How to Calculate a Discount (And Why Stacked Ones Lie)

Two signs, one lie of omission

30% off. Extra 20% off. That looks like 50% off.

It's 44%.

An $80 item comes to $44.80 before tax, not $40. The gap isn't huge here, and it gets wider the bigger the discounts are.

The second discount only cuts what's left

That's the whole thing, and everything else follows from it.

After 30% off you're paying 70% of the price. The extra 20% comes off that — leaving 80% of the 70:

0.70 × 0.80 = 0.56

You pay 56% of where you started. Effective discount: 44%.

The second sign never touches the money the first one already took off. It only ever discounts what you were still going to spend.

It can never reach free

The clearest demonstration:

Stacked	Real discount
20% then 10%	28%
30% then 20%	44%
50% then 20%	60%
50% then 50%	75%
50% three times	87.5%

Two half-price discounts give you 75% off, not 100%. The second half-price applies to the half you had left.

You can keep halving forever and never arrive at free — which is the most intuitive proof that percentage discounts multiply rather than add.

Does tax go before or after?

It doesn't matter to the total. Multiplying by 0.7, then 0.8, then 1.08 gives the same answer in any order — multiplication doesn't care about sequence.

It matters to how the receipt reads, and in most places tax is charged on what you actually pay, so the discount comes first. If a seller ever applies tax to the pre-discount price, that's a different and more interesting conversation to have with them.

What the common offers actually are

Worth knowing, because the arithmetic is done for you on the sign and it's rarely done in your favour:

Offer	Real discount
Buy one get one free	50%
Buy one get one half price	25%
Three for two	33.3%
Buy two get one half price	16.7%
"Up to 70% off"	One item is. Most aren't.

The reframe that handles all of them: work out what you hand over, and divide by what you take home. Buy-one-get-one-half-price means paying for 1.5 items and leaving with 2 — which is 25% off, not 50.

What "you save" really means

The calculator reports you save as the original $80 minus the discounted $44.80 — $35.20, with no tax on either side. Note that isn't measured against the "before tax" output, which is the discounted total; it's measured against where you started.

That's deliberate. Including tax in the saving would inflate it, because you'd be counting tax you were never going to pay as money you kept. The saving on the goods is what the discount is actually worth to you, and it's the figure that compares honestly between shops with different tax rates.

It's also worth noticing how the saving and the percentage diverge. A 44% effective discount sounds smaller than "30% plus 20%", but $35.20 off is $35.20 off — and on a larger purchase, a modest percentage can be worth far more than an eye-catching one on something cheap. Percentages compare deals on the same item; money compares deals across different ones.

Per-unit is the other number that lies

Discounts aren't the only place retail arithmetic is done for you.

Multi-buys and bigger packs are sold on the assumption that more is cheaper per unit — and often it is, but not always, and not reliably. Shelf labels showing price per 100g or per item exist precisely because that comparison is hard to do standing up.

The trap is the same shape as stacked discounts: an offer that sounds proportional usually isn't. Work out what you hand over, divide by what you take home, and compare that.

A percentage is not a price

The thing no discount calculator can tell you: whether the deal is good.

A discount is a percentage off a number the seller chose. Seventy percent off an inflated "original price" can easily be worse than ten percent off a fair one — and "was $X" pricing exists precisely because the percentage is more persuasive than the price.

That's why the primary output here is what you pay, not the percentage. The only honest comparison between two shops is the final amount that leaves your account.

Two more that erase discounts quietly: delivery, which can wipe out a modest saving entirely, and return policies on clearance, which are frequently worse or nonexistent.

And the question underneath all of it — would you buy this at this price if it weren't on sale? If not, the discount isn't a saving. It's a purchase.

Print the sale maths card — it's wallet-sized, which is where the arithmetic is actually needed.