Discount Calculator

The maths behind a price tag

A sign that says 40 percent off is quietly doing some arithmetic at you, and the shop is rather hoping you will not do it back. Most of the time the honest answer, the price you will actually hand over, is easy enough to work out, but it is fiddly to do in your head while standing in an aisle holding two other things.

So this calculator does it for you. Tell it the sticker price, the discount, and the sales tax where you are, and it hands back the real price at the till and how much you are keeping in your pocket. What follows is how to read that, plus a couple of things about discounts that are genuinely worth knowing before your next sale.

The three things you tell it

Original price. The full sticker price, before anything comes off.

Discount. The percentage off, the number on the sign.

Sales tax. The tax rate where you are shopping. This one matters because the calculator gives you the true out the door price, tax included, not just the shelf price. Tax is worked out on the discounted amount, which is exactly how it is done at the register in the US, since you are taxed on what you actually pay, not on the original sticker.

Your real price, and your real saving

Two numbers come back. The final price is what you pay once the discount is taken off and the tax is added on, the honest total. The you save figure is the gap between paying full whack and paying the sale price, and it is measured tax and all, so it counts both the money knocked off the item and the tax you no longer owe on that chunk. That is why the saving comes out a touch larger than a plain percentage of the sticker: skipping part of the price means skipping the tax on it too.

A quick example

Say a jacket is priced at 80, it is 25 percent off, and your sales tax is 8 percent.

A quarter off 80 knocks the shelf price down to 60. Add 8 percent tax on that 60 and you pay 64.80 at the till. Your saving works out to 21.60, which is the 20 off the jacket plus the 1.60 of tax you no longer pay on it. Not a bad haul for a bit of arithmetic you did not have to do.

Why two discounts are never as good as they sound

Here is the one that catches almost everyone. A sign says 50 percent off, and then another says take a further 20 percent off at the till. Your brain adds them and hears 70 percent off. It is not. It is 60.

The reason is that the second discount is not taken off the original price, it is taken off the already reduced one, so it has less to work with. Fifty percent off 80 leaves 40. Then 20 percent off that 40 is only 8 more, landing you at 32, which is 60 percent off the original, not 70. Discounts stacked on top of each other multiply, they do not add, and the combined saving is always less than you would get by adding the numbers up.

Two 50 percent discounts do not make an item free, they leave you paying a quarter of the price, a 75 percent saving. A 20 and a 10 make 28 percent, not 30. If you want the true figure for a stacked deal, run it through this calculator one discount at a time: take the sale price it gives you, then feed that back in as the new original price with the second discount. The final number is the one your brain was rounding up.

Off versus of, and other small traps

A little bit of language trips people up here, and it is worth getting straight. "25 percent off" and "25 percent of" are not the same thing. Twenty five percent off 80 means you pay 60. Twenty five percent of 80 is 20, which is the saving, not the price. Same words, very nearly, opposite meaning.

One more that saves real money. When a deal is offered as a percentage or a flat amount, say 25 percent off versus 15 off, the better one flips depending on the price. Below a certain point the flat amount wins, above it the percentage does. For that pair, the tipping point is 60: on anything dearer than 60, the 25 percent saves you more. Quick mental check before you pick a coupon.

A word on those "was" prices

A discount is only ever as real as the price it is measured against, and that is worth a pinch of salt. A tag that shouts 60 percent off a number the item was never genuinely sold at is not much of a bargain, it is just a big number next to a smaller one.

This is not only cynicism, it is regulated. In the US, the Federal Trade Commission has long-standing guidance against deceptive "was and now" pricing, the trick of quoting an inflated former price to make a routine price look like a steal. So when the saving seems too good, the useful instinct is to ask what the thing actually costs elsewhere, rather than trusting the shop's own before number. The percentage on the sign is only meaningful if the starting price was.

Questions people ask

If I have two coupons, can I just add the percentages?

No, and this is the big one. Stacked percentage discounts multiply rather than add, so the total is always less than the sum. Two 20 percent discounts give you 36 percent off, not 40. Run them one at a time to see the true price.

Does the tax go on the original price or the sale price?

The sale price. You are taxed on what you actually pay after the discount, not on the original sticker, which is how the calculator works it out.

Does the order of two discounts matter?

For pure percentages, no. Twenty percent then ten percent gives the same final price as ten percent then twenty percent. It only starts to matter when a flat dollar coupon is mixed in with a percentage.

What is the difference between percent off and percent of?

Percent off is how much comes down from the price. Percent of is a share of the price itself. 30 percent off 50 means you pay 35. 30 percent of 50 is 15, the amount you save.

References

The discount and tax arithmetic is standard. The guidance on honest sale pricing comes from the consumer protection rules below.

1. Federal Trade Commission. Guides Against Deceptive Pricing, 16 CFR Part 233 (former price comparisons and comparative price advertising). https://www.ecfr.gov/current/title-16/part-233