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Profit and Loss Formula
Profit and loss formulas are used to calculate the profit or loss that has been incurred by selling a particular product. We also have formulas to calculate the profit percentage and loss percentage. They are mainly used in business and financial transactions to depict how much profit or loss a trader has incurred from any particular deal.
What is the Profit and Loss Formula?
Profit and loss are the terms used to identify whether a transaction is profitable or not. Before moving on to the profit and loss formula, we need to understand the terms 'selling price' and 'cost price'. The price at which a product is purchased is called its cost price. The price at which a product is sold is called its selling price. Now, if the selling price is greater than the cost price, then the difference between them is called profit. If the selling price is less than the cost price, then the difference between them is called loss.
Profit Loss Formula
When the selling price and cost price are known, the basic formulas for calculating the profit and loss are:
 Profit = Selling price (S.P.)  Cost price (C.P.)
 Loss = Cost price (C.P.)  Selling price (S.P.)
Derivation of Profit and Loss Formula
The derivation of the profit and loss formulas is simple to understand if the terms 'selling price' and 'cost price' are clear.
Cost price: The price at which an item is purchased.
Selling price: The price at which an item is sold.
Profit Formula
Now, if the selling price of a product is more than its cost price, there is a profit earned in the transaction. In other words, if a product is sold at a higher price than the price at which it was bought, then a profit is earned. This is how the formula for profit is derived.
Profit = Selling Price  Cost Price
Example: Let us find the profit in a transaction if a product is bought at $20 and sold at $50. In this case, Cost price = $20; Selling price = $50. Profit = Selling Price  Cost Price
Profit = 50  20 = 30. Therefore, a profit of $30 is earned in the transaction.
Loss Formula
Similarly, the formula for loss can be derived using the selling price and the cost price. In simple words, if a product is sold at a lesser price than the price at which it was bought, then we have a loss in the transaction. If the cost price of a product is more than its selling price, there is a loss is incurred in the transaction.
Loss = Cost Price  Selling Price
Example: Let us find the loss incurred if a product is bought at $60 and sold at $40. In this case, Cost price = $60; Selling price = $40. Loss = Cost Price  Selling Price
Loss = 60  40 = 20. Therefore, the loss incurred in the transaction is of $20.
Profit and Loss Percentage Formulas
In some cases, after the profit or loss is calculated, it is converted in the form of a percentage. It is used to express the amount of profit or loss incurred in the form of a percentage. This helps in comparing two quantities. Here are the&nbS.P.;profit and loss percentage formulas:
 Profit percentage (P%) = (Profit / Cost Price) × 100
 Loss percentage (L%) = (Loss / Cost price) × 100
But sometimes, profit percentage/loss percentage is given in the question and we are asked to find either the selling price (S.P.) or the cost price (C.P.). In such cases, the following formulas are helpful.
 S.P. = {(100 + P%)/100} × C.P. (if S.P. > C.P.)
 S.P. = {(100 – L%)/100} × C.P. (if S.P. < C.P.)
 C.P. = {100/(100 + P%)} × S.P. (if S.P. > C.P.)
 C.P. = {100/(100 – L%)} × S.P. (if S.P. < C.P.)
Examples Using Profit Loss Formula

Example 1: A shopkeeper buys juice cans in bulk for $30 each. He sells them for $20 each. Calculate the loss and the loss percentage.
Solution:
To find: Loss and Loss Percentage
Given: Selling price = $20; Cost price = $30
Using the profit and loss formula, Loss = C.P.  S.P.
Loss = $30  $20 = $10
Using Loss Percentage Formula, Loss% = (loss/ C.P.) × 100
Loss Percentage = (10 /30) × 100
= 33.33%
Answer: Loss = $10 and loss percentage = 33.33%.

