ReckonBoxWhat you pay, and what you save
A discount calculator finds the price after a markdown and the amount you keep in your pocket. A single percent off is one multiplication; where it gets interesting is when two discounts stack, because they never add up the way the signs suggest.
A 20% discount on a $100 item leaves $80 and saves $20. Add a further 10% coupon on top and the price drops to $72, an overall saving of $28. That is a 28% discount, not the 30% you would get by adding the two signs together.
Why 20% plus 10% is 28%, not 30%
Stacked discounts multiply rather than add, because the second discount applies to the already-reduced price. The math is $100 times 0.80 times 0.90, which is $72.
Most discount calculators handle only a single markdown, so the reader is left to guess at the combined effect and usually guesses high. The second 10% comes off $80, not $100, so it is worth $8, not $10. Two discounts always combine to less than their simple sum, and the more you stack, the wider the gap:
| $100, two discounts | Result |
|---|---|
| 20% off | $80 |
| then 10% off | $72 |
| Effective discount | 28% |
| What adding them suggests | 30% |
The order does not matter, the base does
Whichever discount you apply first, the final price is the same, because multiplication does not care about order. 20% then 10% and 10% then 20% both land on $72.
What changes the answer is the base each percentage bites into, and that is always the running price, whatever the sticker says. A store that advertises "extra 30% off already-reduced prices" is not giving you 30% off the original, and this is the arithmetic that shows exactly how much less. Sales tax, if you add it, goes on the discounted price, since that is what you actually hand over at the register.
Where the numbers come from
A single discount leaves the original price times one minus the rate. Stacked discounts multiply those factors together, so two discounts leave the original times (1 minus the first) times (1 minus the second). The effective discount is one minus that combined factor. To run it backward, divide a known sale price by one minus the discount to recover the original, which is how you check whether a "was" price is real.
Any sales tax is applied last, to the discounted price, because tax is charged on the amount you pay.
What this does not cover
This handles percentage and stacked discounts on a single item's price, not every promotion. It does not model quantity deals like buy-one-get-one or three-for-two, membership pricing that depends on who you are, or rebates that arrive after the sale, each of which changes the effective price in ways a straight percentage does not capture.
None of this is advice on whether a deal is worth taking. It shows what a discount actually costs the seller and saves you. The number on the tag is a starting point, and the math does the rest.
Frequently asked questions
How do I calculate a discount? A discount is the original price times one minus the discount rate. A 20% discount on a $100 item leaves $100 times 0.80, which is $80, saving you $20. To find the discount percent from two prices, divide the amount saved by the original price. A $28 saving on $100 is a 28% discount.
Is 20% off then 10% off the same as 30% off? No, it is 28% off, not 30%. Stacked discounts multiply rather than add: $100 times 0.80 is $80, then times 0.90 is $72, an overall 28% discount. The second discount applies to the already-reduced price, not the original, which is why two discounts never combine to their simple sum.
How do stacked or successive discounts work? Each discount applies to the price left after the one before it, so you multiply the reductions together. Two discounts of d1 and d2 leave the original price times (1 minus d1) times (1 minus d2). The order does not change the final price, but the combined effect is always less than adding the two percentages.
How much do I save with a discount? The saving is the original price minus the discounted price. On $100 with a 20% then 10% stack, the price falls to $72, so you save $28. This calculator shows the saving after both discounts and, if you add sales tax, applies the tax to the discounted price, since tax is charged on what you actually pay.
How do I find the original price from a sale price? Divide the sale price by one minus the discount rate. An item marked $72 after a 28% discount was originally $72 divided by 0.72, which is $100. For a single known discount this reverses the math cleanly, which is useful for checking whether an advertised "was" price is genuine.