Percent off from two prices

Work it out

Want to keep the deal? Write it in your notebook: it strikes the old price and keeps the percent off, the saving and the link together.

The formula

percent off = (old price - new price) / old price x 100

The saving is the old price minus the new one. Take the first example note of the notebook: $1199 down to $999. The saving is $200, and $200 / $1199 = 0.1668, so 16.68%. Dealix rounds to the nearest whole percent and shows 17% off.

Always divide by the old price. $200 / $999 gives 20%: that is how much more the old price was, not the discount.

Worked examples

The last row is a cent off a $10 price: 0.1%, which rounds to 0% off. It is the very case the US Federal Trade Commission gives in its pricing guides: a seller who claims an item is “Reduced to $9.99” when the former price was $10 is misleading the consumer (16 CFR 233.1(e)).

Why 50% off means the old price was double

A discount is measured against the old price, a price rise against the new one. So the same gap gives two different percentages: from $80 down to $60 is 25% off, and from $60 back up to $80 is 33% more. The bigger the discount, the wider the gap between the two numbers.

Two discounts in a row

An extra 10% off an item already 20% off is not 30% off. The second discount applies to the price left after the first: $100, then $80, then $72, so 28% off in all. In general:

total off = 1 - (1 - first off) x (1 - second off)

In the notebook, type the price you actually pay as the deal price: the percent off it shows then covers both discounts.

From a sale price back to the original

old price = new price / (1 - percent off / 100)

A $60 price at 25% off started at $60 / 0.75 = $80. Adding 25% of $60 back gives $75, which is wrong: the 25% was taken from $80, not from $60.

In a spreadsheet

With the old price in A2 and the new price in B2, in Excel or Google Sheets:

• =ROUND((A2-B2)/A2*100, 0) gives the whole percent, the number Dealix shows;
• =(A2-B2)/A2, with the cell formatted as a percentage, gives the exact share;
• =A2-B2 gives the saving.

Is the struck price a real one?

A percent off is only as good as the old price it starts from. In the United States, the Federal Trade Commission's Guides Against Deceptive Pricing (16 CFR Part 233) say a former price is a fair basis for a comparison when it is “the actual, bona fide price at which the article was offered to the public on a regular basis for a reasonably substantial period of time” (section 233.1).

The guides give the counter-example of a pen seller who normally charges $7.50, asks $10 for a few days, then advertises “Were $10, Now Only $7.50”: a false bargain. They also warn that a manufacturer's list or suggested retail price can mislead when it does not match the price at which a substantial number of sales are actually made (section 233.3).

California goes further. Section 17501 of its Business and Professions Code bars a former price unless it was the prevailing market price within the three months before the advertisement, or the advertisement clearly states the date when it was.

In the notebook, the old price is the one you type. Note the price you saw yourself before the sale, and say in the description where it comes from: the store's own earlier price, a list price, or a “compare at” price.