Find the final price and your savings after a discount.
Enter an original price and a discount percentage and the tool returns the amount you save and the price you actually pay. The arithmetic is simple, but discounts are one of the most reliably misread numbers in retail, and the sections below cover the cases where intuition gets it wrong.
The second form of the final-price line is worth remembering, because it is what makes stacked discounts tractable. A 25% discount means you pay 75% of the price, so multiplying by 0.75 gets you there in one step.
A jacket is listed at 4,500 with 35% off.
This is the single most common error. An extra 10% off an item already reduced by 20% is not 30% off. The second discount applies to the already-reduced price, not the original.
Take a 1,000 item. Twenty percent off brings it to 800. A further 10% off that is 80, not 100, so you pay 720. The combined discount is 28%, not 30%. In general, multiply the remaining fractions together:
The gap widens as the discounts get bigger. Fifty percent off plus another 50% off is not free — it is 75% off, because half of a half is a quarter. This is why "50% + 20% extra" is advertised the way it is rather than as "70% off": the true figure is 60%.
| Advertised | Sum of the two | Actual combined discount |
|---|---|---|
| 20% + 10% | 30% | 28% |
| 30% + 20% | 50% | 44% |
| 50% + 20% | 70% | 60% |
| 50% + 50% | 100% | 75% |
| 70% + 30% | 100% | 79% |
The order the discounts are applied in does not change the result — multiplication commutes — so a shop applying the larger one first is not shortchanging you. What does change the result is whether a discount applies before or after tax, and whether a fixed-amount coupon is applied before or after a percentage one. A fixed coupon is worth more when applied after the percentage discount is nowhere near true — it is worth more when applied before a percentage discount only from the shop's perspective. For you, take the percentage first, then the fixed amount: 20% off 1,000 then minus 100 leaves 700, whereas minus 100 then 20% off leaves 720.
Two reverse calculations come up often. To find the original price when you know the sale price and the discount, divide rather than multiply — adding the percentage back on is wrong. An item costing 780 after 35% off was originally 780 / 0.65 = 1,200, not 780 x 1.35 = 1,053.
To find what percentage a discount represents, divide the saving by the original price:
A price cut from 2,400 to 1,800 is a saving of 600, so 600 / 2,400 = 25% off.
A shop that marks a product up by 50% and later discounts it by 50% does not return to cost. Marking 100 up by 50% gives 150; taking 50% off 150 gives 75, which is below where it started. This asymmetry is why "was 200, now 100" and "50% off" describe the same thing, but "50% markup" and "50% discount" do not cancel.
The percentage is only meaningful relative to an honest reference price. A few things worth checking before treating a big number as a bargain: whether the "was" price was ever actually charged for a sustained period; whether the same item is cheaper elsewhere at full price; whether the discount applies to the item you want or only to sizes and colours nobody chose; and whether shipping, which is rarely discounted, erases the saving on a low-value order. Several jurisdictions now require that an advertised reference price be the lowest price charged in the preceding 30 days, precisely because inflated "before" prices were so common.
Because the second discount is calculated on the already-reduced price. On 1,000, the first discount removes 200, leaving 800; the second removes 10% of 800, which is 80 rather than 100. You pay 720, a combined 28%.
Divide the sale price by one minus the discount as a decimal. For 30% off, divide by 0.70. Adding 30% back on to the sale price gives a number that is too low.
In most systems the discount is applied to the pre-tax price and tax is then charged on the reduced amount, so a discount also reduces the tax you pay. Enter the pre-tax price to match how the till will calculate it.
You are better off when the percentage is applied first and the fixed amount is subtracted from the result. Most checkouts apply them in a fixed order you cannot change, but it is worth checking which order yours uses on a large order.
They do not cancel out. A 50% markup on 100 gives 150, and a 50% discount on 150 gives 75. Markup is calculated on cost, discount on the selling price, so the same percentage refers to different bases.