How to Calculate a Discount (and Why Stacked Coupons Lie)
Percent-off maths in plain English: work out a sale price by hand, spot fake discounts, and find out why 20% off twice is never 40% off.
The sign says 40% off. The tag says £129.99. You’re standing in the aisle doing long division in your head while someone waits behind you. This is the actual use case for a discount calculator, and it’s why I keep one open on my phone during sales.
The maths isn’t hard. It’s just annoying to do quickly with awkward numbers, and shops know that.
The one formula you need
Multiply the price by the discount, divide by a hundred, subtract.
£129.99 at 40% off: 129.99 × 40 = 5199.6, divided by 100 is £51.99 off, so you pay £78. That’s it. Everything else on this page is a variation of that.
If you want a shortcut for round numbers, work out 10% first (move the decimal point one place left) and scale it. 10% of £129.99 is about £13, so 40% is roughly £52. Close enough to know whether it’s worth queuing.
Two coupons don’t add up
This is the part that trips people up, and it’s the reason I built the second field into the Discount Calculator.
A jacket costs $100. It’s marked 20% off, and you have a coupon for an extra 20% off sale items. You are not getting 40% off.
The first discount takes $100 down to $80. The coupon then applies to $80, not to $100 — so it takes off $16, not $20. You pay $64. Your real discount is 36%.
It works the same way in the other direction, which is the mildly reassuring part: the order doesn’t matter. Apply the coupon first and you get $80, then 20% off that is still $64. Retailers sometimes claim you have to use the coupon in a specific order to “get the best deal.” Multiplication is commutative. They’re wrong.
The general rule: two discounts of a and b percent combine to 1 − (1 − a)(1 − b). For anything above single digits, that’s noticeably less than a + b:
- 20% + 20% = 36%
- 30% + 20% = 44%
- 50% + 30% = 65%
- 70% + 20% = 76%
The bigger the discounts, the wider the gap between what you assume and what you get.
Was/now prices deserve suspicion
The other direction — you see an old price and a new price, and you want to know the actual percentage — is the reverse calculation. Subtract, divide by the original, multiply by 100.
Was £200, now £149. That’s £51 off £200, which is 25.5%. Not the “up to 50%” the window promised.
This matters more than it sounds. In the UK, the Competition and Markets Authority has repeatedly gone after retailers for reference pricing — quoting a “was” price that the item barely ever sold at. A 2016 CMA review of the furniture and carpet sector found that some products had spent almost their entire commercial life “on sale.” The percentage on the sign is real arithmetic performed on a fictional number.
So the reverse calculator answers a narrow question: given these two numbers, what’s the discount? Whether the first number ever meant anything is a separate problem, and no calculator will help you there.
Where tax fits
Sales tax and VAT go on the discounted price, not the original one. Calculate the discount first, then add tax to what’s left. Doing it the other way around inflates the tax and gives you the wrong total — though it’s a common enough mistake in spreadsheets that it’s worth checking whoever built yours got the order right.
Worth knowing
A 50% markup and a 50% discount don’t cancel out. Take $100, add 50% to get $150, then knock 50% off and you’re at $75. Percentages are always relative to whatever number they’re standing next to, which is the whole reason discount arithmetic feels slippery.
Punch your numbers into the Discount Calculator — it runs entirely in your browser, so it works in a shop basement with no signal.