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How to use this calculator#
- Enter the original priceUse the price the item genuinely sold at before the promotion, not the inflated 'was' price on the tag. During large sale events the reference price is often the highest price charged for a few days in the previous quarter.
- Choose percent off or a fixed amount offA $20 coupon and a 20% coupon are identical only at $100. Below that the fixed amount wins, above it the percentage does — worth a moment's thought when a retailer lets you choose.
- Add a second discount to stack itThe second percentage always applies to the already-reduced price, which is how retailers actually process codes. That is why 20% + 20% is 36% off, not 40%.
- Add sales tax lastTax is charged on what you actually pay, so a deeper discount shrinks the tax too. The exception in several US states is a manufacturer's coupon, where tax is computed on the pre-coupon price because the retailer gets reimbursed.
The formula#
Discount, stacked discount and effective saving
Sale = P × (1 − d₁) Stacked = P × (1 − d₁) × (1 − d₂) Effective = [1 − (1 − d₁)(1 − d₂)] × 100 Original = Sale ÷ (1 − d)
- P
- Original price
- d₁, d₂
- Discounts as decimals: 25% becomes 0.25
- Sale
- Price after the discount
- Effective
- The single discount equivalent to both applied in sequence
Discounts multiply, they never add. Order does not matter when both are percentages — (1 − d₁)(1 − d₂) is commutative — but it matters enormously as soon as one is a fixed amount. To reverse a discount, divide rather than multiply: a 30% reduction is undone by dividing by 0.7, not by adding 30%.
Stacked discounts never add up#
Two 20% discounts are not 40% off. Each one applies to whatever price is left after the previous one: 100 becomes 80, then 80 becomes 64 — an effective 36% reduction. The combined factor is always (1 - d1) x (1 - d2). Three stacked 20% coupons take 100 down to 51.20, a 48.8% saving rather than the 60% that intuition suggests.
Order matters as soon as a fixed amount joins a percentage. A 20% discount followed by 10 off leaves 70 on a 100 item, while 10 off followed by 20% leaves 72. Retailers usually apply percentage codes first, so check the receipt whenever two promotions run together and the total looks off by a couple of units.
Working backwards from a sale tag#
To recover the original price from a sale price, divide by 1 minus the discount: 63 after 30% off means 63 / 0.7 = 90. This is worth doing during large sale events, because a big percentage off an inflated pre-sale price can still leave you paying more than the item sold for six weeks earlier. Price history is the only honest check on a headline discount.
Where the tax lands#
Sales tax and VAT are charged on the discounted price rather than the original, so a deeper discount also shrinks the tax. On a 200 jacket at 25% off with 8% sales tax you pay 150 plus 12 of tax, totalling 162. Manufacturer coupons are treated differently in some US states, where tax is still computed on the pre-coupon price because the retailer is reimbursed for the difference.
Worked examples#
One discount plus sales tax
A $200 jacket at 25% off, in a jurisdiction charging 8% sales tax.
- Discount = 200 × 0.25 = 50.00
- Sale price = 200 − 50 = 150.00
- Sales tax = 150 × 0.08 = 12.00
- Final price = 150 + 12 = 162.00
$162.00 at the register, with $50.00 saved and $12.00 of tax — $4.00 less tax than at full price.
Stacking a sale with an extra coupon
A $180 coat at 40% off, with an extra 20% code at checkout and 6% sales tax.
- After the sale: 180 × 0.60 = 108.00
- After the coupon: 108 × 0.80 = 86.40
- Effective discount = 1 − (0.60 × 0.80) = 1 − 0.48 = 52%, not 60%
- Sales tax = 86.40 × 0.06 = 5.18
- Final price = 86.40 + 5.18 = 91.58
$91.58 paid and $93.60 saved — a real 52% off. The 60% you would get by adding the two percentages together would have been $72.00, and no retailer prices it that way.
