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Discount Calculator (Sale Price and Percent Saved)

Sale price from a percentage off, or the percent saved from an original and a sale price.

Inputs

Sale price
91

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What each Discount input means

Find
Sale price from a percentage off, or the percentage off from the original and sale prices — the question to ask of a 'was/now' price tag.
Original price
The price before the discount: the 'was' or list price.
Discount
The percentage off, from 0 to 100. For two discounts in a row, run the page twice: the first sale price becomes the second original.
Sale price (for % saved)
In '% saved' mode, the price you would pay now. It must be between 0 and the original price.

Discount formula

discount = original × rate · sale price = original − discount · percent saved = (original − sale price) ÷ original × 100

sale=P(1−r)r=P−saleP\text{sale} = P(1 - r) \qquad r = \frac{P - \text{sale}}{P}

A percentage discount is a fraction of the original price taken off it. Multiply the original by the rate to get the amount saved, and subtract it for the sale price — or, in one step, multiply the original by (100% − rate): 35% off means you pay 65%. The reverse question, what percent off a marked-down price represents, is the saving divided by the original price, not by the sale price; a {{$140}} item reduced to {{$91}} is 35% off because {{$49}} is 35% of {{$140}}. Both directions are on this page.

Discount worked example

A $140 dress marked 35% off: the discount is $140 × 0.35 = $49, and the sale price is $140 − $49 = $91. The same answer comes from paying 65%: $140 × 0.65 = $91. Run backwards, an item that was $140 and is now $91 is ($140 − $91) ÷ $140 = 35% off.

More Discount examples

A $2,999 laptop at 20% off: 2,999 × 0.20 = 599.80 off, so the sale price is 2,399.20 before tax.

A jacket that was $80 and is now $60: the saving is $20, and $20 ÷ $80 = 25% off. Measured against the sale price instead, the same $20 would look like 33%, which is the mistake to avoid.

Where the Discount calculator can give the wrong answer

  • Percent saved is always measured against the original price. Dividing the saving by the sale price instead gives a bigger, wrong number — {{$49}} ÷ {{$91}} is 54%, and the dress is not 54% off.
  • Two discounts do not add. 20% off and then a further 10% off is 28% off in total, because the second 10% is taken from the already-reduced price: pay 80%, then 90% of that, is 72%.
  • Sales tax is usually added after the discount, so a 35% discount on a taxed item leaves the tax on {{$91}}, not on {{$140}}. Use the sales tax calculator on the result.
  • A '35% off' badge on an original price that was itself raised the week before is still 35% off that number. The page cannot see what the price was last month.
  • Discounts above 100% are refused; a 100% discount is free.

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Discount reference table

Two discounts in a row: the total discount is less than the sum
First discountThen a furtherTotal discountYou pay
20%10%28%72%
20%20%36%64%
25%10%32.5%67.5%
30%20%44%56%
40%10%46%54%
50%20%60%40%
50%50%75%25%
Source: Arithmetic: you pay (1 − first) × (1 − second) of the original, so the total discount is 1 minus that

Discount FAQ

Multiply the original price by the percentage as a decimal to get the saving, then subtract it: 35% off {{$140}} is {{$140}} × 0.35 = {{$49}} off, {{$91}} to pay. Quicker: multiply by what you pay, 100% − 35% = 65%, so {{$140}} × 0.65 = {{$91}}.