How to Calculate Discounts (And Spot a Bad One)
A discount is a percentage off, and the quickest way to calculate it is to work out what you are paying rather than what you are saving. The Discount Calculator does both.
Multiply, do not subtract
A 30 per cent discount means you pay 70 per cent. So multiply the price by 0.7 and you have the answer in one step, rather than calculating 30 per cent and then subtracting it.
The mental shortcuts worth having: 10 per cent is moving the decimal point one place. 20 per cent is that doubled. 25 per cent is a quarter, so halve it twice. 33 per cent is roughly a third. 50 per cent is half.
Combining those covers most cases. 35 per cent off is 25 plus 10 - a quarter off, then a tenth off the original.
Stacked discounts do not add
This is the one that catches people. An extra 20 per cent off an item already reduced by 30 per cent is not 50 per cent off.
The second discount applies to the already-reduced price. 0.7 times 0.8 is 0.56, so you pay 56 per cent - a 44 per cent discount, not 50. The gap widens with bigger numbers: 50 and 50 stacked is 75 per cent off, not 100, which is the obvious proof that they cannot add.
Worth knowing the order does not matter. 30 then 20 gives the same result as 20 then 30, because multiplication commutes.
Two tricks that make a saving look bigger
The inflated "was" price. A discount is a percentage of a reference price, and if that reference was never a price anyone paid, the percentage is meaningless. Many jurisdictions require the higher price to have been charged for a period before it can be advertised as a previous price, which is worth knowing exists. The useful question is not the percentage but whether the final price is good.
Percentage off versus money off. "40 per cent off" on a cheap item is a smaller saving than "15 off" on an expensive one, and the larger percentage feels like the better deal. Convert both to currency before comparing.
A third, smaller one: discount on the pre-tax or post-tax price. The order changes the total slightly, and reputable sellers discount before tax - the Sales Tax Calculator covers that interaction.
Working backwards
If you know the sale price and the discount and want the original, divide rather than adding the percentage back. A price of 56 after 30 per cent off was 56 divided by 0.7, which is 80 - not 56 plus 30 per cent, which gives 72.8 and is wrong. That mistake is the single most common error in discount arithmetic.
Common questions
How do I compare two offers quickly?
Convert both to the price you would actually pay. Percentages are not comparable across different starting prices.
Is "buy one get one free" 50 per cent off?
Yes, if you wanted two. If you only wanted one, it is nothing off.
What about a percentage off the second item?
Half the stated discount across the pair. "Second item half price" is 25 per cent off the two together.
Got a discount to work out?