The Discount Math
Example — $129.99 at 30% off
| You save | 129.99 × 0.30 | $39.00 |
| You pay | 129.99 × 0.70 | $90.99 |
Mental shortcut: compute 10% (move the decimal) and scale — 30% of $129.99 ≈ 3 × $13 = $39. Fast enough to use mid-aisle.
Stacked Discounts: Where Shoppers Get Fooled
"30% off, plus an extra 20% off at checkout" is not 50% off. Sequential discounts multiply, each applying to the already-reduced price:
| Stack | Feels like | Actually |
|---|---|---|
| 20% + 20% | 40% | 36% |
| 30% + 20% | 50% | 44% |
| 50% + 30% | 80% | 65% |
| 50% + 50% | 100% | 75% |
The gap between "feels like" and "actually" is the retailer's favorite illusion. The calculator's stacked mode runs the true multiplication for any two rates.
Discounts, Taxes, and Order of Operations
Discounts apply before sales tax — you're taxed on what you actually pay:
$100 item, 25% off, 8% tax → 100 × 0.75 × 1.08 = $81.00. (Compute the tax leg with the Sales Tax Calculator.) Coupons phrased as fixed amounts ($15 off) subtract before percentage math when combined — sequence matters, and store policies dictate it; when allowed to choose, apply the percentage to the higher price first for maximum savings.
Is the "Deal" Real? Quick Checks
- Reverse the discount: a "$68 after 15% off" claim implies an $80 original — if the item never sold at $80, the discount is theater. (Reverse math: final ÷ (1 − rate); details in the Percentage Calculator.)
- Compare unit prices, not discount sizes — 40% off an inflated price can beat nothing.
- Per-use math beats sticker math: a $90 tool used weekly costs less per use than a $30 one used twice.
- Anchor check: "was $199, now $89" only matters if $199 was ever the real market price.
The Bottom Line
Two formulas cover every sale rack: multiply by (1 − rate) for the price, and multiply the survivors together when discounts stack. Run the true number before the register does — especially on "extra % off" promotions, where the gap between marketing arithmetic and actual arithmetic is the whole trick.
Stacked Discounts: Why 20% + 10% Is Not 30% Off
Retailers love stacking offers — "20% off, plus an extra 10% off at checkout!" — because most shoppers mentally add them into 30% off. The maths disagrees. Discounts apply sequentially, each one to the already-reduced price. On a $100 item: 20% off brings it to $80, then 10% off $80 removes $8, leaving $72. Your true saving is 28%, not 30%.
The general formula for stacked discounts is: final price = original × (1 − d1) × (1 − d2). Order never matters for the final number — 10% then 20% lands on the same $72 — but the size of the base shrinks with each step, which is why stacked percentages always under-deliver versus their sum. Run any combination through the calculator above before a sale day: the gap between the advertised "total" discount and the real one is often worth several dollars per item, and much more on appliances, laptops and furniture. If percentages themselves ever feel slippery, our percentage calculator breaks any of them into plain numbers.
Discount, Tax and Tip: The Order That Decides What You Pay
A discounted price is rarely the final price, because sales tax is calculated after the discount, on the reduced amount. An $80 jacket at 25% off costs $60, and with 8% tax the till asks for $60 × 1.08 = $64.80 — not the $69.12 you would pay if tax were charged on the original $80. Stores that advertise a discount are (in most jurisdictions) required to tax the discounted price, which is a small, legal second saving hiding inside the first.
Tipping works the other way round: etiquette says calculate the tip on the pre-discount price of a meal, since the server did the same work whatever coupon you used. The practical routine is three steps — discount first, tip on the original, tax on the discounted price — and this calculator handles the first step exactly. Knowing the order turns confusing receipts into arithmetic you can check on your phone in seconds.