The profit formula is: $\text{Profit} = \text{Selling Price} - \text{Cost Price}$ — the amount earned above what was paid to acquire or produce an item.
Quick Reference:
Basic Profit Formula: $\text{Profit} = \text{SP} - \text{CP}$
Profit Percentage: $\text{Profit\%} = \dfrac{\text{Profit}}{\text{CP}} \times 100$
Gross Profit: $\text{Gross Profit} = \text{Revenue} - \text{Cost of Goods Sold (COGS)}$
Net Profit: $\text{Net Profit} = \text{Gross Profit} - \text{Operating Expenses}$
Selling Price from Profit%: $\text{SP} = \text{CP} \times \left(1 + \dfrac{\text{Profit\%}}{100}\right)$
Type: Arithmetic / Commercial Mathematics
Used in: Commerce, accounting, business mathematics, everyday transactions
Full Definition
Profit is the positive difference between the selling price and the cost price of an item or service. When SP > CP, the transaction results in profit.
When CP > SP, the transaction results in loss. When SP = CP, there is neither profit nor loss.
At the business level, the profit formula extends: gross profit subtracts the direct cost of producing goods from revenue; net profit further subtracts all operating costs (salaries, rent, utilities) from gross profit.
Variable Key
Symbol | Meaning |
|---|---|
CP | Cost Price — what was paid to buy or produce the item |
SP | Selling Price — what the item is sold for |
Profit | SP − CP (when positive) |
Profit% | Profit ÷ CP × 100 |
Revenue | Total income from sales (business context) |
COGS | Cost of Goods Sold — direct production costs |
Gross Profit | Revenue − COGS |
Net Profit | Gross Profit − all operating expenses |
Origin
Commercial arithmetic — including profit and loss calculations — was formalised in European mathematics during the 14th–16th centuries as trade expanded. Luca Pacioli (1447–1517, Italy) documented the double-entry bookkeeping system in Summa de Arithmetica (1494), which systematised profit and loss accounting and remains the basis of modern accounting practice.
Worked examples
Example 1: Basic profit calculation
A trader buys a mobile phone for $200 and sells it for $260. Find the profit and profit percentage.
$$\text{Profit} = 260 - 200 = \$60$$
$$\text{Profit\%} = \frac{60}{200} \times 100 = 30\%$$
Final answer: Profit = $60; Profit% = 30%
Example 2: Finding selling price
A manufacturer wants to earn 25% profit on a product that costs $80 to produce.
$$\text{SP} = 80 \times \left(1 + \frac{25}{100}\right) = 80 \times 1.25 = \$100$$
Final answer: Selling Price = $100
Example 3: Gross and net profit (business level)
A company earns $50,000 in revenue. COGS = $30,000. Operating expenses = $12,000.
$$\text{Gross Profit} = 50{,}000 - 30{,}000 = \$20{,}000$$
$$\text{Net Profit} = 20{,}000 - 12{,}000 = \$8{,}000$$
Final answer: Gross Profit = $20,000; Net Profit = $8,000
Common Confusions With The Profit Formula
Profit% is always calculated on CP, not SP. Dividing profit by the selling price gives a different (lower) percentage that is non-standard and will not match textbook answers.
Gross profit and net profit are not the same. Gross profit subtracts only direct production costs from revenue.
Net profit subtracts all costs — including salaries, rent, and overhead. A company can have high gross profit and negative net profit if operating expenses exceed the gross profit margin.
Profit is not the same as revenue. Revenue is total income; profit is what remains after subtracting costs. Confusing the two is one of the most common errors in business math problems.
Where The Profit Formula Appears in Real Life
The basic profit formula drives retail pricing, salary negotiation, investment return calculations, and tax reporting. At the business level, gross profit margin — gross profit divided by revenue — is a key indicator of operational efficiency used by investors and analysts worldwide. Net profit margin — net profit divided by revenue — determines a company's actual financial health and is reported quarterly by all publicly listed companies under both US GAAP and IFRS international accounting standards.
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