Reference tables#
| % off | $20 | $50 | $80 | $100 | $200 |
|---|---|---|---|---|---|
| 10% | $18.00 | $45.00 | $72.00 | $90.00 | $180.00 |
| 15% | $17.00 | $42.50 | $68.00 | $85.00 | $170.00 |
| 20% | $16.00 | $40.00 | $64.00 | $80.00 | $160.00 |
| 25% | $15.00 | $37.50 | $60.00 | $75.00 | $150.00 |
| 30% | $14.00 | $35.00 | $56.00 | $70.00 | $140.00 |
| 40% | $12.00 | $30.00 | $48.00 | $60.00 | $120.00 |
| 50% | $10.00 | $25.00 | $40.00 | $50.00 | $100.00 |
| 60% | $8.00 | $20.00 | $32.00 | $40.00 | $80.00 |
| 70% | $6.00 | $15.00 | $24.00 | $30.00 | $60.00 |
| 75% | $5.00 | $12.50 | $20.00 | $25.00 | $50.00 |
Mental shortcut for 30%: take 10% by shifting the decimal, triple it, subtract. On $80 that is 8 → 24 → $56.
| First discount | +10% | +20% | +25% | +30% | +50% |
|---|---|---|---|---|---|
| 10% | 19.0% | 28.0% | 32.5% | 37.0% | 55.0% |
| 20% | 28.0% | 36.0% | 40.0% | 44.0% | 60.0% |
| 25% | 32.5% | 40.0% | 43.8% | 47.5% | 62.5% |
| 30% | 37.0% | 44.0% | 47.5% | 51.0% | 65.0% |
| 40% | 46.0% | 52.0% | 55.0% | 58.0% | 70.0% |
| 50% | 55.0% | 60.0% | 62.5% | 65.0% | 75.0% |
Every cell is below the sum of the two percentages, and the gap widens as the discounts get bigger. Three stacked 20% codes take $100 to $51.20 — 48.8% off, not 60%.
| Discount shown | Multiply sale price by | A $63 sale price was |
|---|---|---|
| 10% off | 1.1111 | $70.00 |
| 20% off | 1.2500 | $78.75 |
| 25% off | 1.3333 | $84.00 |
| 30% off | 1.4286 | $90.00 |
| 40% off | 1.6667 | $105.00 |
| 50% off | 2.0000 | $126.00 |
| 60% off | 2.5000 | $157.50 |
| 70% off | 3.3333 | $210.00 |
Use this to audit a headline claim. If the recovered original is far above what the item sold for last month, the discount is measured from a price nobody paid.
Common mistakes#
- Adding stacked discounts togetherTwo 20% discounts feel like 40% and deliver 36%. On a $500 item that is a $20 gap between what you expected to pay and what the till says — small enough to shrug at, frequent enough to matter, and entirely predictable.
- Applying a fixed amount and a percentage in the wrong orderOn a $100 item, 20% off then $10 off leaves $70; $10 off then 20% off leaves $72. Retailers almost always apply percentage codes first, so if the receipt shows the other order you have been charged $2 more than the best available combination.
- Trusting the reference price on the tagA 70% discount from an inflated 'was' price can still be more than the item cost six weeks earlier. Price history, not the percentage, is the only honest test of whether a sale is a sale.
- Misreading buy-one-get-one offersBuy one get one free is 50% off only if you genuinely want two. Buy one get one half price is a 25% discount across the pair, and 3-for-2 is 33.3% off — none of them are the headline number they appear to be.
Frequently asked questions#
How do I calculate 30% off in my head?
Take 10% by moving the decimal one place left, multiply it by three, then subtract. On 80: 10% is 8, so 30% is 24 and the sale price is 56.
Can two coupon codes be combined?
Only where the retailer permits stacking, and the second code almost always applies to the already-reduced price. Store and manufacturer coupons stack more often than two store codes.
Does buy-one-get-one equal 50% off?
Buy one get one free is 50% off only if you actually want both items. Buy one get one half price works out at a 25% discount across the pair.
Key terms#
- Stacked discount
- Two or more reductions applied in sequence, each to the price left by the previous one. The combined factor is (1 − d₁)(1 − d₂).
- Effective discount
- The single percentage equivalent to all discounts combined. Always less than the sum of the individual percentages.
- Reference price
- The 'was' price a discount is measured against. Advertising rules in most countries require it to be a price genuinely charged for a defined recent period.
- Manufacturer's coupon
- A discount funded by the producer rather than the shop. In several US states sales tax is still charged on the pre-coupon price, because the retailer is reimbursed in full.
- Markdown
- A permanent reduction to clear stock, as opposed to a temporary promotion. Retailers plan markdown cadence, which is why waiting often beats the current coupon.
Sources#
- Advertising FAQs — rules on price comparisons and 'was' pricing — Federal Trade Commission
- Guide against deceptive pricing (16 CFR Part 233) — Federal Trade Commission
- UK advertising codes — rules on price and savings claims — Advertising Standards Authority
Figures last checked .
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