Percent Off Calculator

Money taken off ＝ list price × percent off ÷ 100　｜　Price to pay ＝ list price − money taken off

listPrice

The price before the discount. Both money rows are derived from it, which is why a price of zero is refused: it would produce a panel of zeroes rather than an answer

percentOff

The reduction, as a percentage of the original price. One rate, not two: the page is about what a single discount comes to, and a second reduction on top is a different page

savings

The money the discount takes off. It is the main figure here, rounded to the cent before anything else is computed from it

finalPrice

What is left to pay, taken as the original price minus the money saved rather than as the original price times the remaining share

percentPaid

The share of the original price you still pay. It is the complement of the rate you entered — thirty percent off means seventy percent paid — rather than a figure derived back out of the two money rows

Use this calculator when a single reduction is quoted and you want the money: a sale tag that gives a rate and no price, a coupon expressed as a percentage, a comparison between two offers quoted in different units. Use the stacked-discount page when a second reduction applies on top of the first, because a single rate cannot express two.

1. Default case: 30 percent off 80

   1. Money taken off: 80 × 30 ÷ 100 ＝ 24.00
   2. Price to pay: 80.00 − 24.00 ＝ 56.00
   3. Share paid: 100 − 30 ＝ 70.00%

   Thirty percent off eighty is the cleanest way into the page, because both halves of the phrase are round numbers: 24.00 comes off, 56.00 is left, and the share paid reads 70. That last row is the point of the page as much as the money is — a tag saying thirty percent off and a tag saying seventy percent of the price are the same offer, and the panel makes that visible in one glance.

2. A price with cents: 15 percent off 129.99

   1. Money taken off: 129.99 × 15 ÷ 100 ＝ 19.4985, rounded to two decimals ＝ 19.50
   2. Price to pay: 129.99 − 19.50 ＝ 110.49
   3. Share paid: 100 − 15 ＝ 85.00%

   The price row here is a subtraction rather than a multiplication, and this example is where the difference can be seen. Computing what is left directly would give 129.99 × 0.85 ＝ 110.4915, which also rounds to 110.49 — the two agree here, and the page still uses the subtraction, because the two rows have to add up on screen and only one of the two conventions guarantees that every time.

3. A small rate on a small price: 5 percent off 40

   1. Money taken off: 40 × 5 ÷ 100 ＝ 2.00
   2. Price to pay: 40.00 − 2.00 ＝ 38.00
   3. Share paid: 100 − 5 ＝ 95.00%

   Small rates are where the complement row earns its place, because five percent off is not a number most people can turn into ninety-five percent paid without pausing. Nothing changes in the arithmetic at the shallow end of the range; what changes is that the panel is now saying something the price tag did not.

4. Where the order of rounding is visible: 50 percent off 0.05

   1. Money taken off: 0.05 × 50 ÷ 100 ＝ 0.025, rounded to two decimals ＝ 0.03
   2. Price to pay: 0.05 − 0.03 ＝ 0.02
   3. Share paid: 100 − 50 ＝ 50.00%

   Half of five cents is two and a half cents, which has to land somewhere, and rounding it up to three means the two rows no longer halve exactly. Computing the price to pay directly would give 0.025 as well, which also rounds to 0.03 — and that would print 0.03 taken off and 0.03 left to pay out of a 0.05 price, an addition that does not close. The page takes the saving first so that the pair adds back up, and the cost is that the discount looks slightly deeper than half.

5. The smallest price the field accepts, at half off

   1. Money taken off: 0.01 × 50 ÷ 100 ＝ 0.005, rounded to two decimals ＝ 0.01
   2. Price to pay: 0.01 − 0.01 ＝ 0.00
   3. Share paid: 100 − 50 ＝ 50.00%

   One cent at half price is free, because half a cent is not a price and rounding it up takes the whole thing. This is the case that shows why the share paid is a complement rather than a figure derived from the money: working it out from the two rows would give a payment of zero percent beside a reduction of fifty percent, and a panel that says half off and nothing to pay looks broken. The complement is the honest answer to the question the row is asking, which is what the discount is called rather than what the cents came to.

