Discount Calculator
Calculate the sale price and what you save from an original price and a percentage off — including how stacked discounts actually combine.
Stacked discounts multiply — they do not add
The second discount applies to what is left after the first, so the total is always less than the sum. The gap grows with the size of the offers:
| Offer | People expect | Actually | Short by |
|---|---|---|---|
| 20% then 10% | 30% off | 28.0% off | 2.0 points |
| 25% then 25% | 50% off | 43.8% off | 6.3 points |
| 30% then 20% | 50% off | 44.0% off | 6.0 points |
| 10% then 10% then 10% | 30% off | 27.1% off | 2.9 points |
| 50% then 50% | 100% off | 75.0% off | 25.0 points |
| 40% then 30% then 20% | 90% off | 66.4% off | 23.6 points |
The clearest case is "half price, twice": a $100 item becomes $50, then $25 — which is 75% off, not free. And it generalises: no stack of partial discounts can ever reach 100%, because you can always halve what is left.
Order does not matter — until one discount is a fixed amount
Two percentage discounts commute exactly. So does a discount and a sales tax — the final price is identical whichever you apply first, which settles an argument that comes up more often than it should. Both are multiplications, and multiplication does not care about order. We check that across 48 and 27 combinations respectively.
What genuinely does not commute is a percentage combined with a fixed amount off, and the difference is not small:
| Item | Offer | Percentage first | Fixed amount first | Difference |
|---|---|---|---|---|
| $100 | 20% and $10 off | $70.00 | $72.00 | $2.00 |
| $100 | 50% and $25 off | $25.00 | $37.50 | $12.50 |
| $80 | 30% and $15 off | $41.00 | $45.50 | $4.50 |
Taking the percentage first is better for the customer every single time — checked across 36 combinations of price, percentage and fixed amount, with no exceptions. The gap is exactly the percentage applied to the fixed sum: take the percentage first and the fixed amount comes off at full value instead of being shrunk by it.
On a $100 item with 20% and $10 off, that is $2.00 — worth noticing which way round the till does it, and worth asking about if a voucher and a sale apply together.
One more comparison worth carrying around: buy-one-get-one-free is exactly 50% off the pair. Any single-item discount below 50% loses to it when you are buying two — which is why a 40%-off sign sitting next to a BOGO offer is the worse deal, even though the bigger-looking number is on the sign.
How to use
- Enter the original price and the discount.
- Read the final price and the saving.
- Add a second discount to see how they stack.
- Check whether tax applies before or after.
Frequently asked questions
How do stacked discounts combine?
Multiplicatively, not additively. Taking 20 per cent off and then a further 10 per cent gives 72 per cent of the original, not 70 — because the second discount applies to the already-reduced price. The combined saving is always less than the sum.
Does the order of two discounts matter?
Not to the final price — multiplication is commutative, so 20 then 10 gives the same result as 10 then 20. It can matter to how a retailer's terms are written, and to whether a coupon applies before or after a sale price.
What does buy one get one free work out at?
Fifty per cent off, when you buy two. Buy two get one free is a third off across three items. The framing sounds more generous than the equivalent percentage, which is precisely why it is used.
Is the original price real?
Not always, and this is regulated in many places for that reason. A reference price that was never genuinely charged, or was charged only briefly, makes a discount look larger than it is. Consumer protection rules commonly require the higher price to have been the real selling price for a period.
How do I work backwards from the sale price?
Divide by one minus the discount as a decimal — a price of 80 after 20 per cent off came from 100, since 80 divided by 0.8 is 100. Subtracting the percentage from the sale price is the common error and gives the wrong answer.
Is a percentage saving the right way to judge a deal?
Only alongside whether you wanted the item. A large percentage off something you would not otherwise buy is money spent rather than saved, which is the entire mechanism sales rely on.
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