Enter the two you know out of cost, revenue, margin (%) and profit, leave the others blank, and press "Calculate". The blank fields and the markup are calculated, and a pie chart shows how the revenue breaks down.
Fill in exactly two fields (three or more cannot be calculated). Enter the margin as a percentage (for 25%, enter "25"). If revenue is below cost (a loss), profit and margin are calculated as negative values.
Result and graph
Enter values in two of the fields on the left and press "Calculate". The result and a pie chart will appear here.
Table of Contents
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What you can do on this page
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What is this calculation used for?
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How to Use
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Formulas and figures
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Symbols and terms
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Good to know before you start
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How to calculate it in Excel
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How to calculate it in Google Sheets
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How to calculate it in Python
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How to write it in LaTeX and other math languages (copy and paste)
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How to have ChatGPT do the calculation
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DataChef Features
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Related Features
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NumberChef Calculators List
What you can do on this page
- Enter any two of cost, revenue, margin (%) and profit, and the other two are calculated, along with the markup (profit as a percentage of cost)
- "If I buy at $12 and sell at $16, what is my margin?" "What price gives a 20% margin on a $10 cost?" - pricing and profit questions answered in one place
- A pie chart shows at a glance how revenue splits into cost and profit
- A plain-language explanation of the formulas and copy-and-paste formulas for Excel, Google Sheets and Python are all on this page
On this page, "margin" is profit as a percentage of revenue (profit margin). Profit as a percentage of cost is shown separately as "markup". Cost and revenue must be greater than 0, and the margin must be under 100% (any currency works).
What is this calculation used for?
Pricing handmade goods and resale items (side business)
Say an item costs you $8 in materials and shipping, and you want a 40% margin. The price is \(8 \div (1 - 0.4) \approx 13.33\) dollars, so a price of about $13.50 works.
If you just pick $10, the margin is only 20% (a $2 profit), and after marketplace fees almost nothing is left. The numbers help you avoid that mistake before you list the item.
How the restaurant "30% food cost" rule sets menu prices
Restaurants often aim for a food cost of about 30% of the menu price. A 30% food cost is the same as a 70% gross margin, so a dish with $3 of ingredients is priced at \(3 \div 0.3 = 10\) dollars.
"$10 for $3 of food?" you may think, but the restaurant pays wages, rent and utilities out of the remaining $7 of gross profit. This formula shows how restaurant prices work.
Reading the operating margin in earnings news (financial literacy)
If the news says "revenue of $100 billion and operating income of $8 billion", the operating margin is \(8 \div 100 \times 100 = 8\)% (operating income is gross profit minus operating expenses such as wages).
Typical margins vary a lot by industry, but the calculation "profit ÷ revenue × 100" is the same as on this page. With this, you can judge for yourself how well a company makes money, whether you are investing or choosing where to work.
Not confusing a "20% markup" with a "20% margin" (business practice)
If you mark up a $1,000 item by 20% and sell it for $1,200, the markup is 20%, but the margin is only \(200 \div 1200 \times 100 \approx 16.67\)%. If your goal is a 20% margin, the right price is \(1000 \div 0.8 = 1250\) dollars.
It looks like a small difference, but on $10 million in sales it adds up to more than $300,000 in profit a year. It is a well-known mix-up in real businesses.
Knowing how far a markdown can go (still profitable at half price?)
A deli sandwich that costs $1.50 to make and sells for $5 has a margin of \((5 - 1.5) \div 5 \times 100 = 70\)%. Even at half price, $2.50, just before closing, the margin is \((2.5 - 1.5) \div 2.5 \times 100 = 40\)%, so it still makes money.
But a discount that takes the price below the $1.50 cost means a loss. This calculation is behind a store's decision that "half price is better than throwing it away".
