than adding the percentages implies.
Order makes no difference
Applying 10% first gives $224.10, then 30% off that gives $156.87 — identical to $156.87. Multiplication is commutative, so no sequencing trick will improve the deal.
How to read your score
Frequently asked questions
Why is 30% plus 10% not 40%?
Because the second discount is taken from the reduced price, not the original. Ten percent of the reduced price is a smaller sum than ten percent of the list price, so the combined saving always falls short of the sum of the percentages.
Is tax charged before or after the discount?
After, in almost every system. You are taxed on what you actually pay, so the discount reduces the tax as well as the price. That is why the tax here is applied to the discounted figure.
How do I work out the percentage off from two prices?
Divide the saving by the original price. If something falls from 80 to 60, the saving is 20 and 20 ÷ 80 is 25% off. Dividing by the new price instead gives 33%, which is the markup back to the old price, not the discount.
What does "up to 70% off" usually mean?
That at least one item carries that reduction. It is a ceiling, not an average, and the deepest discounts are typically on the least popular sizes and colours.
Do coupon codes stack this way?
When they stack at all, yes — each applies to the running total. Many retailers explicitly forbid stacking, or apply a code only to the pre-sale price, so the arithmetic here is the best case.
Stacked discount reference
| First discount | +10% more | +20% more | +30% more | +50% more |
|---|---|---|---|---|
| 10% | 19.0% | 28.0% | 37.0% | 55.0% |
| 20% | 28.0% | 36.0% | 44.0% | 60.0% |
| 30% | 37.0% | 44.0% | 51.0% | 65.0% |
| 40% | 46.0% | 52.0% | 58.0% | 70.0% |
| 50% | 55.0% | 60.0% | 65.0% | 75.0% |
| 60% | 64.0% | 68.0% | 72.0% | 80.0% |
Every figure is below the sum of the two percentages, because the second applies to a smaller base.