🏷 Discount Calculator
Work out what you actually pay after a discount, how much you save, and what a second discount on top is really worth. It also runs backwards from a sale price to the original.
What a discount is actually worth, and why two discounts are not one big one
A discount is a percentage taken off a price, so the arithmetic is one multiplication. The interesting part is everything retailers do around that multiplication: stacking offers, quoting the saving instead of the price, and anchoring against a number nobody ever paid.
sale price = original × (1 − discount/100) saving = original − sale price
Stacked discounts multiply, they do not add
This is the single most profitable piece of consumer arithmetic you can learn. A 20% discount followed by a further 20% is not 40% off. The second discount applies to the already reduced price:
| Offer | You pay | Actual discount |
|---|---|---|
| 20% then 20% | $64.00 | 36% |
| 30% then 20% | $56.00 | 44% |
| 50% then 20% | $40.00 | 60% |
| 25% then 25% | $56.25 | 43.75% |
| 10% then 10% then 10% | $72.90 | 27.1% |
The general rule is that the combined multiplier is the product of the individual ones: 0.8 × 0.8 = 0.64, so 36% off. To get the true figure quickly, multiply what remains rather than adding what is taken: two 20% discounts leave 80% of 80%, which is 64%.
The order of stacked discounts does not matter for the final price, since multiplication is commutative. It can matter for tax, if tax is applied between them, and for loyalty points calculated on the intermediate amount.
Working backwards from a sale price
If something costs $68 after 15% off, the original was not $68 plus 15%. The $68 represents 85% of the original, so divide: 68 / 0.85 = $80. Adding 15% to $68 gives $78.20, which is wrong by $1.80. The error grows with the discount: at 50% off, adding the percentage back understates the original by a quarter.
original = sale price / (1 − discount/100)
Percentage off versus fraction off versus BOGO
| Offer | Equivalent discount | Note |
|---|---|---|
| Buy one get one free | 50% | Only if you wanted two |
| Buy two get one free | 33.3% | Only if you wanted three |
| Buy one get one half price | 25% | Across the pair |
| Third item free | 33.3% | On three identical-priced items |
| $20 off a $80 item | 25% | Fixed amounts are worth more on cheaper items |
| Extra 20% off sale items | varies | Stacks multiplicatively with the sale price |
Buy-one-get-one is a 50% discount only if you genuinely wanted two of the thing. If you wanted one, it is a 0% discount and a 100% increase in what you spend. This is not a trick question; it is the mechanism that makes the offer profitable.
Reference pricing
A discount is only meaningful relative to a price someone actually paid. Consumer protection rules in the EU, the UK and several US states require that a crossed-out reference price be the lowest price the seller charged over a defined prior period, commonly 30 days, precisely because inflated reference prices were so widespread. If an item has been on permanent sale for six months, the discount is the price.
A worked example
A jacket listed at $220, with 30% off in the sale and a further 15% with a code, in a state with 7.5% sales tax. After the first discount: $154. After the second: $130.90. Tax adds $9.82, so you pay $140.72. The combined discount is 40.5%, not 45%, and the saving against the list price before tax is $89.10.
Frequently Asked Questions (FAQs)
How do I calculate 20% off?
Multiply the price by 0.8, which is what remains after taking 20% away. On $45 that is $36. The mental shortcut is to find 10% by moving the decimal point one place left, double it, and subtract.
Why is 20% off twice not 40% off?
Because the second discount applies to the reduced price, not the original. $100 becomes $80, then $80 becomes $64, which is 36% off. The multipliers compound: 0.8 × 0.8 = 0.64.
How do I find the original price from a sale price?
Divide by one minus the discount as a decimal. A $68 item after 15% off was originally 68 / 0.85 = $80. Adding the percentage back to the sale price always gives too low an answer.
Is a buy-one-get-one-free offer really 50% off?
Only if you wanted two. For one item it is no discount at all and double the spend. The same applies to three-for-two and similar offers, which are designed to move volume rather than to save you money.
Does the order of two discounts matter?
Not for the final price, because multiplying 0.8 by 0.7 gives the same result in either order. It can matter if tax is applied between them, or if the retailer calculates loyalty points on the intermediate figure.
What does a fixed dollar discount work out to as a percentage?
Divide the discount by the original price and multiply by 100. $15 off a $60 item is 25%; the same $15 off a $200 item is 7.5%. Fixed-amount offers are worth proportionally more on cheaper items, which is why they usually come with a minimum spend.