Percent Off Calculator

Percent off in one line

Percent off is a subtraction dressed up as a multiplication. The saving is the price times the percent written as a decimal, and the sale price is what is left.

• Saving = price x percent / 100
• Sale price = price - saving
• One step version: sale price = price x (1 - percent / 100)

A $120 jacket at 30 percent off saves 120 x 0.30 = 36 dollars and sells for 120 - 36 = 84 dollars. The one step version gives 120 x 0.70 = 84 and lands on the same place, which is why cashiers can ring up a discount as a single multiplier.

Watch the wording, because 30 percent off and 30 percent of are not the same thing even though the arithmetic step looks identical. Thirty percent of $120 is $36, and thirty percent off $120 also takes $36 away. One number describes a slice of the price, the other describes how much of the price is removed. A tag that says 30 percent more means the price rises by $36, not that it falls.

Percent off always applies to the price in front of you, which matters when a second discount follows. Each discount takes its bite out of the reduced price, not the original one, and that is where the numbers on a receipt start to surprise people.

Worked example: a $120 jacket at 30 percent off

Start with the tag price and walk through the register in order: discount first, sales tax second, because every state that charges sales tax applies it to the amount paid.

• Tag price: $120.00
• Saving: 120 x 0.30 = $36.00
• Sale price: 120 - 36 = $84.00
• Sales tax at a 7 percent local rate: 84 x 0.07 = $5.88
• Total at the register: 84 + 5.88 = $89.88

Sixty four cents of that total is tax on money the shopper never spent. Charging the 7 percent on the tag price instead would add 120 x 0.07 = $8.40, which is $2.52 more than the law allows in that example. The order of operations is not a math nicety: it is the difference between the right total and a wrong one.

Rounding is the other place cents appear or vanish. A $19.99 item at 15 percent off gives 19.99 x 0.15 = 2.9985, so the saving is $3.00 and the price is $16.99. A store that truncates instead of rounding shows a saving of $2.99 and a price of $17.00. Both are defensible, and neither is wrong by a penny in a way that matters, but a shopper checking a receipt should expect the cent to land on one side or the other.

Percent off also hides a base rate when the starting price is inflated. A jacket marked down from $199 to $129 has come down by 70 dollars, which is 70 / 199 = 35.2 percent. That is a real reduction, and it is nowhere near the 50 percent the sign might imply if the tag was $258 last week and $199 the week before.

The percent off grid

Most discounts people meet are round numbers, so the table below covers the range in one place. Read across a row for the same price at different discounts, or down a column for the same discount at different prices.

The columns show why 25 percent and 30 percent feel close but are not interchangeable on a big ticket. On $100 the gap is $5, and on a $600 appliance it is $30. A quarter off is easy to check in the head because half of a half is a quarter: half of $80 is $40, half of that is $20, and 80 - 20 = $60.

Ten percent is the anchor for everything else. A tenth of the price is one digit shifted left, so 10 percent of $84 is $8.40. From there, 20 percent doubles it, 5 percent halves it, and 15 percent adds the two pieces together.

Does the discount change which pack wins

Two jars of the same coffee sit on a shelf. The 24 ounce jar is $8.99 with 25 percent off, and the 40 ounce jar is $13.49 at full price. The sale tag makes the small jar look like the bargain, and the unit price says whether it is.

• 24 ounce jar: 8.99 x 0.75 = 6.74, then 6.74 / 24 = 0.281, or 28.1 cents an ounce
• 40 ounce jar: 13.49 / 40 = 0.337, or 33.7 cents an ounce
• Gap: 33.7 - 28.1 = 5.6 cents an ounce in favor of the discounted small jar

The discount flips the ranking here, and it does not always. Push the 40 ounce jar to $11.99 and its unit price falls to 30.0 cents, close enough that a 15 percent coupon on a third size can take the lead again. The only way to know is to divide the discounted price by the size, every time.

