Key takeaway
Sale price = list × (1 − rate). Instead of computing the discount first, multiply by the share you keep — one step at the register, before the sales tax hits.
Scope and assumptions
Single percentage discount off the list price; rate as decimal (15% = 0.15).
You're standing at the register with a $45 jacket under a "15% OFF" sign, and your brain freezes trying to work out the discount first. In our retail testing, the fastest way to judge a real deal is to ignore the discount entirely. Instead, multiply the list price by the share you actually keep. At 15% off you keep 85%, so 45 × 0.85 = $38.25 — one multiplication that tells you what leaves your wallet, before the sales tax ever hits the receipt.
The one multiplication that beats the tag
Sale Price = List Price × (1 − rate)
The bracketed term is the complement of the discount — the share you hand over. You never compute "how much comes off"; you go straight to what stays.
Your share, not the discount
| Tag | You keep | $100 item | $45 item |
|---|---|---|---|
| 10% off | 90% | $90.00 | $40.50 |
| 15% off | 85% | $85.00 | $38.25 |
| 20% off | 80% | $80.00 | $36.00 |
| 25% off | 75% | $75.00 | $33.75 |
| 30% off | 70% | $70.00 | $31.50 |
Reading down the "you keep" column is the whole skill. Ten percent off is a decimal shift; twenty-five off is a quarter gone; thirty off means you keep seventy.
Off and keep are one instruction
Retailers print "20% off" because it sounds bigger than "pay 80%". The arithmetic prefers the second: a single multiplication with no subtraction. Once you internalise the pair — off% and (100 − off)% — the register stops being a place to do mental arithmetic and becomes a place to compare deals.
The percent is not a dollar amount
This is the error that survives longest. A 15% discount on $45 is not "$15 off" — it's $6.75. The percent rides on the price, so it grows and shrinks with it. Treating it as a flat amount only happens to be right when the price is exactly $100.
Real checkout scenes
- Online cart. A $79.99 item at 25% off: 79.99 × 0.75 = $59.99. If the cart total differs, check for a hidden "convenience fee" before blaming the discount.
- Stacked promos. "20% off, then another 10% at checkout" is not 30%. Chain the complements: 0.80 × 0.90 = 0.72, so you pay 72% — a real 28% off.
- Sales-tax timing. In virtually every US state, tax is charged on the discounted price. Discount first, tax second — reversing the order overpays.
Rounding: last, not first
Keep full precision through the multiplication and round the final sale price to the nearest cent. Rounding the complement first (0.85 → 0.9) overstates the discount and shifts larger baskets by several cents.
Mental Shortcuts That Overshoot
Subtracting the percent as if it were dollars; multiplying by the rate instead of its complement (that returns the discount, not the price); forgetting 20% means 0.20; rounding mid-calculation; and adding two stacked rates instead of chaining their complements.
See the full formula index
If you're weighing all three discount calculations — dollars off, price to pay, and headline percent — the hub page Discount Formula lines them up so you grab the right one first.
FAQ
Does sales tax apply before or after the discount is taken? After, in virtually every US state. Tax is charged on the discounted price, so the order is discount first, then tax — the reverse overpays.
How do I handle a discount given as a dollar amount instead of a percent? Just subtract it. The (1 − rate) trick only applies to percentages; a flat $20 off needs no conversion.
How do I apply two stacked percentage discounts? Chain the complements. 20% off then another 10% off means × 0.80 × 0.90 = 0.72, so you pay 72% of the original.
Why is my calculated sale price a cent off from the receipt? Almost always rounding. Keep full precision through the multiplication and round only the final price; rounding the complement first shifts the last digit.
If the shelf price and the discount tag disagree, which one applies? In most US jurisdictions the price you're charged must match the advertised one, and many states' weights-and-measures rules back that up, as do the FTC's pricing guides. If a tag overstates the discount, you're generally entitled to the lower shown price. The UK's Consumer Protection from Unfair Trading Regulations 2008 set the same expectation.
Sources: Khan Academy, Percent word problems; Maths is Fun, Percentages.
Disclaimer: Illustrative. Stacked or conditional discounts change the result; verify at checkout. Informational only.
Sources and references
- Khan Academy — Percent word problemshttps://www.khanacademy.org/math
- Maths is Fun — Percentageshttps://www.mathsisfun.com/percentage.html
- FTC — Guides Against Deceptive Pricinghttps://www.ftc.gov/business-guidance/resources/guides-against-deceptive-pricing-practices
Maintenance and corrections
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