Percentages are crucial in many business fields for analyzing performance, growth, and profitability because they provide a standardized way to express proportions, such as discounts, growth rates, profit margins, and market share. Common problems like profit margins, discount percentages, and growth rates are often handled using basic percentage formulas. Understanding and applying these calculations helps make informed decisions in business operations.
In the following lines, we will expand on all the details related to calculating percentages.
A percentage expresses a value as a fraction of 100. It is a ratio of a part to a whole, representing the whole by 100. Percentages are often used to describe changes, proportions, or rates. The term percentage comes from “per centum.”
Here are some examples of percentages:
To calculate a percentage, follow these simple steps:
The percentage formula is:
Where:
Let’s dive into the several types of percentage problems that are known.
The best way to understand how to apply percentage calculation in day-to-day use is to have specific examples that you can apply at work of home. We have compiled a selection with 10 problems, their solutions and the metod to reach the answer.
1. Product Sales
Problem: A smartphone is on sale for 20% off its original price of $800. How much will you pay for the smartphone?
Solution:
Answer: You will pay $640 for the smartphone.
2. Tips and Gratuities
Problem: If your restaurant bill is $50 and you want to leave a 15% tip, how much will you pay in total?
Solution:
Answer: You will pay $57.50 in total.
3. Interest Rates
Problem: You deposit $1,000 into a savings account with a 5% annual interest rate. How much will you have in the account after one year?
Solution:
Answer: You will have $1,050 in the account after one year.
4. Percentage Increase
Problem: A company's profits increased from 100,000 to 120,000. What is the percentage increase?
Solution:
Answer: The company's profits increased by 20%.
5. Percentage Decrease
Problem: The number of employees decreased from 80 to 60. What is the percentage decrease?
Solution:
Answer: The company has 25% fewer employees than it had initially.
6. Calculating Profit Margin
Problem: A business has $5000 in revenue and $1500 in profit. What is the profit margin?
Formula: Profit margin = Profit / Revenue ×100
Solution: Profit Margin=(1500/5000)×100=30%
Answer: The profit margin for a business with $5000 revenue and $1500 profit is 30%.
7. Calculating Discount Percentage
Problem: A product originally priced at $200 is on sale for $160. What is the discount percentage?
Formula: Discount Percentage=((Original Price−Sale Price)/Original Price)×100
Solution: Discount Percentage=(200−160)/200)×100=20%
Answer: The discount percentage for a product that went from $200 to $160 is 20%
8. Calculating Growth Rate
Problem: A company’s revenue grew from $50,000 to $60,000. What is the growth rate?
Formula: Growth Rate=((New Value−Old Value)/Old Value)×100
Solution: Growth Rate=((60,000−50,000)/50,000)×100=20%
Answer: The growth rate for a company that went from $50k to $60k is 20%.
9. Calculating Percentage Change in Costs
Problem: If the cost of raw materials increases from $4000 to $5000, what is the percentage change between the old and new costs?
Formula: Percentage Change=((New Cost−Old Cost)/Old Cost)×100
Solution: Percentage Change=(5000−4000)/4000)×100=25%
Answer: The increase in raw materials represents a 25% percentage change in costs.
10. Calculating Market Share
Example: A company generates $500,000 in sales while the total market sales are $2,000,000. What is the company’s market share?
Formula: Market Share=(Company’s Sales/Total Market Sales)×100
Solution: Market Share=(500,000/2,000,000)×100=25%
Answer: The market share of a company generating $0.5M out of a $2M market is 25%.
A percentage chart can help you make the percentage calculations much faster.
Fraction | Percentage |
1/2 | 50% |
1/3 | 33.33% |
2/3 | 66.67% |
1/4 | 25% |
3/4 | 75% |
1/5 | 20% |
2/5 | 40% |
3/5 | 60% |
4/5 | 80% |
1/6 | 16.67% |
2/6 | 33.33% |
3/6 | 50% |
4/6 | 66.67% |
5/6 | 83.33% |
How to convert between percentages and decimals:
To convert a percentage to a decimal, divide the percentage by 100.
How to convert between percentages and decimals?
To convert a decimal to a percentage, multiply the decimal by 100.
How to convert fractions to percentages?
To convert a fraction to a percentage, divide the numerator (top number) by the denominator (bottom number) and multiply by 100.
Example: 3/4 = (3 ÷ 4) × 100 = 75%
What are the differences between percentage and percent?
Percentage and percent are often used interchangeably, but there is a subtle difference:
Percentage is a specific value or amount expressed as a fraction of 100.
Example:
"The percentage of students who passed the exam is 80%" (referring to a specific value).
Percent is a unit of measurement used to express a proportion or rate.
Example:
"The interest rate is 5 percent per annum" (referring to a unit of measurement).
What percent of X is Y?
To calculate what percent of X is Y, we use this formula (Y/X)*100 = P%.
For example John worked this week 25 hours out of 40 that is standard. What percent is 25 out of 40 hours weekly? (25/40)*100 = 62.5%.
What is 16 out of 20 as a percentage?
Let's use again the formula (Y/X)*100 = P%.
16/20 * 100 = 0.8 * 100 = 80%.
What is X is percent of Y?
To find out X if it is P% of Y, we use this formula: Y/P% = X.
For example, $5000 is 20% of what amount?
X = $5000/20% = $5000/(20/100) = $5.000/0.20 = $250.000.
So, $5000 is 20% of $250.000.
How do you calculate 20% in Excel?
To figure out 20% in Excel, apply the formula "=number*0.2". Replace "number" with the exact value you want to compute 20% of. Multiplying the integer by 0.2 yields a result that is 20% of the original value.
If you want to calculate 20% of $75, then you will get the result by writing = $75 *0.2 = 15
Tip: We expand on this topic on this dedicated article: How to calculate percentages in Excel?
X is what percent of Y?
For example, 21 days is what percent of 31 days?
We have the following formula: Y = P% * X, this means that P% = Y÷X.
In this sense, 21/31 = 0.67%.
Convert the decimal to percent P% = 0.67 * 100 = 67%
Therefore, 21 is 67% of 31.
X is P percent of what?
We start with the equation: X = P% * Y.
For example, the department A has 15 employees which is 60% of the total workforce, and we need to know the number of total employees.
In this case X = 15 ÷ 60%. In this sense 15/0.6 = 25. So, 15 employees is 60% of 25 employees total.
Key takeaways on percentages:
By understanding these key points and practicing real-life problems, you can gain confidence and proficiency in working with percentages. Regular practice with real-life problems will help you apply percentage calculations to various situations with ease.