Scope and assumptions
Markup % is on cost; discount % is on the selling (list) price. Same numeric percent, different base.
A 20% markup followed by a 20% discount sounds like a round trip. It isn't. You start at $50 cost, mark up to $60, discount back to $48, and end up two dollars below where you began — having done nothing obviously wrong.
The culprit is the base. Markup climbs from cost; discount falls from price. Once those two numbers differ, equal percentages stop being equal.
Two percentages, two anchors
| Term | Measured against | Formula |
|---|---|---|
| Markup | Cost | Price = Cost × (1 + markup) |
| Discount | Selling price | Sale = Price × (1 − discount) |
| Margin | Selling price | Margin = (Price − Cost) ÷ Price |
Markup and discount are opposites in direction. Markup and margin share a base but not a numerator — which is a third source of confusion worth keeping separate.
The same 20%, twice
- Cost $50, 20% markup → 50 × 1.20 = $60
- Then 20% discount → 60 × 0.80 = $48
Twenty percent of $50 is $10; twenty percent of $60 is $12. The discount removes two more dollars than the markup added, and that asymmetry is the whole story.
Why they never cancel
For a markup and a discount to cancel exactly, the discount would have to be measured against the marked-up price with a rate of:
Discount needed = 1 − 1 ÷ (1 + markup)
At 20% markup that's 1 − 1/1.2 ≈ 16.7%. Apply 16.7% off $60 and you land on $50. Apply 20% and you land on $48.
So a markup of m is undone by a discount of about m ÷ (1 + m) — always slightly smaller than m. Never equal.
Markup versus margin
This pair is confused just as often, and the conversion is worth memorising:
- 25% markup → 25 ÷ 1.25 = 20% margin
- 50% markup → 50 ÷ 1.5 = 33.3% margin
A business that says "we run on 25%" without naming the base can be describing two quite different levels of profitability.
Using both deliberately
Set prices upward from cost using markup, then model promotions downward from price using discount. A $50 product marked up 20% to $60, then discounted 20%, nets $48 — below cost on paper, before any overhead. The arithmetic isn't pessimistic; it's what equal percentages actually do.
Running the cancellation formula before announcing a sale is the cheap safeguard: if you plan to discount, know what markup you need to survive it.
Why Markup and Discount Get Confused
Assuming a markup and an equal discount cancel; applying the discount to cost rather than price; mixing the two formulas in one calculation; quoting a single percentage without naming its base; treating markup and margin as synonyms; and expecting a "matched" promo to preserve the original price.
Related discount guides
Markup and discount share the "%" sign but not the base. For the full discount formula index start at the hub: Discount Formula; for the price-to-pay method see Sale Price After Percent Off.
FAQ
What discount percentage exactly cancels a 30% markup? About 23.1%. The cancellation condition is 1 − 1 ÷ 1.3 = 0.2308, so a 30% markup is undone by roughly a 23% discount — never by 30%.
Is a 50% discount the same as a 100% markup? No. A 100% markup doubles the cost; a 50% discount halves the price. They can look numerically related and describe unrelated moves.
How do I convert markup percentage into margin percentage? Margin = markup ÷ (1 + markup). A 25% markup is a 20% margin.
Why do pricing errors cluster around these two terms? Because both are called percentages and both describe prices, but they're measured from different bases. Quoting a number without its base is the actual mistake.
Is it legal to show a 'discount' from a made-up higher price? No. In the US the FTC's guides against deceptive pricing treat a fabricated reference price as a fake discount, and the UK's Consumer Protection from Unfair Trading Regulations 2008 prohibit the same practice. A '50% off' means little if the anchor was never charged.
Sources: Investopedia, Markup; Khan Academy, Percent word problems.
Disclaimer: Illustrative. Real pricing also includes overhead, taxes, and margins; consult a bookkeeper. Informational only.
Sources and references
- Investopedia — Markuphttps://www.investopedia.com/terms/m/markup.asp
- Khan Academy — Percent word problemshttps://www.khanacademy.org/math
- FTC — Guides Against Deceptive Pricinghttps://www.ftc.gov/business-guidance/resources/guides-against-deceptive-pricing-practices
Maintenance and corrections
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