Profit and Loss Formula – Calculation & Examples
Profit and Loss Formula – Calculation & Examples
TL;DR
This guide covers the profit and loss formula in full — profit, loss, profit percentage, loss percentage, cost price, and selling price — with step-by-step worked examples drawn from realistic retail and exam contexts. By the end you will be able to calculate any profit-and-loss problem accurately and identify which formula a question is testing.
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: Profit=SP−CP (when SP > CP)
Loss: Loss=CP−SP (when CP > SP)
Profit %: Profit%=Profit/CP×100
Loss %: Loss%=Loss/CP×100
Selling Price from Profit %: SP=CP×(1+Profit%/100)
Selling Price from Loss %: SP=CP×(1−Loss%/100)
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 standardized through Italian merchant mathematics of the 14th–15th centuries.
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.
Profit=SP−CP=1000−800=₹200
Profit%=200/800×100=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?
SP=120×(1+15/100)=120×1.15=$138
Final answer: Selling Price = $138
Example 3: Finding loss percentage
An item bought for $250 is sold for $200. Find the loss percentage.
Loss=250−200=$50
Loss%=50/250×100=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).
Frequently Asked Questions
What is the profit and loss formula in simple terms?
The profit and loss formula compares what an item costs to what it sells for: Profit = SP − CP when SP is higher; Loss = CP − SP when CP is higher. Percentages use CP as the base: Profit% = (Profit ÷ CP) × 100.
Why is profit percentage calculated on cost price, not selling price?
Because cost price represents the actual investment. Profit percentage on SP would give a different number for the same transaction and make comparison across deals misleading. CP is the standard base internationally.
If an item is bought for $100 and sold for $110, what is the profit percentage?
Profit = $10. Profit% = (10 ÷ 100) × 100 = 10%.
What is the formula to find cost price when profit percentage is known?
CP = SP / (1 + Profit%/100)