Formulas and figures
Formula for profit
Figure
Standard notation
(the usual math form)
\(P\)
\(=\)
\(R\)
\(-\)
\(C\)
In words
(symbols replaced with words)
③
\(P\): profit
\(=\)
①
\(R\): revenue
\(-\)
②
\(C\): cost
The formula in words
①
From the
\(R\): revenue
,
②
subtract the
\(C\): cost
,
③
and you get the
\(P\): profit
Quick example
The profit on an item bought for $1,200 and sold for $1,600 is
\(P\): profit
\(=\)
revenue ($1,600)
\(-\)
cost ($1,200)
\(1600 - 1200 = 400\)
Key idea
The "profit" here is revenue minus only the cost of the goods, which is called gross profit. It is the profit before expenses such as wages and rent, so a business pays those expenses out of its gross profit, and what is left is its final profit (net profit).
Formula for the profit margin
Figure
Standard notation
(the usual math form)
\(M\)
\(=\)
\(P\)
\(\div\)
\(R\)
\(\times\)
\(100\)
In words
(symbols replaced with words)
④
\(M\): margin (%)
\(=\)
①
\(P\): profit
\(\div\)
②
\(R\): revenue
\(\times\)
③
\(100\): percent base
The formula in words
①
Take the
\(P\): profit
②
divide it by the
\(R\): revenue
,
③
multiply by the
\(100\): percent base
to turn it into a percent,
④
and you get the
\(M\): margin (%)
Quick example
The margin when the profit is $400 and the revenue is $1,600 is
\(M\): margin (%)
\(=\)
profit ($400)
\(\div\)
revenue ($1,600)
\(\times\)
\(100\)
\(400 \div 1600 \times 100 = 25\ \ (25\%)\)
Key idea
The margin tells you what percent of revenue is profit. The key point is that you divide by revenue. It is easy to confuse with the markup in the next formula, which divides by cost. The "operating margin" you see in business news also uses revenue as the base in the same way.
Formula for markup
Figure
Standard notation
(the usual math form)
\(K\)
\(=\)
\(P\)
\(\div\)
\(C\)
\(\times\)
\(100\)
In words
(symbols replaced with words)
④
\(K\): markup (%)
\(=\)
①
\(P\): profit
\(\div\)
②
\(C\): cost
\(\times\)
③
\(100\): percent base
The formula in words
①
Take the
\(P\): profit
②
divide it by the
\(C\): cost
,
③
multiply by the
\(100\): percent base
to turn it into a percent,
④
and you get the
\(K\): markup (%)
Quick example
The markup when the profit is $400 and the cost is $1,200 is
\(K\): markup (%)
\(=\)
profit ($400)
\(\div\)
cost ($1,200)
\(\times\)
\(100\)
\(400 \div 1200 \times 100 \approx 33.33\ \ (33.33\%)\)
Key idea
The markup tells you by what percent the price was raised above cost. For the same sale (cost $1,200, revenue $1,600), the margin is 25% but the markup is about 33.33%. Margin uses revenue as the base and markup uses cost as the base. Only the denominator differs; both describe the same $400 profit.
Formula for revenue (from cost and margin)
Figure
Standard notation
(the usual math form)
\(R\)
\(=\)
\(C\)
\(\div\)
\(\left(1 - \dfrac{M}{100}\right)\)
In words
(symbols replaced with words)
③
\(R\): revenue
\(=\)
①
\(C\): cost
\(\div\)
②
\(1 - M \div 100\): 1 minus the margin as a decimal
The formula in words
①
Take the
\(C\): cost
②
divide it by
\(1 - M \div 100\): 1 minus the margin as a decimal
(the share of revenue that is cost),
③
and you get the
\(R\): revenue
Quick example
The revenue (selling price) that gives a 20% margin on an item that costs $1,000 is
\(R\): revenue
\(=\)
cost ($1,000)
\(\div\)
\(1 - 20 \div 100\)
\(1 - 20 \div 100 = 0.8\)
\(1000 \div 0.8 = 1250\)
Key idea
Wanting a 20% margin does not mean adding 20% to the cost (\(1000 \times 1.2 = 1200\) dollars). That price gives a 20% markup, and the margin is only \(200 \div 1200 \times 100 \approx 16.67\)%. The right price is $1,250. Check: profit \(250\) ÷ revenue \(1250\) × 100 = 20%.
