The profit and loss formula calculates the financial gain or shortfall from a transaction — the difference between the selling price and the cost price.
Quick Reference:
Profit: $\text{Profit} = \text{SP} - \text{CP}$ (when SP > CP)
Loss: $\text{Loss} = \text{CP} - \text{SP}$ (when CP > SP)
Profit %: $\text{Profit\%} = \dfrac{\text{Profit}}{\text{CP}} \times 100$
Loss %: $\text{Loss\%} = \dfrac{\text{Loss}}{\text{CP}} \times 100$
Selling Price from Profit %: $\text{SP} = \text{CP} \times \left(1 + \dfrac{\text{Profit\%}}{100}\right)$
Selling Price from Loss %: $\text{SP} = \text{CP} \times \left(1 - \dfrac{\text{Loss\%}}{100}\right)$
Type: Arithmetic / Financial Mathematics
Used in: Commerce, economics, everyday transactions, accountancy
Definition of Profit and Loss
Profit occurs when the selling price (SP) exceeds the cost price (CP) — the amount paid to acquire or produce the item. Loss occurs when the cost price exceeds the selling price. Both profit and loss are calculated relative to the cost price, never the selling price.
Profit and loss percentage express the gain or shortfall as a fraction of the cost price, scaled to 100. This makes percentages comparable across transactions of different scales — a 20% profit on a $10 item and a 20% profit on a $10,000 transaction both represent the same relative gain.
Variable Key
Symbol | Meaning |
|---|---|
CP | Cost Price — the original price paid to acquire or produce the item |
SP | Selling Price — the price at which the item is sold |
Profit | SP − CP (positive when SP > CP) |
Loss | CP − SP (positive when CP > SP) |
Profit% | Profit expressed as a percentage of CP |
Loss% | Loss expressed as a percentage of CP |
MP | Marked Price — the listed price before discount (used in some problems) |
Discount | MP − SP (reduction from marked price to selling price) |
Origin and Context
Profit and loss calculations are among the oldest recorded mathematical operations. Babylonian merchants documented trading gains and losses on clay tablets around 2000 BCE. The formal algebraic treatment — expressing profit as a percentage of cost — became standardised through Italian merchant mathematics of the 14th–15th centuries, codified in works like Luca Pacioli's Summa de Arithmetica (1494, Italy), which laid the foundation for modern bookkeeping and commercial arithmetic.
Worked Examples
Example 1: Finding profit and profit percentage
A trader buys a watch for ₹800 and sells it for ₹1,000. Find the profit and profit percentage.
$$\text{Profit} = \text{SP} - \text{CP} = 1000 - 800 = ₹200$$
$$\text{Profit\%} = \frac{200}{800} \times 100 = 25\%$$
Final answer: Profit = ₹200; Profit% = 25%
Example 2: Finding selling price from profit percentage
A shopkeeper buys a jacket for $120 and wants to make a 15% profit. What should the selling price be?
$$\text{SP} = 120 \times \left(1 + \frac{15}{100}\right) = 120 \times 1.15 = \$138$$
Final answer: Selling Price = $138
Example 3: Finding loss percentage
An item bought for $250 is sold for $200. Find the loss percentage.
$$\text{Loss} = 250 - 200 = \$50$$
$$\text{Loss\%} = \frac{50}{250} \times 100 = 20\%$$
Final answer: Loss = $50; Loss% = 20%
Common Confusions With The Profit And Loss Formula
Profit and loss percentages are always calculated on the cost price, not the selling price. A common error is dividing the profit by the selling price rather than the cost price — this gives a smaller and incorrect percentage.
The marked price (MP) and cost price (CP) are different values. MP is the listed price; SP is what the item actually sells for after any discount. Profit or loss is still calculated relative to CP, not MP.
Profit% and Loss% cannot coexist in the same transaction. Either SP > CP (profit) or SP < CP (loss) or SP = CP (no profit, no loss).
Was this article helpful?
Your feedback helps us write better content