Almost everyone can work out 10% off in their head. Far fewer can say what a jacket originally cost when the tag reads "$45, was 25% off" — and almost nobody gets stacked discounts right on the first try. These are not obscure edge cases; they are the three calculations that decide whether a sale is actually a saving. This guide covers all three, with the formulas, worked examples, and the specific mistakes that cost shoppers money.
The One Idea That Makes Everything Else Easy
Stop thinking about the percentage you save and start thinking about the fraction you still pay. A 25% discount means you pay 75%, so the multiplier is 0.75. A 40% discount means you pay 60%, so the multiplier is 0.6. In general the multiplier is 1 − (discount ÷ 100).
This single reframing collapses three separate procedures into one. Forward calculations become a single multiplication. Reverse calculations become a single division. Stacked discounts become a chain of multiplications. Every mistake described later in this article comes from someone adding and subtracting percentages instead of multiplying and dividing fractions.
Forward: What Will I Pay?
The saving is the original price times the discount as a decimal, and the sale price is what remains:
- Saving = original × (discount ÷ 100)
- Sale price = original − saving, or equivalently original × (1 − discount ÷ 100)
A $60 jacket at 25% off: the saving is 60 × 0.25 = $15, so you pay $45. Using the multiplier directly, 60 × 0.75 = $45 in one step. For mental arithmetic the one-step version is far more reliable, because you never have to hold the intermediate saving in your head while subtracting.
A useful habit for awkward percentages is to build them from 10% and 5%. Ten percent of $84 is $8.40; five percent is half that, $4.20. So 15% off $84 is a $12.60 saving, and you pay $71.40. Most real-world discounts are combinations of 10s, 5s, and halves.
Reverse: What Did It Cost Before?
This is the direction that catches people out. Suppose a coat is $80 after 20% off. What was the original price?
The intuitive move — add 20% to $80 — gives $96. It is wrong. The 20% was taken from the original price, which is larger than $80, so 20% of the original is more than the $16 that adding 20% to $80 produces.
Because the sale price is the original times the multiplier, the original is the sale price divided by that multiplier:
- Original = sale ÷ (1 − discount ÷ 100)
So $80 ÷ 0.8 = $100. Check it forwards: 20% of $100 is $20, and $100 − $20 = $80. The numbers reconcile. The $96 answer never does, and that is the tell — if your recovered original price does not produce the sale price when you run the discount forwards, you have added instead of divided.
The error is not small, and it grows with the discount:
- 10% off, $90 sale price: true original $100; the shortcut says $99. Out by 1%.
- 30% off, $70 sale price: true original $100; the shortcut says $91. Out by 9%.
- 50% off, $50 sale price: true original $100; the shortcut says $75. Out by 25%.
- 70% off, $30 sale price: true original $100; the shortcut says $51. Out by 49%.
At clearance depths the shortcut understates the original price by roughly half. If you are reselling, insuring, valuing stock, or simply checking whether a "was" price is believable, this is the calculation that matters.
Finding the Percentage from Two Prices
When both prices are visible and you want to know how good the deal really is:
- Discount % = (original − sale) ÷ original × 100
A camera reduced from $250 to $175 has been cut by 75 ÷ 250 = 30%.
The critical detail is the denominator: it is the original price. Dividing the same $75 by the $175 sale price gives 43%, which is a different quantity altogether — that is the markup from the sale price back to the original, not the discount. Retailers and marketplaces occasionally quote the larger figure because it sounds better. If a claimed discount seems higher than the prices justify, check which number the percentage was divided by.
Stacked Discounts: Why "30% Plus 20%" Is Not 50%
"Take an extra 20% off already-reduced prices" is among the most effective signs in retail, because shoppers add the two numbers. They should be multiplied.
You pay 70% of the original after the first discount, then 80% of that after the second. The combined multiplier is 0.7 × 0.8 = 0.56, so you pay 56% of the original — a 44% discount, not 50%. On a $200 coat that is a $112 price rather than the $100 the intuitive sum implies. The $12 gap is the entire value of the misunderstanding, per item.
