Sale Price Calculator

The sale price formula

A discount is a share of the original price, so the sale price is whatever is left after that share is removed. One line covers every percentage discount you will meet:

• Sale price = original price x (1 - discount / 100)
• Money saved = original price x discount / 100
• Discount percent = money saved / original price x 100

The decimal form is the fast way to do it in your head. Ten percent off means multiply by 0.9. Twenty five percent off means multiply by 0.75. Fifty percent off means multiply by 0.5, which is the same as halving the price. Once you know the multiplier, the discount rate stops mattering and the arithmetic becomes one multiplication.

Percentages are reversible, which is a useful trick at the shelf. Thirty percent of $80 is the same as 80 percent of $30, and the second is easier to work out. The same rule applies to the discount: 15 percent of $60 equals 60 percent of $15, which is $9.

Worked example: $80 at 30 percent off

An $80 item with a 30 percent discount.

• Multiplier: 1 - 0.30 = 0.70
• Sale price: 80 x 0.7 = $56.00
• Money saved: 80 x 0.3 = $24.00
• Check: 56 + 24 = $80.00

The check matters. A discount is easy to apply and easy to misapply, and adding the sale price and the saving back together catches most slips in a second.

Now add the second discount that shows up on the same tag, the extra 20 percent off at the register.

• Second multiplier: 1 - 0.20 = 0.80
• New price: 56 x 0.8 = $44.80
• Total saved: 80 - 44.80 = $35.20
• Effective discount: 35.20 / 80 x 100 = 44 percent

Two discounts of 30 and 20 percent produced 44 percent off, not 50. The second discount was applied to $56 rather than to $80, so it removed $11.20 instead of $16. That gap is the reason stacked offers feel better than they are, and the reason the arithmetic has to be done in order.

Stacked discounts do not add up

When a store takes a percentage off a price that is already reduced, multiply the two multipliers. The result is always smaller than the sum of the two discounts.

The last row is the one that surprises people. Half off, then half off again, is 75 percent off, not free. The second half is taken from the half that is left, so a quarter of the original price survives. On $100 that is $25.

The order does not change the result. Thirty percent then 20 percent gives the same 44 percent as 20 percent then 30 percent, because multiplication does not care about order. What does change the result is a discount that is fixed in dollars rather than percent: a $10 coupon applied before a 20 percent discount removes more money than the same coupon applied after.

Common discounts on $80 and $120

The same rates on two common price points, so you can check a tag against a number you already know.

Two anchors are worth memorizing. A 25 percent discount takes a quarter off, so the price drops by a quarter. A 70 percent discount leaves 30 percent of the price, which on $80 is $24. Those two cover a large share of retail tags, and both can be done without a calculator.

Watch the difference between a discount on the item and a discount on the order. A 20 percent off one item coupon does not touch the other items in the cart, while 20 percent off the order applies to all of them and usually has a higher value.

Sales tax lands on the sale price

Sales tax is charged on what you pay for the item, so it comes after the discount. Taking the example through the register: $80 at 30 percent off is $56, with an extra 20 percent off it is $44.80, and at 8 percent tax the total is 44.80 x 1.08 = $48.38.

• Sale price: $44.80
• Tax at 8 percent: $3.58
• Total at the register: $48.38

Applying the tax to the original $80 would give $52.80, which overstates the bill by $4.42. The order of operations is discount first, tax second, and that order is set by state law rather than by the store.

Coupons and rebates complicate it slightly. A store coupon usually reduces the taxable price. A manufacturer rebate paid after the purchase does not, so the tax is charged on the full amount and the rebate arrives separately. A few states tax the pre-discount price on certain promotions, which is worth checking if the total looks off. The IRS directory of state government websites links to each state's rules.

Working backwards: what was the original price

Going from a sale price back to the original is the same formula solved the other way. Divide by the multiplier instead of multiplying.

A jacket marked $56 after 30 percent off: 56 / 0.7 = $80.00. The common mistake is to add 30 percent to the sale price, which gives 56 x 1.3 = $72.80. That answer is wrong because the 30 percent was taken from $80, not from $56. Adding 30 percent to $56 only adds $16.80, while the real discount was $24.

The size of the error grows with the discount. At 50 percent off, a $50 sale price comes from $100, while adding 50 percent gives the right answer by luck, because 0.5 and 2 are reciprocal. At 75 percent off, a $25 sale price comes from $100, while adding 75 percent gives $43.75, which is off by more than half.

Use the reverse direction to judge a claim. If a store advertises 60 percent off and the tag says $40, the implied original price is 40 / 0.4 = $100. If that item never sold for $100, the discount is a story rather than a saving.

Is the discount real

A percentage is only as good as the price it is applied to. The FTC guide to advertising claims says price comparisons and sale claims must be truthful, and a former price has to be one the item genuinely sold at, not a number invented for the tag.

Three checks do most of the work:

• Compare the unit price. Cost per ounce, per pound or per item is the only fair comparison between sizes and brands. A 30 percent discount on a large box can still be dearer per ounce than a small box at full price.
• Check the terms. The FTC online shopping guidance points out that sale and clearance items often carry different return policies, so a discount can cost you the right to send it back.
• Check the shipping and fees. Free shipping thresholds change the real discount. A $44.80 cart that needs $5.20 more to reach free shipping is a $50 purchase, and the 44 percent saving shrinks to about 37 percent if the extra item is something you did not want.

None of this means discounts are fake. It means the number on the tag is a starting point. The price you pay after tax, shipping and returns is the one that decides whether the deal was worth taking.