 # How To Calculate Percentage Of Marks

tl;dr
To calculate the percentage of marks, divide the marks obtained by the total marks and multiply the result by 100. In cases where the subject's total marks vary, use weighted average calculation, which assigns different weights to different components and then averages the weighted marks to arrive at the percentage of marks. Calculating the percentage of marks is an essential task for students, teachers, and parents alike. It helps in understanding a student's performance and evaluating their progress over time. However, many students struggle with calculating percentage due to a lack of knowledge or improper methodology. In this article, we will guide you on how to accurately calculate the percentage of marks.

Before we dive into the calculation process, it’s essential to understand what percentage means. Percentage is a way of representing a fraction in terms of 100. For instance, 25% means 25 out of 100 or 1/4th. However, in the case of marks, percentage represents the number of marks obtained by a student out of the total marks and is expressed in the form of a percentage.

To calculate the percentage of marks, follow these simple steps:

Step 1: Determine the total marks

The first step in calculating the percentage of marks is to identify the maximum marks for a particular subject. For instance, if you are calculating the percentage for an exam of Mathematics where the maximum marks were 100, then 100 is the total marks.

Step 2: Calculate the marks obtained

Next, calculate the marks obtained by the student in that subject. For instance, if a student has obtained 75 marks in mathematics, then 75 is the marks obtained.

Step 3: Divide the marks obtained by the total marks

The third step is to divide the marks obtained by the total marks, and then multiply the result by 100 to get the percentage. For example, to calculate the percentage of marks obtained in mathematics (assuming total marks is 100 and marks obtained is 75), use the following formula:

Percentage of marks = (Marks obtained/Total marks) x 100

= (75/100) x 100

= 75%

Therefore, the percentage of marks obtained by the student in Mathematics is 75%.

Sample Problem:

Suppose a student scored 78 marks out of 100 in a science exam, then what is the percentage of marks obtained by the student?

Solution:

Total Marks = 100

Marks obtained = 78

Percentage of marks = (Marks obtained/Total marks) x 100

= (78/100) x 100

= 78%

Therefore, the percentage of marks obtained by the student in Science is 78%.

The above method can be applied to find the percentage of marks for any subject, including Mathematics, Science, Language, or any other subject. However, it is essential to keep in mind that this method of percentage calculation is only valid when the total marks for a subject is constant. If the total marks for a subject varies, then a different approach is required.

Another method to calculate the percentage of marks is using weighted average. Weighted average assigns different weights to different components of an aggregate, and then average weighted marks are calculated to arrive at the percentage of marks.

For instance, in some cases, a subject is divided into different components such as class participation, homework, assignments, quizzes, and exams. Each of these components may carry different weights, and the total weightage assigned to the different components should add up to 100%. In such cases, weighted average is used to calculate the percentage of marks.

To calculate the weighted percentage of marks, follow these simple steps:

Step 1: Determine the weightage

In the first step of calculating the weighted percentage of marks, it is essential to identify the weightage assigned to each component of the subject. For instance, if an examination is divided into four different components such as class participation 10%, homework 20%, quizzes 30%, and exams 40%, then add up all the weightages.

Step 2: Calculate the contribution

The next step is to calculate the student's contribution to each component as per the weightage assigned. For instance, if a student scores 9 marks out of 10 in class participation, 16 marks out of 20 in homework, 27 marks out of 30 in quizzes, and 32 marks out of 40 in exams, then the contribution would be calculated as follows:

Class participation = (9/10) * 10 = 9

Homework = (16/20) * 20 = 16

Quizzes = (27/30) * 30 = 27

Exams = (32/40) * 40 = 32

Step 3: Calculate the weighted average

The final step is to calculate the weighted average, which is the sum of the contribution of each component divided by the total weightage assigned.

Weighted Average = Sum of contributions / Total weightage

= (9+16+27+32) / (10+20+30+40)

= 84/100

Therefore, the percentage of marks obtained by the student in the examination is 84%.

Sample Problem:

Suppose a student scores 20 out of 25 in homework (weightage 30%), 9.5 out of 10 in class participation (weightage 15%), 15 out of 20 marks in quizzes (weightage 20%), and 31 out of 40 marks in the final exam (weightage 35%). What is the weighted average percentage of the student in the subject?

Solution:

Total Weightage= 100%

Homework Marks (30%) = 20

Class participation marks (15%) = 9.5

Quizzes marks (20%)= 15

Final exam marks (35%)= 31

Homework contribution = (20/25) * 30 = 24

Class participation contribution = (9.5/10) * 15 = 14.25

Quizzes contribution = (15/20) * 20 = 15

Final exam contribution = (31/40) * 35 = 27.12

Weighted average = (24 + 14.25 + 15 + 27.12) / 100 * 100

= 80.37%

Therefore, the weighted average percentage of marks scored by the student is 80.37%.

To summarize, calculating the percentage of marks is an essential task for students, teachers, and parents. The percentage of marks can be calculated by dividing the marks obtained by the total marks and multiplying the result by 100. In cases where the subject's total marks vary, weighted average calculation can be used, which assigns different weights to different components and then averages the weighted marks to arrive at the percentage of marks. It is essential to use the appropriate formula, keeping in mind the total marks and weightage assigned to different components, to arrive at accurate percentage calculations.