Percent Off Calculator: Discount, Sale Price and Savings

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How to use this discount calculator

Put in the original price and the percent off. You get the sale price, the money saved and the total for however many you are buying. That covers the common case in one step.

The mode selector handles the other three questions people actually have. If you know the original and the sale price, it tells you what percentage the discount was. If you know the sale price and the percentage, it works back to the original. And if the sign says an amount off rather than a percentage, it converts that into a percentage so you can compare offers properly.

The extra percent off box is for the take a further 20 percent at the till offers. It stacks the second markdown correctly, which is not what the signs imply, and the section below explains why.

Why 30 percent off plus an extra 20 is not 50 percent off

This is the single most useful thing on the page. Stacked discounts multiply, they do not add.

Take a 100 item at 30 percent off. It is now 70. The extra 20 percent comes off that 70, not off the original 100, so it takes 14 rather than 20. You pay 56. That is 44 percent off in total, not 50. The sign has promised six points more than it delivers.

The rule is to multiply what is left rather than add what is taken. Thirty percent off leaves 0.7 of the price and twenty percent off leaves 0.8, so together they leave 0.7 times 0.8, which is 0.56. Subtract from one and you have 44 percent off.

The effect gets stranger at the deep end. Fifty percent off followed by another fifty percent off is 75 percent off, not 100. You never get anything free by halving repeatedly, you just get closer and closer. And three separate 20 percent discounts come to 48.8 percent rather than 60.

One small consolation: the order does not matter. Thirty then twenty gives exactly the same price as twenty then thirty, because multiplication does not care about sequence.

What multi buy offers are actually worth

Buy one get one free sounds like a hundred percent off the second item, and it is, but you are paying full price for the first. Averaged across both, it is 50 percent off.

Buy two get one free is 33.3 percent off, buy three get one free is 25 percent, and buy one get one half price is only 25 percent off despite sounding much better than that. The table in the tool lays all of these out so a shelf full of competing offers can be compared on one scale.

A worked check you can repeat on paper

Take 40 percent off 100. Ten percent of 100 is 10, so 40 percent is 40. Take it off and you pay 60. The tool agrees.

Now something less round. Twenty five percent off 89.99. A quarter of 89.99 is 22.4975, so you pay 67.4925, which rounds to 67.49. Checking backwards, 67.49 divided by 89.99 is 0.75, confirming a quarter off.

Now the reverse question. You see 75 on a tag marked 70 percent off and want the original. Seventy percent off leaves 30 percent, so 75 is 0.3 of the original. Divide 75 by 0.3 and the original was 250.

Finally with tax. Forty percent off 100 gives 60, and 15 percent tax on that discounted 60 is 9, for a total of 69. Tax is always charged on what you actually pay, never on the ticket price, which is worth knowing because it means a discount saves you the tax on the discounted portion too.

Mistakes that catch people out

Adding stacked discounts together. Thirty and twenty is forty four, not fifty. Any sign offering an extra percentage off an already reduced price is quietly delivering less than the arithmetic suggests.

Adding a discount and a tax rate. Twenty percent off followed by twenty percent tax does not return you to the original price. It leaves you at 96 percent of it, because the tax is charged on the smaller number.

Comparing an amount off against a percentage. Twenty off is a 25 percent discount on an 80 item and a 40 percent discount on a 50 one. The amount alone tells you nothing about which offer is better.

Reading buy one get one half price as half off. It is 25 percent off across the two items. The word half is doing a lot of work in that sign.

Working the reverse the wrong way. To find the original price from a sale price, divide rather than multiply. A price 20 percent off is not the sale price plus 20 percent, it is the sale price divided by 0.8, and those give different answers.

Percent off calculators for every discount

The discount rates people search for most, each opening the calculator ready to go with its own address.

By discount percentage

Discount on a specific price

How this was checked

The straightforward cases were checked by hand: 40 percent off 100 gives 60, 25 percent off 89.99 gives 67.49, and 70 percent off 249.99 gives 75.00. The reverse directions were checked against the same numbers, so that 100 down to 60 reports 40 percent and 75 at 70 percent off reports an original of 250.

The stacking maths was verified two ways. Applying the discounts one after another to a real price gave the same answer as the closed formula, which is one minus the product of what each discount leaves. Thirty then twenty came to 44.0 percent on both routes, two fifties came to exactly 75, and three twenties came to 48.8. Reversing the order was also checked and produces an identical figure, as multiplication requires.

Round tripping was checked separately: taking a discount off a price and then working backwards from the sale price returns the original to the cent. The multi buy figures were derived from first principles rather than assumed, giving 50 percent for buy one get one free, 33.33 for buy two get one, 25 for buy three get one, and 25 again for buy one get one half price.

Related Calculators and Reference

• Discount and Sales Tax Calculator for the sales tax side in more depth, including working backwards from a taxed total to the price before tax.
• Percentage Calculator for percentage change, difference and error rather than discounts.
• Markup and Margin Calculator for the seller's side, and why a 50 percent markup is not a 50 percent margin.
• Unit Price Comparison Calculator for comparing a discounted large pack against a full price small one.
• Tip Calculator for the other percentage that gets added at the till.