Discount Calculator

How this is calculated

Each discount is applied to whatever is left after the one before it, not to the original price. That is why stacked discounts never add up the way they look. Take 30 percent off and you pay 70 percent. Take a further 20 percent off THAT and you pay 80 percent of the 70, which is 56 percent - so the effective discount is 44 percent, not the 50 the two signs suggest. The second discount only ever applies to money you were still going to spend. The gap widens as the discounts get bigger. Two 50 percent discounts stacked are 75 percent off, not 100 - the second half-price applies to the half you had left, and no sequence of percentage discounts can ever reach free. Tax is applied last, to the discounted price, which is the normal order almost everywhere: you are taxed on what you actually pay rather than on the ticket price. Note that this ORDER does not matter arithmetically - multiplying by 0.7, then 0.8, then 1.08 gives the same answer in any sequence, because multiplication does not care. It only matters for how a receipt reads. The money saved is measured against the ORIGINAL price with no tax on either side - not against the 'before tax' figure, which is the discounted total. So it is the saving on the goods themselves. Adding tax to both ends would inflate the apparent saving by counting tax you were never going to pay as money you kept. What this cannot tell you is whether the deal is good. A discount is a percentage off a price the seller chose, and a large percentage off an inflated starting price is worth less than a small one off a fair price. The only figure that matters when comparing two shops is the final amount you hand over.

Common questions

Why isn't 30% then 20% off the same as 50% off?

Because the second discount applies to what is LEFT, not to the original price. After 30 percent off you are paying 70 percent; taking 20 percent off that leaves 80 percent of the 70, which is 56 percent of where you started - an effective discount of 44 percent. The second sign only ever discounts money you were still going to spend, which is why stacked offers always look better than they are.

Can stacked discounts ever reach 100%?

No, and this is the clearest way to see the maths. Two 50 percent discounts give 75 percent off, not 100 - the second half-price applies to the half you had left. Three of them give 87.5 percent. You can keep halving forever and never arrive at free, because each discount only ever removes a fraction of the remainder.

Does it matter whether tax is added before or after the discount?

Not to the total, no. Multiplying by 0.7, then 0.8, then 1.08 gives the same answer in any order, because multiplication does not 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 applies tax to the pre-discount price, that is a different and more interesting conversation.

Why is the saving calculated before tax?

Because it is the saving on the GOODS. Including tax in the saving figure would inflate it - you would be counting tax you were never going to pay as money you saved. The pre-tax figure is what the discount is actually worth to you, and it is the number to compare between shops.

Is a bigger percentage always the better deal?

No. A discount is a percentage off a price the seller chose, and a large percentage off an inflated starting price is worth less than a small one off a fair price. The only figure that compares two shops honestly is the final amount you hand over - which is why that is the primary output here and the percentage is not.

What about 'buy one get one half price'?

That is a 25 percent discount across the two items, not 50 - you pay 1.5 items' worth for 2. The same reframing catches most retail offers: work out what you actually hand over and divide by what you actually take home. Three for two is 33.3 percent off, and buy one get one free is 50, not 100.

Take it further with AI

Copy this into ChatGPT or Claude with your own numbers filled in. It hands over the figures this calculator worked out, so the answer is built on real arithmetic instead of a guess.

I used the Discount Calculator at https://www.bfcbrilliance.com/tools/discount-calculator.

What I entered:
- Original price ($): ___
- First discount (%): ___
- Extra discount on top (%): ___
- Sales tax (%): ___

What it calculated:
- You pay: ___
- Before tax: ___
- You save: ___
- Effective discount: ___
- What adding the two signs suggests: ___

Use those figures as given — they are already worked out, so please don't recalculate or estimate your own. Help me turn them into a plan: what to buy or do, in what order, roughly what it should cost, and the mistakes people most often make with this job.

Keep this general and do not give financial advice — flag where I should talk to a qualified adviser.

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