How a percentage discount is applied
A discount of D% means you pay (100 − D)% of the original price. Enter the Original price and the Discount (%), and the calculator multiplies the price by what is left, then shows what you pay and what you save. A 25% discount leaves 75% to pay, so a price of 80 becomes 60 and you keep 20.
Promotions often add a second reduction, such as “an extra 10% at checkout”. Put it in the optional Extra discount (%) field. It is applied after the first one, to the price that is already reduced, and the tool reports the effective discount: the single percentage that would have produced the same final price on its own.
If you already know both prices, the Sale price known section works backward from the original and sale price to the percent off. A sale price above the original is reported as a percent more instead.
Nothing here depends on the currency. The arithmetic is the same in dollars, euros, pounds, rupees or yen; only the smallest coin you round to differs.
Discount formulas
The calculator works with unrounded values and rounds only for display. A shop rounds to the smallest coin at the till, so a receipt can differ from an exact result by a fraction of a cent.
Worked examples
- Share left to pay: 1 − 0.25 = 0.75.
- Final price: 80 × 0.75 = 60.
- Saved: 80 − 60 = 20.
- First discount: 150 × 0.80 = 120.
- Extra discount on the reduced price: 120 × 0.90 = 108.
- Saved: 150 − 108 = 42, and 42 ÷ 150 = 28%.
- Difference: 49.99 − 34.99 = 15.
- Divide by the original: 15 ÷ 49.99 = 0.30006.
- Multiply by 100: 30.006%, or 30.01% to two decimals, which a shop would advertise as 30% off.
Why stacked discounts are less than their sum
The second percentage is taken from a smaller number. In the example above, the extra 10% is 10% of 120 (12), not 10% of 150 (15), so the total saving is 42 instead of 45. The order does not matter: 10% followed by 20% also ends at 28% off, because multiplication gives the same product in either order.
| First discount | Extra discount | Effective discount |
|---|---|---|
| 15% | 15% | 27.75% |
| 20% | 10% | 28% |
| 25% | 10% | 32.5% |
| 30% | 20% | 44% |
| 40% | 10% | 46% |
| 50% | 20% | 60% |
Two 50% reductions do not make an item free either: a price of 200 halved and halved again is 50, a 75% discount.
Buy one, get one 50% off
With two items at the same price, this offer works out to 25% off each. Two items at 30 cost 30 + 15 = 45 instead of 60, and 15 is a quarter of 60. If the prices differ, the terms decide which item is half price, and it makes a difference. For items at 40 and 20, halving the cheaper one means paying 40 + 10 = 50 instead of 60, only 16.67% off the pair; halving the dearer one would mean paying 20 + 20 = 40, or 33.33% off.
Rounding to the cent
Most currencies have a minor unit, such as the cent or the penny, and prices are rounded to it. A price of 19.99 at 15% off is 16.9915 exactly, which rounds to 16.99, a saving of 3.00. Rounding each item separately and rounding the basket total can give results a cent apart. Three items at 1.17 with 15% off are 0.9945 each, which rounds to 0.99, so 2.97 for the three; 15% off the total of 3.51 is 2.9835, which rounds to 2.98. The ISO 4217 currency list gives the Japanese yen no minor unit, so yen amounts round to whole yen instead.
Reference prices are not always genuine
A percent off is only as meaningful as the “was” price it starts from. In the United States, the FTC’s Guides Against Deceptive Pricing (16 CFR 233.1) say a former price is a legitimate basis for a comparison when it is the actual, bona fide price at which the article was offered to the public on a regular basis for a reasonably substantial period of time. In England, Scotland and Wales, the Guidance for Traders on Pricing Practices, originally produced by the Chartered Trading Standards Institute and published on Business Companion, covers the same ground in its section on reference prices. The calculator can confirm the arithmetic of an offer; it cannot tell whether the starting price was real.
Where discount sums go wrong
- Adding stacked discounts. 20% and then 10% is 28% off, not 30%. Use the extra discount field to get the exact figure.
- Measuring the saving against the sale price. From 49.99 to 34.99, the 15 saved is 30.01% of the original. Dividing by 34.99 instead gives 42.87%, which overstates the deal.
- Undoing a discount by adding the percent back. A price of 60 after 25% off came from 80, but 60 plus 25% is only 75. The reverse percentage calculator finds the true original.
- Comparing offers by percent alone. 30% off an item that costs more per kilogram or per liter can still be the worse buy, which a unit price comparison shows.
Advertised percentages are usually rounded to a whole number. When the exact figure matters, type the original and the sale price into Sale price known.
Sources
- 16 CFR Part 233, Guides Against Deceptive Pricing, Electronic Code of Federal Regulations (US Federal Trade Commission rules).
- Guidance for Traders on Pricing Practices, Chartered Trading Standards Institute, Business Companion (UK).
- ISO 4217 currency code list (List One, with minor units), SIX, ISO 4217 Maintenance Agency.