# How to Calculate Percentage - Percentage Formula, Steps, Examples (2023)

Before understanding how to calculate a percentage, let us know what a percentage is. Percentage means a number or a ratio expressed in terms of fractions of 100. It is denoted using the percentage sign “%”. The abbreviation used to represent the percentage is “pct” or “pc”. In other words, the percent or the percentage is defined as how much of one quantity is made by the different quantity, and it is evaluated at about 100.

In this article, you will learn how to calculate the percentage, how to calculate the percentage increase, decrease and difference along with the respective percentage formulas and examples.

• Percentage Formula
• Percentage of a Number
• Percentage of Marks
• Percentage Change
• Percentage Increase
• Percentage Decrease
• Difference Between Percentage and Percentile
• Solved Examples
• Practice Problems
• FAQs

## How to Calculate Percentage Using Formula

We can use the formula to calculate the percentage easily and quickly. The formula to calculate percentage is equal to the ratio of the actual value to the total value multiplied by 100. The percentage formula is:

$$\begin{array}{l}Percentage = \frac{Actual\ Value}{Total\ Value} \times 100\end{array}$$

Let us understand this concept and formula with the help of an illustrative example given below:

Example: A circle below has ten divisions, and a few parts are shaded. Calculate the percentage of shaded parts (in the figure) in the circle.

Solution:

Total number of divisions in the circle = 10

Number of shaded parts = 2

We know that,

Percentage, % = (Actual Value / Total Value) × 100

Thus, the percentage of the shaded part of the circle = [(Number of shaded divisions)/ (Total number of divisions)] × 100

= (2/10) × 100

= 20%

Therefore, 20 percent, i.e. 20% of the circle has shaded portions.

Also, try: Percentage Calculator

## How to Calculate Percentage of a Number

It is possible to calculate the percentage in three simple steps. They are:

Step 1: Identify the original form of the number, i.e. fraction or decimal. The original format will define the following mathematical operation on the number. Suppose a decimal number is 0.25, which may be the calculated ratio of the values we are comparing, while an example of a fraction is 4/15.

Step 2: Perform the mathematical operation on the number. That means, if the given number is a fraction, convert it to a decimal number. If the given number is a decimal number, then leave it as it is.

(Video) Math Antics - Finding A Percent Of A Number

For example, 4/15 = 0.267

Step 3: Multiply the result obtained in the previous step by 100 and the resulted value should be expressed as a percentage. For example, 0.267 × 100 = 26.7%.

Learn how to convert decimal to fraction here.

Alternative Method:

We can also calculate the percentage of a number by changing the number into a fraction with the denominator 100. This can be understood in a better way from the example given below:

Example:

Convert 3/20 to a percentage.

Solution:

The given fraction is 3/20.

Let us convert the denominator to 100.

(3/20) × (5/5) = 15/100

Now, multiply the result by 100.

(15/100) × 100 = 15

Therefore, 3/20 = 15%

Note: This method of calculating the percentage is applicable only when the denominator is a factor of 100. Otherwise, we can use the regular method to calculate the percentage.

## How to Calculate Percentage of Marks

Most of the students get a question on how to calculate the percentage of marks obtained in exams. Here is the answer to this question along with the example. Two simple steps give you the percentage of marks. They are:

Step 1: Divide the obtained marks by the maxim marks of the test.

Step 2: Multiply the result by 100.

Go through the example given below to understand the process of finding the percentage of marks.

Example 1: A student scored 1156 marks in the examination out of 1200 marks. Calculate the percentage of marks secured by the student.Go through the example given below to understand the process of finding the percentage of marks.

Solution:

Number of marks scored = 1156

Maximum marks = 1200

$$\begin{array}{l}Percentage~ of ~marks = \frac{Marks ~ obtained}{Maximum ~ marks}\times 100\end{array}$$

(Video) How To Apply Percentage Formula in Microsoft Excel | How To Find percentage in Excel | calculate %

Percentage of marks =(1156/1200) × 100

Percentage= 0.9633…. × 100

Therefore, the percentage of marks obtained is 96.3%

## How to Calculate Percentage Change

Let’s learn how to calculate the percentage difference between two numbers. The percentage difference is the variation in the value of a number or quantity over a while in terms of percentage.

