How to Calculate Percentage

Before knowing about how to calculate a percentage, let us know what a percentage is? In this article, we will discuss in detail what is a percentage, how to calculate the per cent increase and decrease, how to estimate the per cent of a number using the percentage formula with examples. The topics related to percentage have been introduced to student in Class 7 and Class 8 syllabus.

The concept of percentage is used to measure the tendency of value with respect to the original value. This has a huge application in business while computing profit and loss percentage. Also, in schools and colleges, the marks obtained by the students are estimated with the percentage formula. Percentage basically defines the ratio of any value to a whole value multiplied by 100. The symbol used to denote per cent is “%”. Let us learn how to calculate the per-cent value.

Also, Read:

Percentage Meaning

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 per cent or the percentage is defined as how much of one quantity is made by the other quantity and it is evaluated in relation to 100.

Percentage Formula

Now, to calculate the percentage we have know its formula. 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:

Percentage, % = (Value * 100) / Total Value

Some other important percentage formulas are

Percentage Change Formula

% change = ((New value – Original Value) * 100) / Original Value

There are two different types of percentage change. They are

    • Percentage Increase
    • Percentage Decrease

Percent Increase

When the new value is greater than the original value, then the percentage change in the value shows the per cent increased in the original number, such that:

Percent Increase (% Increase) = Increase in Value/Original Value x 100

where Increase in Value = New Value – Original Value

Percent Decrease

When the new value is lesser than the original value, then the percentage change in the value shows the per cent decreased in the original number, such that:

Percent Decrease (% Decrease) = Decrease in Value/Original Value x 100

where Decrease in Value = Original Value – New Value

Percentage Error Formula

% error = (error * 100) / real value

How to calculate the Percentage of a Number

Generally, the numbers that are converting into percentage is given in two formats.

  • Decimal form – If the number is given in decimal format, it is easy to find the percentage. To obtain the percentage, multiply the given number by 100. For example, the given number is 0.45. To convert into a percentage, 0.45 * 100 = 45%
  • Fraction form: If the number is given in fractional format, first convert into decimal value by dividing the top value by the total value and then multiply with 100.

By using percentage formulas, it is easy to know how to calculate the percentage of marks, discount etc.

How to calculate Percentage of  Marks

A percentage is a number that is expressed as a fraction of 100. Here, how to calculate the percentage of marks is explained in detail.

To find the percentage of the marks, divide the total scores with marks obtained in the examination and multiply the result with 100.

Example: If 1156 is the total score obtained in the examination out of 1200 marks, then divide 1156 by 1200, and then multiply it by 100.

It means that,

Percentage of marks =(1156/1220) x 100

Percentage= 0.9633 x 100

Therefore, the percentage of marks obtained is 96.3%

Difference Between Percentage and Percentile

In most of the 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 not a value in below which certain values are found Percentile is a value below which certain values are found
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

Calculating Percentage Examples

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

Therefore, the percentage of boys in class = ( 60 *100)/120

= 600/12 = 50

So, the percentage of boys in class = 50%

Question 2: To find 25 % of 10.

Solution:

Remember that “of” means “times”

So, Percentage = (25/100) * 10

% = 0.25* 10 = 2.5

Therefore, 25% of 10 is 2.5

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

Solution: Given, total number of apples = 60

Number of riped apples = 10

Percentage of riped apples = 10/60 x 100

= 1/6 x 100

= 16.666666

=16.67%

Question 4: There are 150 people present in a cinema hall. Number of men are 80 and the number of women are 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

Percentage of men = (80 x 100)/150

= 53.33%

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

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

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