Also, the denominator of this formula is \(1 - M \div 100\), so if the margin \(M\) is 100% or more, the denominator is 0 or less and revenue cannot be found. The shape of the formula itself shows that a profit larger than revenue is impossible.
Profit is "revenue − cost", and the margin is "profit ÷ revenue × 100", a percentage based on revenue. Markup uses cost as the base instead, so the first thing to check is which amount a percentage is based on.
Symbols and terms
Symbols
| \(C\) | see | Cost. What it cost to buy or make the item. (Example - if you bought it for $1,200, \(C = 1200\)) |
| \(R\) | are | Revenue. The money you receive when you sell the item (the selling price). |
| \(P\) | pee | Profit. Revenue minus cost (gross profit). It is found with \(P = R - C\). |
| \(M\) | em | Margin. Profit as a percentage of revenue. It is found with \(M = P \div R \times 100\). |
| \(K\) | kay | Markup. Profit as a percentage of cost. There is no standard one-letter symbol for it, so this page uses \(K\). It is found with \(K = P \div C \times 100\). |
Terms
| profit margin | Profit as a percentage of revenue, often just called "margin". It shows what percent of revenue you keep as profit. The "gross margin", "operating margin" and "net margin" in company earnings reports all use revenue as the base in the same way. |
| markup | Profit as a percentage of cost. It shows by what percent the price was raised above cost. Retailers often set prices by adding a markup to the cost. |
| gross profit | Revenue minus only the cost of the goods. It is the profit before expenses such as wages and rent. "Profit" on this page means gross profit. |
| cost of goods sold (COGS) | What it cost to buy or make the goods you sold. For a store, it is the wholesale price it paid; for a manufacturer, it is the materials and production costs. It is the "cost" on this page. |
| cost percentage | Cost as a percentage of revenue. It adds up to exactly 100% with the margin (cost percentage = 100 − margin). Restaurants use it as "food cost percentage", often aiming for about 30%. |
| revenue (sales) | The money received from selling goods or services. For a single item, it is the selling price. |
Good to know before you start
Here is what helps you use the calculation on this page with real understanding, not just by pressing the button.
| Percents (Grade 6) |
|
| Percent problems: part, whole and percent (Grades 6–7) |
|
| Multiplying and dividing decimals (Grades 5–6) |
|
| Rearranging formulas (Grades 7–8) |
|
How to calculate it in Excel
Copy the whole table below and paste it into cell A1 in Excel. It works as is.
Table to find the profit
| Cost C | 1200 |
| Revenue R | 1600 |
| Profit P | =B2-B1 |
Table to find the margin
| Profit P | 400 |
| Revenue R | 1600 |
| Margin M (%) | =B1/B2*100 |
Table to find the markup
| Profit P | 400 |
| Cost C | 1200 |
| Markup K (%) | =B1/B2*100 |
Table to find the revenue (from cost and margin)
| Cost C | 1000 |
| Margin M (%) | 20 |
| Revenue R | =B1/(1-B2/100) |
After pasting, B1 and B2 are your inputs and B3 is calculated automatically.
B3 shows 400 in the first table (a $400 profit), 25 in the second (a 25% margin), about 33.33 in the third, and 1250 in the fourth (a $1,250 selling price). Just replace B1 and B2 with your own numbers.
B3 shows 400 in the first table (a $400 profit), 25 in the second (a 25% margin), about 33.33 in the third, and 1250 in the fourth (a $1,250 selling price). Just replace B1 and B2 with your own numbers.
How to calculate it in Google Sheets
Copy the whole table below and paste it into cell A1 in Google Sheets. It works as is.