The formula gives Percentage change (Or Percentage difference) is:

% change =[(Change in Value) / Original Value] × 100

Here,

Change in Value = New value – Original value

The change in the value could be positive or negative. Positive difference means there is a percentage increase in the value, otherwise, it is called percentage decrease.

Thus, there are two types of percentage change in mathematics. They are:

• Percentage increase
• Percentage decrease

### How to Calculate Percentage Increase

When the new value is greater than the original value, the percentage change in the value shows the percent increase in the original number. This can be calculated as:

$$\begin{array}{l}Percent~Increase = \frac{Increase~ in~ value}{Original~ value}\times 100\end{array}$$

Here,

Increase in value = New value – Original value

### How to Calculate Percentage Decrease

When the new value is lesser than the original value, the percentage change in the value shows the percent decrease in the original number. The formula for percentage increase is given by:

$$\begin{array}{l}Percent~Decrease =\frac{Decrease~ in~ value}{Original~ value}\times 100\end{array}$$

Here,

Decrease in value = Original value – New value

Also check: Percentage Increase and Decrease

There exists one more change in a percentage called percentage error. Generally, this kind of error occurs when we deal with weights.

(Video) How To Calculate Percent Or Percentage Explained - Formula For Percent Or Percentage

Percentage Error Formula

$$\begin{array}{l} Percentage\ Error = \frac{Error}{Real ~value}\times 100\end{array}$$

### Difference Between Percentage and Percentile

In most cases, many people might get confused with percentage and percentile. Both are different. Here, the difference between percentage and percentile is given in detail.

 Percentage Percentile The percentage represents the number out of 100 Percentile is not a number out of 100 It can be written as ratios or proportions It cannot be written as ratios or proportions A percentage is obtained by multiplying the ratio of two numbers with 100 A percentile is a percentage of values that can be found below a specific value It is not based on ranking numbers It is based on ranking numbers It is written in the form of x% It is written in the form of xth It is based on one case Comparison of one case with other It does not rely on the normal distribution It relies on the normal distribution

Also, read:Difference Between Percentage And Percentile

### Solved Examples of Calculating the Percentage

Question 1: There are 120 students in a class. Out of them, 60 students are boys. Find the percentage of boys in the class.

Solution:

Given:

Total number of students in class = 120

Number of boys in class = 60

$$\begin{array}{l}\text{Therefore, the percentage of boys in class} = \frac{60}{120}\times 100\end{array}$$

= 600/12 = 50

So, the percentage of boys in class = 50%

Question 2: Find 25 % of 10.

Solution:

Remember that “of” means “times”

So, 25% of 10 = (25/100)× 10

0.25× 10 = 2.5

Therefore, 25% of 10 is 2.5.

Question 3: Find the percentage of the ripened apples, if the number of ripe apples is 10 and the total number of apples in the basket are 60.

Solution: Given, the total number of apples = 60

Number of ripe apples = 10

Percentage of ripe apples = (10/60)× 100

= (1/6)× 100

(Video) How to Calculate Percentages in Excel with Formulas

= 16.666666

=16.67%

Question 4: There are 150 people present in a cinema hall. The number of men is 80 and the number of women is 70 in the hall. Calculate the percentage of men present in the hall.

Solution: Total number of people present in cinema hall = 150

Number of men = 80

$$\begin{array}{l}Percentage~of~men=\frac{Number~of~men}{Total~number~of~people}\times 100\end{array}$$

Percentage of men = (80 x 100)/150

= 53.33%

Question 5: What is 15% of 75 equal to?

