Scope and assumptions
Discount percentage compares the reduction to the ORIGINAL list price, not the sale price. Figures are illustrative.
A price tag carries two numbers and expects you to want a third. The list price and the sale price are sitting right there; the missing figure is the percentage, and turning the gap into a percent takes one division — as long as you divide by the right price.
Gap over original
Discount % = (List Price − Sale Price) ÷ List Price × 100
Subtract to get the dollars taken off, divide by the original, scale to 100. The denominator is the whole point of the operation, and it's the step that goes wrong most often.
Four tags, one method
| List | Sale | Taken off | Discount |
|---|---|---|---|
| $80 | $60 | $20 | 25% |
| $50 | $35 | $15 | 30% |
| $120 | $90 | $30 | 25% |
| $200 | $150 | $50 | 25% |
Notice the last two: a $30 reduction and a $50 reduction, both 25%. Dollars off scales with the price; the percentage doesn't.
When the tag only gives dollars
"$20 off" with no percentage is common, and it's solvable if you know the original:
$20 off an $80 item → 20 ÷ 80 × 100 = 25%
The dollar figure on its own is not a percentage and can't be compared across items. Twenty dollars off a $40 jacket is a much better deal than twenty off a $400 one, and only the ratio reveals it.
Why the original is the base
The discount is a share of what the item was, not what it is now. Divide by the sale price instead and the number inflates:
| Gap | ÷ list ($80) | ÷ sale ($60) |
|---|---|---|
| $20 | 25% | 33.3% |
The 33.3% isn't imaginary — it's the gap measured against the post-discount price. It's just answering a different question ("how much of the current price did I save?") than the one shoppers are asking.
Catching your own errors
A discount percentage lives between 0% and 100%. Two signals that something went wrong:
- Over 100% — you subtracted in the wrong order, or divided by the gap instead of a price.
- A result noticeably higher than expected — you probably used the sale price as the base.
The cross-check: percent × list price should reproduce the dollars off. 25% × $80 = $20. If it doesn't, redo the division.
Discount Percentages That Read Wrong
Using the sale price as the denominator; skipping the ×100 and reporting 0.25; subtracting sale from list in the wrong direction and getting a negative; treating "$20 off" as "20% off"; comparing percentages across wildly different price points as if the dollars matched; and stacking two discounts by adding the rates instead of multiplying the survivors.
Related discount guides
This page covers the headline-percent direction (two prices → %). For the other forms and the register-speed price-to-pay method, start at the hub: Discount Formula. To see the same gap framed as what you kept, read Calculate Percent Saved.
FAQ
Why does dividing by the sale price give a bigger number? Because it's a smaller denominator. $20 off an $80 item is 25% of $80 but 33% of the $60 sale price — the same gap measured against a shrunken base.
How do I find the discount percent if I only know the final price? You can't, not without the original. The percent is a ratio, and a ratio needs two numbers. Find the list price on the receipt or the tag's previous figure.
Is a 25% discount the same as 25% saved? Yes — both compare the price reduction to the original price. The two phrases describe the same ratio.
How do I combine two successive discounts? Multiply the remaining fractions. 20% off then 10% off leaves 0.8 × 0.9 = 0.72, so the total reduction is 28%, not 30%.
Can a store advertise a discount percentage off a price it never charged? In the US, the FTC's guides against deceptive pricing say a reference ('was') price should reflect a price the item was genuinely offered at. An inflated anchor used to make a markdown look bigger can be treated as a fake discount. The UK applies the same principle under the Consumer Protection from Unfair Trading Regulations 2008. Rules vary, so check local guidance.
Sources: Khan Academy, Percent word problems; Maths is Fun, Percentages.
Disclaimer: Examples are illustrative. Actual promotions may include stacked or conditional discounts; verify the final price 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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