The two money rows are rounded so that they add up on screen, and that convention has a visible cost at the bottom of the range. The money taken off is rounded to the cent first and the price to pay is then the original price minus that figure, rather than being computed from the remaining share. On a price of five cents at half off, this gives three cents off and two cents to pay; computing what is left directly also gives three cents, which would leave a panel reading three off and three left out of five. The page picks the version that closes the addition. The share paid is a different kind of row: it is the complement of the rate you typed rather than a number worked back out of the money, so it stays consistent with the input even when rounding has moved the cents. On the smallest price the page accepts, half off leaves the price at zero and reports one cent saved — half of one cent is not a price, and a price cannot go below its smallest unit. Nothing here asks whether the original price was real, and this page has no second source to check it against. The original price is a number you type in, and a reduction from a price that was never charged is a reduction from nothing; in the United States the Federal Trade Commission's guides against deceptive pricing address that question, two sections of which are cited below, and they are about what a seller may advertise rather than about arithmetic. Everything is a gross figure with no currency attached, since the arithmetic is the same in all of them, and no tax is modelled: a sales tax applies to what is left after the discount, not to the original price, which is why the price row here is not a final total. One rate, one price, no stacking — a second reduction on top of the first is the page this one sits beside, and putting a second rate here would silently compute a smaller reduction than the offer describes.

Is 30 percent off the same as 70 percent of the price?

Yes, and the page prints both so that the two ways of saying it can be compared without arithmetic. A reduction of thirty percent leaves seventy percent of the original price to pay, so a tag written either way describes the same offer: on a price of 80 that is 24.00 off and 56.00 to pay. Shops choose between the two phrasings for effect — a large reduction reads better as a percentage off, a small one reads better as a percentage paid — and the panel makes the translation for you rather than leaving it as something to work out.

Why is the money saved rounded before the price to pay is worked out?

So that the two rows add up. The saved amount is rounded to the cent first, and the price to pay is the original price minus that figure, which means the pair always closes on screen: saved plus paid equals the original price, exactly, on the printed numbers. Computing what is left directly from the remaining share is arithmetically equivalent and can differ by a cent, because it rounds a different quantity — on a price of five cents at half off it would print three cents off and three cents left to pay out of five.

Why does the share paid not match the money rows on a small price?

Because it is the complement of the rate you entered rather than a figure derived from the money. Thirty percent off means seventy percent paid, always, and the row says so regardless of what rounding did to the cents. Working the share out from the money rows instead would break down at the bottom of the range: on a price of one cent at half off, the price to pay rounds to zero, and that calculation would print a reduction of fifty percent beside a payment of zero percent. The question that row answers is what the discount is called, not what the cents came to.

Why does half off a price of one cent make it free?

Because half of one cent is not a price and has to round to something. A hundredth of a unit discounted by half is half a hundredth, which rounds back up to a hundredth — the whole of it — leaving nothing to pay. The page cannot print a price below its smallest unit, so its deepest discount on its smallest price is everything. This is the same rounding that makes the two rows add up everywhere else, and it is the floor of the arithmetic rather than an error in it.

Does the page apply sales tax?

No, and the price row is not a final total. A sales tax applies to what is left after the discount rather than to the original price, so on a discounted purchase the tax is computed on the smaller figure and a tax calculation has to be run after this one rather than before it. Everything here is gross, no currency is attached, and nothing is modelled for shipping, fees or anything else added at the till. If you need the amount that actually leaves your account, take the price row from here and put it into a sales tax calculation.

Can I enter two discounts here?

No, and the field is one rate by design rather than by omission. Two sequential reductions are not the same as one, because the second comes off the price the first one left rather than off the original, so entering only the first rate would understate the saving and entering their sum would overstate it. There is a page beside this one for exactly that case, and it prints the price after each step so the difference between the combined rate and the sum of the two rates can be read off the panel.

• 16 CFR §233.1 — Former price comparisons: a reduction is a genuine bargain only where the former price was the actual, bona fide price the article was offered at on a regular basis, and an artificial inflated price set up to enable a later large reduction makes the advertised bargain a false one — Legal Information Institute, Cornell Law School (United States)
• 16 CFR §233.5 — Miscellaneous price comparisons: the variants of bargain advertising beyond the common forms are controlled by the same general principles, and advertisers should make certain that the bargain offer is genuine and truthful — Legal Information Institute, Cornell Law School (United States)