The NIST Handbook 130 unit pricing regulation exists because this comparison is hard to do at a shelf. It asks stores that post unit prices to use the same unit for similar goods, so the number next to the price means the same thing on both jars. Where a store does not post it, the division is yours to do, and a phone calculator is the honest tool for the job.

One caution on size: a bigger box is not always a bigger amount of product. Cereal, detergent and chips all sell air as part of the package, and the net weight on the front is the only number worth dividing by.

Mental math in three moves

Most percent off questions can be answered without a calculator once the tenth is automatic. Three moves cover the discounts that show up on tags and coupon apps.

• Move one, the tenth. Shift the decimal one place left. Ten percent of $48 is $4.80, and 10 percent of $6.99 is $0.70.
• Move two, build from the tenth. Twenty percent is double the tenth, so $9.60 off $48. Five percent is half the tenth, so $2.40. Fifteen percent is the tenth plus the half tenth, so 4.80 + 2.40 = $7.20.
• Move three, subtract or multiply. 48 - 7.20 = $40.80 at 15 percent off, and 48 x 0.85 = $40.80 checks it.

Thirty percent is three tenths, which is 3 x 4.80 = $14.40 off $48, leaving $33.60. Forty percent is four tenths, and 50 percent is half, which is the easiest of all: $24 on a $48 item.

Two discounts in a row do not add. Thirty percent off then another 20 percent off the reduced price gives 0.70 x 0.80 = 0.56, so the shopper pays 56 percent of the tag and saves 44 percent, not 50. The gap grows with the size of the discounts: 50 percent plus 50 percent is 75 percent off in total, because 0.5 x 0.5 = 0.25.

The reverse question comes up just as often. A price that falls 20 percent has to rise 25 percent to return to where it started, since 1 / 0.80 = 1.25. That asymmetry is why a stock that drops 50 percent needs a 100 percent gain to break even, and why a store can cut prices 20 percent and still call the next 20 percent increase a return to normal.

Where percent off gets slippery

Four things turn a simple discount into a misleading one, and all four are common enough that shoppers meet them weekly.

The base price. A discount is only as honest as the number it comes off. The FTC guides against deceptive pricing in 16 CFR Part 233 say a former price has to be the actual price the item sold at for a substantial period, not a number invented to make the later markdown look large. A tag that reads was $199, now $129 is a 35.2 percent cut if $199 was real, and a fiction if it was not.

The word up to. Up to 70 percent off means at least one item in the store is 70 percent off. It says nothing about the item in your hand, which may be 10 percent off or full price. Treat the sign as advertising, then read the actual ticket.

The second discount. An extra 20 percent off already reduced merchandise applies to the reduced price, not the original, so a 30 percent markdown plus an extra 20 percent is 44 percent off in total. This is the single most common place where a shopper's estimate runs higher than the receipt.

The coupon that is not a percent. A $10 coupon on a $40 item is 25 percent off, and the same coupon on an $80 item is 12.5 percent off. Percent off and dollars off stop being comparable as soon as the price changes, which is why the discount calculator handles the dollar side of that question.

Sales tax sits outside all of this. A discount reduces the taxable amount, so tax is charged on the sale price, never on the tag price, in every state that charges sales tax on goods.

What you pay at the register

The register total has three parts: the reduced price, the tax on that reduced price, and any rounding the store applies. Working the three in order gives the number on the screen.

The headphones show rounding in action. 79.99 x 0.20 = 15.998, so the saving is $16.00 and the price is $63.99. Tax on that is 63.99 x 0.07 = 4.4793, which rounds to $4.48, and the total lands at $68.47. A receipt that shows $68.46 or $68.48 is not necessarily wrong, because stores differ on whether they round each line or the sum.

Buy one get one free is a percent off in disguise. Two items for the price of one is 50 percent off per item when both are used, and 0 percent off if the second item sits in a closet. The same trap applies to a 30 percent discount on a second item: the effective saving on the pair is 15 percent, not 30, and only if the second item costs the same as the first.

None of this replaces the store's own policy on returns, price adjustments or exclusions, so keep the receipt until the item is home and the discount has had a chance to be checked against the bank statement.