Key facts
- Markup and margin measure the same profit against different numbers: markup uses the cost, margin uses the selling price.
- A 30% markup on a cost of 100 gives a selling price of 130 and a margin of 23.08%.
- Markup can exceed 100%; a margin can approach 100% but never reach it.
- To earn a 25% margin on a cost of 60, the selling price must be 80, not 75.
- Discounts of 20% then 10% come to 28% off in total, because the multipliers multiply.
Profit, markup and margin
Profit is the simplest of the three: selling price minus cost. A job that costs you 60 to deliver and sells for 80 makes a profit of 20. The other two figures are ways of expressing that same 20 as a percentage, and the choice of base number is what causes most confusion in trade pricing.
Markup measures profit against the cost. Margin measures profit against the selling price. Both answer a different question: markup tells you how much you added, margin tells you how much of every pound of selling price is left after the cost is paid for.
| Measure | Formula | Value |
|---|---|---|
| Profit | price − cost | 30 |
| Markup | profit ÷ cost × 100 | 30% |
| Margin | profit ÷ price × 100 | 23.08% |
The two percentages are only equal when there is no profit. Any profit at all makes the margin smaller than the markup, because profit is always a smaller share of the selling price than of the cost. A margin of 30% would need the price to be 100 ÷ 0.7 = 142.86, which is a 42.86% markup.
Converting a markup into a margin
Given a markup percentage, divide it by 100 plus itself: margin = markup ÷ (100 + markup) × 100. For a 30% markup that is 30 ÷ 130 × 100 = 23.08%, matching the calculation above.
| Markup | Selling price | Margin |
|---|---|---|
| 25% | 125 | 20% |
| 50% | 150 | 33.33% |
| 100% | 200 | 50% |
| 200% | 300 | 66.67% |
The margins above are shown to two decimal places where they do not terminate. Doubling the markup from 50% to 100% does not double the margin from 33.33% to 66.67%; it reaches 50%, because the base of the percentage has grown too.
Converting a margin into a markup
The reverse conversion divides by what is left after the margin: markup = margin ÷ (100 − margin) × 100. A target margin of 40% means markup = 40 ÷ 60 × 100 = 66.67%. A target margin of 50% means a markup of exactly 100%, which is the one case where the two figures agree.
Why a margin never reaches 100%
A margin of 100% would mean the cost was zero, because profit equals the whole selling price only when the cost is nil. As the price rises the margin climbs towards 100% but never arrives at it: at a 1,000% markup on a cost of 100, the price is 1,100 and the margin is 1,000 ÷ 1,100 = 90.91%. Markup, by contrast, has no such ceiling, since the price can be many times the cost.
To express a margin as markup, divide the margin by 100 minus the margin and multiply by 100. The NumberUtils profit margin calculator gives the margin and the profit from a cost and a selling price, and the markup calculator turns a markup percentage into a selling price.
Setting a price for a target margin
Working backwards from a margin is the most useful of these conversions, because it is what pricing a quote requires. Divide the cost by 1 minus the margin as a decimal: price = cost ÷ (1 − margin ÷ 100).
For a cost of 60 and a target margin of 25%, that gives 60 ÷ 0.75 = 80. Pricing at 75 instead would be adding 25% to the cost, a 25% markup, and would leave a margin of 15 ÷ 75 = 20%.
The formula needs a margin below 100%, since a margin of 100% divides by zero and cannot be reached at any price. A margin of 50% on a cost of 240 needs a price of 480; a margin of 60% needs 240 ÷ 0.4 = 600.
Discounts
A discount works on the selling price rather than the cost: sale price = price × (1 − discount ÷ 100). A 25% discount on the 80 above gives 80 × 0.75 = 60, saving 20 and cutting the margin from 25% to zero, because the price has fallen back to the cost. The NumberUtils discount calculator returns both the reduced price and the amount saved, and accepts any discount from 0% up to 100%, since a discount larger than the full price is not a discount at all.
Stacked discounts multiply, they do not add
Two successive discounts compound. Taking 20% off and then a further 10% off leaves 0.8 × 0.9 = 0.72 of the price, so the total reduction is 28%, not the 30% that adding the two percentages suggests. Two 20% discounts leave 0.8 × 0.8 = 0.64, a 36% reduction, where addition would imply 40%.
A discount that cancels a markup
Marking up 25% and then discounting 20% returns the price exactly to cost, because 1.25 × 0.8 = 1. On a cost of 60 that is 75 marked up, then 60 after the discount. More generally, the discount that undoes a markup of m is m × 100 ÷ (100 + m), which is why a 25% markup pairs with a 20% discount and not with 25%. The percentages guide explains why successive percentage changes behave this way: the second percentage is applied to a base that has already moved.
Selling below cost
A selling price lower than the cost produces a negative margin, which is a loss. A cost of 60 sold at 50 gives a margin of (50 − 60) ÷ 50 × 100 = −20%, and the figure means that 20 pence in every pound of selling price was lost rather than earned. Because the markup calculator only accepts a markup percentage of zero or more, a below-cost price is expressed as a discount rather than as a negative markup.
The calculation rules behind all of this, including how discounts, markups and margins are defined and bounded, are set out in the commercial mathematics methodology.