Scope and assumptions
Comparing a percentage-off vs a fixed-dollar-off on the same item; single discount each.
A $20-off coupon and a 25% tag are not rivals in any fixed sense. On a $40 item the coupon wins; on a $200 item the percentage wins by a distance. Somewhere between them the two deals tie exactly, and that price is the only thing you need to work out.
Set the two equal
The crossover is where the savings match:
Rate × Price = Fixed dollars Crossover Price = Fixed ÷ Rate
For 25% off versus $20 off: 20 ÷ 0.25 = $80. At $80 both deals save exactly $20.
Who wins on either side
| Item price | 25% off saves | $20 off saves | Better deal |
|---|---|---|---|
| $40 | $10.00 | $20.00 | $20 off |
| $60 | $15.00 | $20.00 | $20 off |
| $80 | $20.00 | $20.00 | tie |
| $120 | $30.00 | $20.00 | 25% off |
| $200 | $50.00 | $20.00 | 25% off |
The pattern is structural: a fixed amount is a bigger share of a small price, and a percentage is a bigger absolute amount on a large one.
Why the percentage always wins eventually
A percentage grows with the price; a fixed discount doesn't. So no matter how large the fixed amount, there's a price above which the percentage overtakes it. The crossover tells you where, and it's always Fixed ÷ Rate.
| Deal A | Deal B | Crossover | Wins below | Wins above |
|---|---|---|---|---|
| 10% off | $15 off | $150 | $15 off | 10% off |
| 15% off | $10 off | $66.67 | $10 off | 15% off |
| 30% off | $40 off | $133.33 | $40 off | 30% off |
| 50% off | $30 off | $60 | $30 off | 50% off |
A larger fixed amount pushes the crossover higher, which means the fixed deal wins across more of the price range — but never all of it.
The comparison that doesn't need a crossover
When both offers are percentages off the same list price, skip the analysis: 30% beats 25% at every price. The crossover exists only because a fixed dollar amount and a percentage scale differently. Two percentages scale identically.
Comparisons That Pick the Wrong Deal
Assuming the percentage is always the better deal; assuming a big fixed discount always wins; comparing a fixed amount against a percentage without computing the crossover; ignoring minimum-spend conditions that may put the coupon out of reach; forgetting that stacking changes both sides; and eyeballing rather than dividing.
Related discount guides
Comparing deals. For the single-discount price-to-pay method see Sale Price After Percent Off, and for the full formula index start at the hub: Discount Formula.
FAQ
How do I compare two percentage discounts against each other? Directly — when both are percentages off the same list price, the larger number wins at every price. The crossover problem only arises with fixed-dollar deals.
How do I compare a percentage off with a buy-one-get-one offer? Convert the BOGO to a percentage first. Two items for the price of one is 50% off the pair; three for two is 33.3%.
What if the fixed-dollar coupon has a minimum spend? Then it only exists above that threshold. Check whether the minimum sits above or below the crossover, because a coupon you can't use has no value at any price.
Does sales tax change which deal wins? No. Tax applies to whichever discounted price you reach, so it scales both outcomes and leaves the comparison unchanged.
Are comparative discount claims legally checked? They're constrained. The FTC's guides against deceptive pricing and the UK's Consumer Protection from Unfair Trading Regulations 2008 require comparison prices to be genuine. A 'was $X, now $Y' claim can be challenged if $X was never actually charged.
Sources: Khan Academy, Percent word problems; Maths is Fun, Percentages.
Disclaimer: Illustrative. Real offers may combine or cap discounts; verify at checkout. Informational only.
Frequently asked questions
How do I compare two percentage discounts against each other?
Directly — when both are percentages off the same list price, the larger number wins at every price. The crossover problem only arises with fixed-dollar deals.
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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