Example 2: On selling a table for $987, Jane loses 6%. Using the profit loss formula, find out how much did she purchase it for?
Solution:
To find: Cost price of the table
Given: Loss Percentage = 6%; S.P. = $987
If the loss is 6%, it means that if the cost price is $100, the loss incurred is $6.
When C.P. is $100, S.P.= C.P.  Loss = 100  6 = $94
When S.P. is $94, C.P. = $100
When S.P. is $987, C.P. = 100/94 × 987 = $1050
Answer: Cost price of the table = $1050

Example 3: If the cost of 6 pens is equal to the selling price of 4 pens, find the profit percentage.
Solution:
Let the C.P. of one pen be a.
Then C.P. of 6 pens = 6a
It is given that C.P. of 6 pens = S.P. of 4 pens
Therefore, S.P. of 4 pens = 6a which gives S.P. of 1 pen = 6a/4 = 3a/2
Profit on one pen = S.P. of 1 pen = C.P. of one pen = (3a/2)  a = a/2
Now, using the profit loss formulas:
Profit % = (profit / C.P.) × 100
= (a/2) / a × 100
= 50%
Answer: Therefore, the profit % is 50%
FAQs on Profit and Loss Formula
What is Profit Loss Formula?
The formula used to calculate the profit in a transaction is, Profit = Selling price  Cost price, and the formula used to calculate loss is, Loss = Cost price  Selling price
What are the Applications of the Profit and Loss Formula?
The profit and loss formulas are mainly used in business and financial transactions where the company needs to calculate the profit or loss that has been incurred in their business. On a smaller scale, these formulas can be used to calculate the profit or loss on any basic transaction in which products are purchased and sold. For example, if a shopkeeper buys a set of books for $400 and sells them at $500, then he can calculate his profit using the formula: Profit = Selling price  Cost Price. Substituting the values in the formula: $500  $400 = $100. This shows that he earns a profit of $100 in the transaction.
How to Find SP When CP and Profit Percent is Given?
We can derive the formula to find SP when CP and profit percent are given. We know the formula for profit% to be: P% = profit/CP × 100. Substituting profit = SP  CP in this formula, we get:
P% = (SP  CP) / CP × 100
P%/100 = (SP  CP) / CP
P%/100 = SP/CP  1
1 + P%/100 = SP/CP
(100 + P%)/100 = SP/CP
SP = (100 + P%)/100 × CP
Thus, the SP formula when profit percentage is given is SP = (100 + P%)/100 × CP.
How to Derive the Profit and Loss Formula?
The profit and loss formulas can be easily derived if the terms 'selling price' and 'cost price' are understood. Cost price is the price at which an item is purchased and selling price is the price at which an item is sold.
 Now, if the selling price of a product is more than its cost price, there is a profit earned in the transaction. This derives the formula: Profit = Selling price  Cost Price.
 However, if the cost price of a product is more than its selling price, there is a loss is incurred in the transaction. This derives the formula: Loss = Cost Price  Selling Price.
List Profit and Loss All Formulas.
The following table summarizes all profit and loss formulas.
Quantity  Formula 

Profit  SP  CP 
Loss  CP  SP 
Profit Percentage  Profit/CP × 100 
Loss Percentage  Loss/CP × 100 
CP (when profit% and SP are given)  (100/(100 + P%)) × SP 
CP (when loss% and SP are given)  (100/(100 – L%)) × SP 
SP (when profit% and CP are given)  ((100 + P%)/100) × LP 
SP (when loss% and CP are given)  ((100 – L%)/100) × LP 
What is the Profit and Loss Percentage Formula?
The formula to calculate the profit percentage is: Profit % = Profit/Cost Price × 100. The formula to calculate the loss percentage is: Loss % = Loss/Cost Price × 100.
What is the Selling Price Formula?
Selling price = Cost ( C.P.) + desired profit margin (Profit). In the formula, the revenue is the selling price, the cost represents the cost of goods sold (the expenses you incur to produce or purchase goods to sell) and the desired profit margin is what you hope to earn.
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