Margin vs. markup: formulas, conversion chart and discounts

What is the difference between margin and markup?

Markup states an item’s profit (selling price minus cost) as a percentage of the cost; margin states the same profit as a percentage of the selling price. Whenever you make a profit, the price is larger than the cost, so the margin is always the smaller percentage.

An item that costs $13.20 and sells for $24.00 earns $10.80, which is an 81.82% markup but a 45% margin.

$P$ is the selling price before sales tax and $C$ is what the item cost you. Multiply either result by 100 for a percentage.

A few related terms get mixed up with these two:

• Gross margin is the margin above: price minus the cost of the goods. For a whole business, the gross profit margin ratio is (net sales − cost of goods sold) ÷ net sales.
• Operating expenses such as rent, wages and advertising come out of the gross margin afterwards. What is left is income from operations, so a 45% gross margin is not 45% profit.
• Contribution margin, used for break-even, subtracts every variable cost per unit, not only the product cost. It equals the gross margin only when the product cost is the only cost that rises with each sale.
• Markup on selling price is another name for margin in some business-math textbooks. When someone quotes a markup, check whether they divided by cost or by price.

How do you convert markup to margin, and margin to markup?

Write both as decimals (45% is 0.45), then use:

These come straight from the definitions. A markup $k$ sets the price at $C(1 + k)$, and the profit $Ck$ divided by that price is $k/(1 + k)$. Check it on the candle: its markup is $10.80 ÷ $13.20 = 0.8182, and 0.8182 ÷ 1.8182 = 0.45, the 45% margin found above.

Markup to margin conversion chart

Margin to markup conversion chart

The required markup climbs steeply as the margin target rises, because the cost becomes a thinner slice of the price. Moving from a 50% to a 75% margin means moving from a 100% to a 300% markup, and a 90% margin needs a 900% markup.

How do you set a price for a target margin?

Divide the cost by one minus the margin:

Worked example. The inputs are example assumptions: a shop buys a candle from a wholesaler for $13.20 and wants a 45% gross margin on it.

1. One minus the margin: 1 − 0.45 = 0.55.
2. Price: $13.20 ÷ 0.55 = $24.00.
3. Check: profit is $24.00 − $13.20 = $10.80, and $10.80 ÷ $24.00 = 45%. The markup is $10.80 ÷ $13.20 = 81.82%.

The expensive mistake is multiplying the cost by 1.45, which applies the 45% target as a markup:

The size of the miss is predictable. Priced correctly, the profit is $C \times m/(1 - m)$; priced with the margin used as a markup, it is $C \times m$. The mistake therefore keeps only $(1 - m)$ of the profit you planned: 55% of it at a 45% target ($5.94 instead of $10.80), and less the higher the target.

Two checks before the price goes on the shelf:

• Rounding. If you round to a price point, recalculate the margin. At $23.99 the candle’s margin is 44.98%, not 45%.
• Sales tax. Use the price before tax. In the US, sales tax is set by states and localities and added on top of your price, so it is not part of your margin.

How does a discount change your margin?

A discount comes entirely out of profit, because the item’s cost does not change. Take 15% off the $24.00 candle:

1. Discount: $24.00 × 0.15 = $3.60, so the sale price is $20.40.
2. Profit: $20.40 − $13.20 = $7.20, down from $10.80. That is a third less profit per candle (33.33%).
3. Margin: $7.20 ÷ $20.40 = 35.29%, down from 45%.

With the starting margin $m$ and the discount $d$ as decimals, the new margin is:

For the candle, (0.45 − 0.15) ÷ 0.85 = 35.29%. Two things follow:

• The margin fell by 9.71 percentage points, but profit per candle fell by 33.33%. The margin percentage understates what a sale costs you (the gap between points and percent is one of the common percentage mistakes).
• The deepest discount you can offer before selling at cost equals your margin, not your markup. At a 45% margin (an 81.82% markup), 45% off prices the candle at exactly $13.20.

When only some units sell at the sale price, the margin you actually earn is total gross profit ÷ total revenue. Suppose 80% of candles sell at $24.00 and 20% at $20.40. The average profit is $10.08 on average revenue of $23.28 per candle, a 43.30% margin. Business-math texts call that average profit per unit the maintained markup.

Weighting the two margins by units instead (0.8 × 45% + 0.2 × 35.29%) gives 43.06%, slightly off because each margin is a share of a different price. A plain average of the two, 40.15%, also ignores that most candles sold at full price.

