Margin vs. markup arithmetic

Margin and markup are the two percentages a business attaches to a single sale, and they are endlessly swapped for each other. They describe the same profit — the gap between what an item cost and what it sold for — but they divide that profit by different numbers, so the same sale reports two different percentages. This guide works through the arithmetic the profit margin calculator and the markup calculator perform, shows the exact identity that converts one percentage into the other, and names the misreadings that cost money. Every figure on this page is computed at build time by the same engine behind those tools; see the other guides for the sibling topics.

Two formulas that share a numerator

Both percentages start from gross profit, which is just selling price minus cost. Take the recurring example of a cost of 60 sold for 100: the profit is 40. Margin and markup then part ways only on what they divide that 40 by.

• Margin divides profit by the selling price: margin% = (price − cost) ÷ price × 100. Here 40 ÷ 100 × 100 = 40%. It answers the question "of every unit of money a customer hands over, how much do I keep?"
• Markup divides the same profit by the cost: markup% = (price − cost) ÷ cost × 100. Here 40 ÷ 60 × 100 = 66.67%. It answers "starting from what the item cost me, what percentage did I add on top?"

The profit margin calculator reads a cost and a price and returns gross profit of 40, a margin of 40%, and the equivalent markup of 66.67% beside it. That is the whole confusion in one line: the identical sale is a 40% margin and a 66.67% markup, and neither number is wrong — they answer different questions.

Why markup is always the larger percentage

For any profitable sale the markup percentage comes out higher than the margin percentage, and the reason is purely which denominator each one uses. Cost is smaller than price whenever the sale makes money, so dividing the profit by cost (markup) yields a larger quotient than dividing the same profit by the larger price (margin). The gap is not fixed: it widens as the sale gets more profitable. A cost of 40 sold at 100 is a 60% margin but a 150% markup — the markup is well past 100% while the margin cannot reach it, because profit of 60 is more than the 40 cost it is measured against but can never be more than the 100 price that contains it.

The identity that converts one into the other

Because both percentages are built from the same profit, there is an exact algebraic identity between them — no lookup table needed:

• margin% = markup% ÷ (100 + markup%) × 100
• markup% = margin% ÷ (100 − margin%) × 100

The engine demonstrates both directions. Price a 100 cost at a 25% markup and it sells for 125; the 25 profit is 20% of that price, so a 25% markup is a 20% margin. Run it the other way: a sale with a 20% margin — cost 80, price 100 — reports a 25% markup, and a 25% margin — cost 75, price 100 — reports a 33.33% markup. The two formulas are inverses of each other, which is why a page that shows one figure can always show the other beside it.

A conversion table, every figure computed

Setting a cost of 100 and feeding a series of markups to the engine makes the relationship concrete. The markup column is the labelled input; the price, profit, and margin columns are engine outputs, each computed at build time:

Reading down the margin column shows how slowly it climbs against the markup: doubling the cost (a 100% markup) is only a 50% margin, and even tripling the price (a 200% markup) stops at a 66.67% margin. The margin can approach 100% but never arrives, because some cost always remains inside the price.

Where the displayed digits come from

A 50% markup is a useful case for seeing how the figures are rounded. On a 100 cost it prices the item at 150, and the margin works out to one third — a decimal that never terminates. The engine keeps the full-precision value and the tool normalizes it before display, showing 33.333333% to six decimal places rather than a truncated or endlessly repeating figure. On this page the same value is shown to two places as 33.33% for readability. Both are the one-third margin; they differ only in how many digits are printed, which is exactly the displayed-rounding-versus-internal-precision distinction the methodology page documents.

Common misreadings

The confusion is rarely an arithmetic slip; it is a base error — the right profit divided by the wrong denominator. A few recur:

• Quoting a markup as a margin. A 66.67% markup read aloud as a "66.67% margin" overstates how much of each sale is kept; the real margin on that sale is 40%.
• Targeting a margin but applying a markup of the same number. Wanting a 20% margin and adding a 20% markup instead lands short — a 20% markup is only a 16.67% margin once cost is above zero, so the shop prices lower than it meant to and gives away profit on every unit. To actually reach a 20% margin, the markup has to be 25%.
• Expecting the two percentages to be symmetric. Converting back and forth is not addition and subtraction of the same number; it is the identity above, which bends more as the figures grow. At small percentages the margin and markup look close; by the time a sale is a 150% markup it is a 60% margin — a gap of tens of points.
• Comparing a margin on one product with a markup on another. Two products can look similarly profitable and not be, if one figure is a margin and the other a markup. Put both on the same base before comparing.

When the sale loses money

Neither percentage stops working when the price falls below cost; both simply go negative. A cost of 100 sold for 80 loses 20 on the sale, which the engine reports as a -25% margin and a -20% markup. The two negative percentages still differ for the same reason the positive ones do — different denominators — and the identity between them continues to hold. A clearance price below cost is the everyday case, and the arithmetic treats it as an ordinary result rather than an error, so the sign itself tells you the sale lost money.

Frequently asked questions

Every figure here is computed in the browser by the same tested engine that powers the calculators, on fictional example inputs; nothing you enter into the tools is transmitted anywhere. These are the general mathematical definitions of margin and markup — the calculator implements the general definition, and your jurisdiction's or contract's conventions may differ. Implementation details and the rounding policy are on the methodology page.