Margin, markup, and the price each one needs

What this works out

The profit on a sale, and the two percentages people use to describe it. Type a cost and a price and it gives you both; type a cost and a target and it gives you the price that hits it.

The table underneath shows the price and the equivalent markup for a range of target margins, which is the conversion worth keeping.

One profit, two percentages

This is the whole tool, and it is worth being precise about:

cost 60, sold for 100

profit  = 100 - 60 = 40
margin  = 40 / 100 = 40%     <- against the price
markup  = 40 /  60 = 66.67%  <- against the cost

Same transaction. Same 40 of profit. Two percentages, because they are measured against two different things.

Markup is always the larger number, and the gap widens as the figures rise:

Margin	Markup
10%	11.11%
20%	25%
25%	33.33%
33.33%	50%
40%	66.67%
50%	100%
60%	150%
75%	300%

At the bottom of the table they are nearly the same and the confusion costs little. At the top they diverge without limit, because margin has a ceiling of 100% that it can never reach and markup has no ceiling at all.

The mistake this exists to prevent

Setting a target in margin and applying it as a markup.

target: a 40% margin on a cost of 60

right:  60 / (1 - 0.40) = 100     profit 40, margin 40%
wrong:  60 x (1 + 0.40) =  84     profit 24, margin 28.57%

Sixteen less profit on every unit, and nothing about the wrong answer looks wrong. The price is plausible, the arithmetic is simple, and the shortfall only appears in the accounts a quarter later.

The error grows with the target. At a 60% margin, adding 60% to the cost lands at 37.5%. At 75%, it lands at 43%.

1. margin = profit / price

   The definition. The profit is measured against the price — the number you do not have yet.

2. price - cost = profit

   And the profit is whatever the price leaves after the cost.

3. price x (1 - margin) = cost

   Substitute and rearrange. The cost is the share of the price the margin does not take.

4. price = cost / (1 - margin)

   Divide. A 40% margin on a cost of 60 is 60 / 0.6 = 100, not the 84 that adding 40% gives.

Figure	Cost plus 40%a 40% markup	Priced for a 40% margin	Difference
Selling price	84.00	100.00	+16.00
Profit	24.00	40.00	+16.00
Margin it actually makes	28.57%	40.00%	+11.43%
Markup it actually is	40.00%	66.67%	+26.67%

Adding 40% to the cost makes a 28.57% margin, not a 40% one. To make a 40% margin on a cost of 60 you have to add 66.67%. The gap widens as the target climbs, and at a 50% margin the markup is 100% — which is where the two words are furthest apart and most often swapped.

Selling price

100

Markup needed

66.67%

Profit

40

Target margin

40%

Every value

Target margin	Selling price	Markup needed	Profit
5%	63.16	5.26%	3.16
10%	66.67	11.11%	6.67
15%	70.59	17.65%	10.59
20%	75	25.00%	15
25%	80	33.33%	20
30%	85.71	42.86%	25.71
35%	92.31	53.85%	32.31
40%	100	66.67%	40
45%	109.09	81.82%	49.09
50%	120	100.00%	60
55%	133.33	122.22%	73.33
60%	150	150.00%	90
65%	171.43	185.71%	111.43
70%	200	233.33%	140
75%	240	300.00%	180
80%	300	400.00%	240

Solving for a price is a division, because the margin is measured against the thing you do not have yet. That is the same shape as taking a tax out of an inclusive total, and wrong in the same way if you subtract instead of divide.

Which one to use

Set targets in margin. Apply them in markup.

Margin is what matters, because it is the share of revenue that survives and it compares products with completely different costs. Markup is what you can act on at the counter, because it works forward from a number you already have.

That is why the two exist and why both are quoted: suppliers and buyers talk in markup because they are working up from a cost they just paid, and finance talks in margin because it is working down from revenue. The same sale, described from both ends, which is exactly how a target set in one gets applied in the other.

A worked example

From a cost and a price. 60 in, 100 out:

Profit	40.00
Selling price	100.00
Margin	40.00%
Markup	66.67%

From a target margin. The same 40%, applied to a cost of 60, gives a price of exactly 100 — the two modes agree, and a test asserts that they do.

From a target markup. 40% added to a cost of 60 gives 84.00, a profit of 24.00 and a margin of 28.57%. This is the wrong-direction case, and it is in the tool so the size of the error is visible rather than described.

The discount case. Ten per cent off that 100 leaves a price of 90, a profit of 30 and a margin of 33.33%. A tenth off the price, a quarter off the profit.

These are the same figures asserted in this tool’s test file, so the page and the formula cannot drift apart without the build going red.

What it does not do

It does not decide what belongs in the cost — direct costs give a gross margin, everything-in gives a net margin, and the arithmetic is identical either way, so the label on the answer is yours. It does not model discounts, returns, shrinkage, payment processing or tax. It prices one unit rather than a mix, and a blended margin across a range is not the average of the individual ones.

For the general question of what a percentage is measured against, the percentage calculator is the tool, and it is the same idea underneath.

From a cost and a price:
  profit = price - cost
  margin = profit / price
  markup = profit / cost

Setting the price from a target:
  from a margin   price = cost / (1 - margin)
  from a markup   price = cost x (1 + markup)

Converting one percentage to the other:
  markup = margin / (1 - margin)
  margin = markup / (1 + markup)

round = to the nearest minor unit for money,
        and to two places for the percentages.