Stacked percentages multiply
Thirty percent off leaves 70 percent of the price. Taking another 10 percent off that leaves 90 percent of 70 percent, which is 63 percent. You paid 63 and saved 37, not 40. The general form is that two discounts of a and b combine to a + b minus ab/100. For 30 and 10 that is 40 minus 3, so 37. The larger the two percentages, the wider the gap: 50 and 50 stacked is 75 percent off, not 100.
| Advertised | Added up | Actually | On $100 |
|---|---|---|---|
| 20% + 10% | 30% | 28% | $72.00 |
| 30% + 10% | 40% | 37% | $63.00 |
| 40% + 20% | 60% | 52% | $48.00 |
| 50% + 50% | 100% | 75% | $25.00 |
A phrase like "up to 60 percent off" on a rack marked 40 plus an extra 20 is using the added figure. It is not necessarily false, but it is not the price you will pay.
Flat coupons behave differently
A percentage is scale-free: 20 percent off is 20 percent off whether the item is $10 or $1,000. A flat $10 coupon is a 50 percent discount on a $20 item and a 1 percent discount on a $1,000 one. That is why stores cap them with a minimum spend, and why the usual advice to apply a flat coupon to the cheapest qualifying basket is arithmetic rather than a trick.
Order of operations matters for flat coupons in a way it does not for percentages. Two percentages give the same answer in either order. A flat amount taken before a 30 percent markdown is worth only 70 percent of its face value, because the markdown then shrinks it too. This calculator applies the flat amount last, which is the more common checkout behaviour and the more favourable one, and it tells you what the other order would be worth.
Working the discount backwards
Fill in the sale price field and the calculator solves for the percentage instead. An item listed at $89 and selling at $59 is (89 minus 59) divided by 89, or 33.7 percent off. This is the useful direction when a tag shows two prices and no percentage, and it is also how to check whether a "50 percent off" sign matches what the register charges.
Multi-buy offers need a per-unit view
Buy one get one free is 50 percent off only if you wanted two. If you wanted one, it is not a discount at all, and the second unit is a cost rather than a saving. Three for two is 33.3 percent off per unit; three for the price of two and a half is 16.7 percent. The comparison that holds is the unit price at the quantity you would actually have bought, and that is a different figure from the one on the sign whenever the offer requires buying more than you need.
Questions people ask
Why is 30% plus 10% not 40% off?
Because the second percentage is taken from the already-reduced price, not from the list price. After 30 percent off, $89 becomes $62.30. Ten percent of $62.30 is $6.23, not the $8.90 that ten percent of the original would be. The final price is $56.07, which is 37 percent below $89. The shortcut for two stacked discounts is a + b minus (a x b)/100, and it always comes out below the sum.
Should a flat coupon go before or after the percentage discount?
After, from your point of view, and that is the order this calculator uses. A $10 coupon applied after a 30 percent markdown takes the full $10 off. Applied before it, the markdown then reduces the coupon effect to $7. Most checkouts apply store-wide markdowns first and coupon codes second, but not all, and stacking rules vary by retailer. If it matters, put the item in the cart and read the total rather than trusting either the sign or this page.
Does the discount reduce sales tax too?
In the United States, tax is generally charged on the price actually paid, so a store discount reduces the taxable amount and the tax with it. Manufacturer coupons are treated differently in a number of states, where tax may be calculated on the pre-coupon price because the retailer is reimbursed. The rules are set at state and sometimes local level. This calculator does not include tax at all, so the figure it gives is the pre-tax price.
What is a fair way to compare two offers?
Convert both to the final price for the quantity you would buy anyway, then compare those two numbers. Percentages, loyalty points, cashback rates and free shipping thresholds are not comparable in their advertised forms, and any of them can be made to look larger by changing what it is a percentage of. If one offer requires buying more units than you need, count the surplus at full cost, not at zero.