Solution: 15% of 75 = (15/100)× 75 = 11.25

• Interpreting Converting Percentages
• Profit and Loss Percentage
• Ratio to Percentage

### Practice Problems

1. Jaanu scored 34, 65, 58, 70, 50 in 5 subjects of a monthly test in which themaximum marks for each subject is 100. Calculate the percentage of marks scored in 5 subjects.
2. The price of a toy was increased by 30% to Rs. 120. What was the original price?
3. Convert the fraction 7/18 to a percentage.
4. A student increased the value of a number from 65 to 110. Find the percentage change in the number.

To learn more interesting topics in Maths, register with BYJU’S – The Learning App and also watch engaging videos.

## Frequently Asked Questions on Finding Percentage

### What is the percentage?.

The percentage can be defined as the dimensionless ratio of two numbers. It can be used to compare two numbers and find out how much one is more than the other or compare the two numbers against a common scale.

### What is the Formula for Percent into Decimal?

To convert percent to decimal, drop the percent symbol (%), divide it by 100, and write the decimal form of the fraction thus obtained.

### Can Percent be More Than 100?

Yes, percentage can be more than 100 when we have a value that is larger than the total value.

### How do I calculate x percent of y?

To calculate x percent of y: Divide x by 100. Multiply x by y. The resultant number is x% of y.

(Video) The Percent Equation

## FAQs

### How do you figure out percentages step by step? ›

To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.

How do you calculate percentages examples? ›

If you are required to convert a decimal number like 0.57 to a percentage, you simply multiply it by 100. That is, 0.57 x 100 = 57. Therefore, 0.57 as a percentage equals 57%. Another example is 0.03 x 100 = 3%.

How many steps do you complete to find the percent of a number? ›

Here are three steps to calculate a percentage:
1. Determine the total amount of what you want to find a percentage. You first need to determine the total amount. ...
2. Divide the number to determine the percentage. Using the example above, you determined it rained 15 of the 30 days in April. ...
3. Multiply the value by 100.
Feb 25, 2020

How do you calculate total steps? ›

Divide the rise by 6 or 7 inches (15 or 18 cm) to find the total number of stairs. For larger stairs, divide by 6 and for smaller stairs, divide by 7.

What is the trick to percentages? ›

So what's the secret formula? It's simple: x% of y = y% of x. Stephens explains, “So, for example, if you needed to work out 4% of 75 in your head, just flip it and and do 75% of 4, which is easier.” If you haven't already worked it out, the answer is 3, and the easy trick can be applied to any set of numbers.

How do you complete a percent table? ›

Computing a Percentage From a Table of Values
1. Step 1: Identify the whole from the given table. Take a look at the table and find the whole. ...
2. Step 2: Find the part from the given table of values. Part is the number for which we are required to find the percentage. ...
3. Step 3: Compute the percentage using the formula.

What is the easiest way to understand percentages? ›

Percentages are essentially fractions where the denominator is 100. To show that a number is a percent, we use the percent symbol (%) beside the number. For example, if you got 75 questions right out of 100 on a test (75/100), you would have scored 75%.

How do you find 40% of a number? ›

You get 40 percent of a number by multiplying it by . 40 or the fractional equivalent, 2/5. So, 40 percent of 20 is 8.

How do you work out 40% of 80? ›

Answer: 40% of 80 is 32.

How do you calculate percentage short tricks? ›

Percentages: Formulas, Tricks and Shortcuts
1. Percent implies “for every hundred”. ...
2. To calculate p % of y. ...
3. To find what percentage of x is y: y/x × 100.
4. To calculate percentage change in value. ...
5. Percentage point change = Difference of two percentage figures.
6. Increase N by S % = N( 1+ S/100 )
7. Decrease N by S % = N (1 – S/100)

### What will be the 40% of 25? ›

Answer: 40% of 25 is 10.

Is it possible for 20% of 45 to be 9? ›

Answer: 20% of 45 is 9.

How do you find 30% of 90? ›

Answer: 30% of 90 is 27.

How much percent is 28 out of 70? ›

The total answers count 70 - it's 100%, so we to get a 1% value, divide 70 by 100 to get 0.70. Next, calculate the percentage of 28: divide 28 by 1% value (0.70), and you get 40.00% - it's your percentage grade.

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