Table to find the profit
| Cost C | 1200 |
| Revenue R | 1600 |
| Profit P | =B2-B1 |
Table to find the margin
| Profit P | 400 |
| Revenue R | 1600 |
| Margin M (%) | =B1/B2*100 |
Table to find the markup
| Profit P | 400 |
| Cost C | 1200 |
| Markup K (%) | =B1/B2*100 |
Table to find the revenue (from cost and margin)
| Cost C | 1000 |
| Margin M (%) | 20 |
| Revenue R | =B1/(1-B2/100) |
The same formulas as in Excel work as is. Copy the whole table, paste it into cell A1, and replace B1 and B2 with your own numbers.
How to calculate it in Python
cost = 1200 # cost
revenue = 1600 # revenue
profit = revenue - cost # profit
margin = profit / revenue * 100 # margin (%)
markup = profit / cost * 100 # markup (%)
print(f"Profit: {profit}")
print(f"Margin: {margin}%")
print(f"Markup: {markup}%")
# Working backward: find the revenue (selling price) from the cost and a target margin
cost2 = 1000 # cost
target_margin = 20 # target margin (%)
revenue2 = cost2 / (1 - target_margin / 100)
print(f"Revenue for a {target_margin}% margin: {revenue2}")
Runs with the standard library only. In this example the profit is 400, the margin is 25.0%, the markup is about 33.33%, and the revenue found by working backward is 1250.0. Replace the cost and revenue at the top with your own numbers and run it.
How to write it in LaTeX and other math languages (copy and paste)
Formula for profit
P = R − C
P = R - C
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>P</mi>
<mo>=</mo>
<mi>R</mi>
<mo>−</mo>
<mi>C</mi>
</mrow>
</math>
P = R - C
r - c
P := R - C;
P = R - C;
P = R - C
Formula for the profit margin
M = P ÷ R × 100
M = \dfrac{P}{R} \times 100
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>M</mi>
<mo>=</mo>
<mfrac><mi>P</mi><mi>R</mi></mfrac>
<mo>×</mo>
<mn>100</mn>
</mrow>
</math>
M = P/R xx 100
p/r*100
M := P/R*100;
M = P/R*100;
M = P/R × 100
Formula for markup
K = P ÷ C × 100
K = \dfrac{P}{C} \times 100
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>K</mi>
<mo>=</mo>
<mfrac><mi>P</mi><mi>C</mi></mfrac>
<mo>×</mo>
<mn>100</mn>
</mrow>
</math>
K = P/C xx 100
p/c*100
K := P/C*100;
K = P/C*100;
K = P/C × 100
Formula for revenue (from cost and margin)
R = C ÷ (1 − M/100)
R = \dfrac{C}{1 - M/100}
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<mi>R</mi>
<mo>=</mo>
<mfrac>
<mi>C</mi>
<mrow><mn>1</mn><mo>−</mo><mi>M</mi><mo>/</mo><mn>100</mn></mrow>
</mfrac>
</mrow>
</math>
R = C/(1 - M/100)
c/(1 - m/100)
R := C/(1 - M/100);
R = C/(1 - M/100);
R = C/(1 - M/100)
How to have ChatGPT do the calculation
You are a calculation assistant for profit and pricing. Do the following calculations by actually running Python code, and base your answer only on the numbers from the execution result (do not answer by mental math or guessing). An item bought for $1,200 is sold for $1,600. Find each of the following: 1. The profit (revenue − cost) 2. The profit margin (profit ÷ revenue × 100, in %) 3. The markup (profit ÷ cost × 100, in %) 4. For a different item: the selling price that gives exactly a 20% margin on a cost of $1,000 (price = cost ÷ (1 − 20/100)) Show the formulas you used and the numbers from the execution result.
How to Use
-
1Enter your numbersType the numbers you want to calculate with into the input fields
-
2CalculatePress the "Calculate" button
-
3Check the resultThe result appears on the spot. The same page also explains the idea behind the calculation and the formula
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Percentage Change Calculator (Increase and Decrease)
Finds "by what percent did it go up or down?" Useful for year-over-year sales growth
ROI Calculator (Return on Investment and Annualized ROI)
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