More tiers make it worse:
- 20% + 20%: feels like 40%, actually 36% (0.8 × 0.8 = 0.64).
- 30% + 20%: feels like 50%, actually 44%.
- 50% + 20%: feels like 70%, actually 60%.
- 20% + 20% + 20%: feels like 60%, actually 48.8%.
The rule is short enough to memorise: stacked discounts multiply the fractions you still pay, and never add the fractions you save. A useful consequence is that order does not matter — 30% then 20% gives exactly the same result as 20% then 30% — so a shop offering to "apply the bigger discount first" is offering you nothing.
One genuine exception: a flat-amount voucher ("$20 off") is not a percentage, so its position in the sequence does matter. Applying $20 off before a 25% discount saves you less than applying it after, because the percentage then works on a smaller base. If you can choose the order, take percentage discounts first and flat vouchers last.
Where Sales Tax and VAT Fit
Tax is charged on what you actually pay, so it comes after the discount. On a $200 item at 50% off with 10% sales tax, the tax is calculated on the discounted $100, giving $110 total — not $120. A discount therefore saves you the tax on the discounted portion as well, a small bonus that is easy to forget when budgeting.
The exception is a manufacturer's rebate or coupon that the retailer processes after tax has been computed. Some jurisdictions treat that as a payment rather than a price reduction, so tax is assessed on the pre-coupon price. If a receipt shows more tax than you expect, this is usually why.
Is the Discount Even Real?
A percentage only means something relative to an honest starting price. This is why the EU's Omnibus Directive requires that an announced price reduction state the lowest price the trader applied in the previous 30 days, and why the US Federal Trade Commission's guidance on former-price comparisons treats an inflated "regular" price as deceptive. Both rules exist because a fictitious reference price turns any discount into theatre.
Reverse mode gives you a fast sanity check. Recover the implied original price from the sale price and the advertised discount, then ask whether the item has ever plausibly sold at that figure. If a gadget is "70% off" at $30, the implied original is $100 — and if it has been $40 all year, the claim is doing more work in the marketing than in your wallet.
Totalling a Whole Basket
With several items at different discounts, the number worth knowing is the blended rate across the basket — and it must be weighted by value, not averaged across items.
Consider a $2 keyring at 50% off and a $900 laptop at 10% off. Averaging the percentages gives 30%, which is nonsense: you saved $1 on the keyring and $90 on the laptop, so $91 off a $902 basket. The real blended discount is 91 ÷ 902 = 10.1%, barely different from the laptop's own rate, because the laptop is almost the entire basket.
The correct method is always the same: total the basket before discounts, total it after, and express the difference as a percentage of the pre-discount total. This matters whenever you are judging a "spend more, save more" promotion, because adding a heavily discounted cheap item barely moves the blended rate while adding meaningfully to what you spend.
The Mistakes, Collected
- Adding the percentage back to reverse a discount. Divide by the multiplier instead. The error reaches 49% at a 70% discount.
- Adding stacked discounts. Multiply the fractions you still pay. "30% plus 20%" is 44%, not 50%.
- Dividing the saving by the sale price. The discount percentage uses the original price as its denominator; dividing by the sale price inflates it.
- Averaging percentages across a basket. Weight by value, or one cheap item distorts the whole figure.
- Assuming tax is unaffected. Tax follows the discounted price, so a markdown reduces the tax too.
- Trusting the reference price. Recover the implied original and ask whether the item has ever sold for it.
Try It
Our discount calculator solves all three directions — sale price, original price, and discount percentage — from whichever two values you have, and includes a bulk table showing the price at every discount from 0% to 50% plus a 20-item cart that blends discounts by value. Everything runs in your browser, so nothing you type is uploaded.
For the underlying percentage arithmetic in isolation, the percentage calculator handles increases, decreases, and percentage differences. If you are pricing goods for sale rather than buying them, the VAT calculator covers the tax side, including the reverse calculation that pulls VAT back out of a gross price — the same divide-don't-subtract principle described here, applied to tax instead of discounts.