How many more units do you need to sell after a discount?

To keep the same gross profit, unit sales must rise by the factor $m/(m - d)$, which is an increase of $d/(m - d)$. For the candle, 0.45 ÷ 0.30 = 1.5, so the shop needs 50% more unit sales during the discount just to earn the same gross profit.

Extra unit sales needed to keep the same gross profit, by the margin before the discount:

A 30% discount on a 30% margin sells at cost, so no amount of extra volume restores the profit. The thinner the margin, the more volume each point of discount has to buy back.

What does a discount do to break-even and profit?

A discount cuts what each sale contributes toward fixed costs, so break-even rises and profit at your usual volume falls much faster than the margin does. Break-even units are fixed costs ÷ (price − variable cost per unit). More example assumptions: the shop’s fixed costs are $2,700 a month, the $13.20 wholesale cost is the candle’s only variable cost, and the shop normally sells 400 candles a month at full price.

The arithmetic: 400 × $10.80 − $2,700 = $1,620 at full price, and 400 × $7.20 − $2,700 = $180 on sale. The margin only slipped from 45% to 35.29%, yet profit after fixed costs fell by 88.89% at the same volume, because the fixed costs don’t shrink with the price. To earn the same $1,620 on sale, the shop has to sell 600 candles and take in $12,240 instead of $9,600: more revenue, more stock and more orders for the same profit.

Whether the sale is worth it depends on whether it actually brings in those extra buyers, and the arithmetic can’t tell you that.

Can margin be negative, or more than 100%?

Margin is capped at 100%, and it gets there only if the item costs nothing. For anything with a cost, a target margin of 100% or more has no price that achieves it: the formula would divide by zero or by a negative number. Markup has no upper limit.

Below cost, both turn negative, but they run out of room in opposite directions:

• Markup can’t fall below −100%, which means giving the item away. Margin has no floor: it keeps falling as the price nears zero and can’t be calculated at zero, because there is no price to divide by.
• When the cost is zero, the reverse happens: margin is 100% on any positive price and markup can’t be calculated, because there is no cost to divide by.

Which should you use, margin or markup?

Neither is more correct. They answer different questions, and the losses come from mixing them up.

• Markup is quick when you price from cost: one multiplier (1.5 for a 50% markup) turns every cost into a price. Many firms use it internally because their records start from cost.
• Margin tells you what share of each sales dollar is left for operating expenses and profit. It matches the gross profit margin on an income statement, and it is the number to hold up against a discount.
• Say which base you mean. A margin target applied as a markup, or a supplier’s suggested markup compared with your margin goal, is where the money goes. Write “45% margin” or “81.82% markup on cost”, never just “45%”. Across several products, add up the profit and the revenue and divide, rather than averaging the percentages.

What do these formulas leave out?

• Cost per unit is treated as fixed. Supplier volume pricing, freight and exchange rates can move it.
• Other per-sale costs are left out. If you pay packaging, shipping or fees charged as a percentage of each sale, those are variable costs too. Add them to the variable cost when you work out break-even; they make the real profit per unit lower than price minus product cost.
• Fixed costs are assumed flat. That only holds within the relevant range. Selling 600 candles instead of 400 might need more staff, space or equipment.
• Demand isn’t modeled. The unit targets say how many sales you would need, not whether customers will buy them.
• Returns and damaged stock reduce the margin you actually keep below the one you priced for.

Try it

• In the margin and markup calculator, under What you know choose Cost and margin: find price, then enter a cost of 13.20 and a profit margin of 45: the selling price is $24.00, the profit $10.80 and the markup 81.82%. Add a sale discount of 15 to see the $20.40 sale price, a 35.29% margin at that price (54.55% markup) and 1.5 times the unit sales needed for the same profit. For the mistake, clear the sale discount, choose Cost and markup: find price and enter a markup of 45: the price is $19.14 and the margin 31.03%.
• In the discount calculator, enter an original price of 24 and 15 as the percent off: the sale price is $20.40 and you save $3.60.
• In the break-even calculator, press Reset first, because the example carries its own target profit and expected sales. Then enter monthly fixed costs of 2,700, a price per unit of 24 and a variable cost per unit of 13.20. Break-even is 250 units, with break-even revenue of $6,000.00. Add a target profit of 1,620 to get 400 units. Change the price to 20.40 and break-even rises to 375 units, with 600 needed for the same target profit.