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What are the difference among GPA, CGPA and SGPA?

The Grade Point Average (GPA) is an calculation used to find the average result of all grades achieved for your course or semester. GPA for a semester is called as Semester Grade Point Average (SGPA).The CGPA (Cumulative Grade Point Average) is the cumulative aggregation or the average of all your individual GPAs/SGPAs of all semesters/courses you have studied till date.Hope this make sense!! :)

Which scale is better between CGPA & CPI?

How is gpa calculated in iits?

I will talk about my alma mater, IIT Indore, which adopted its system from IIT Bombay, the mentor institute. However, all IITs mostly follow a similar system, but for a few minor changes. Also, I will only talk about a 'vanilla' B.Tech. degree (sans any minors/majors), and assume that the programme is completed without any backlogs.I will use the following terminology (followed at IIT Indore):SPI (Semester Performance Index): A number indicative of your performance for a specific semester. A student has a separate SPI for each semester.CPI (Cumulative Performance Index): A number indicative of your cumulative performance upto a certain point of time. A student has one overall CPI. This is also called GPA (Grade Point Average) or CGPA (Cumulative Grade Point Average) in some institutes.CreditsSo here we go.We have 8 semesters in total. Each semester consists of a specific number of courses, which may be mandatory or electives. Each course has associated with itself a certain number, called credits. This number indicates the weightage of that particular score in the calculation of your overall performance. For example, if the Introduction To Data Structures course has 3 credits, and the History Of Indian English Literature course has 1.5 credits, it means that the former has twice as much weightage as the latter, while calculating your SPI or CPI. This means that your grade in Introduction To Data Structures is twice as important as your grade in History Of Indian English Literature.These credits are arrived at by using the following formula: C = L + T + 0.5P whereL: Number of theory lecture hours per weekT: Number of tutorial hours per weekP: Number of practical lab hours per weekThis formula usually varies from institute to institute.GradesNow, let's talk about grades. There are eight grades you could possibly get - AA, AB, BB, BC, CC, CD, DD, FR. (Well, there are others too, like AP, XX, II, PP, NP, but they are irrelevant to this discussion. Still, if someone wants to know about them, please let me know in the comments.) Each grade has associated with itself a number called grade point. The grade points for the grades listed above are as follows:AA - 10AB - 9BB - 8BC - 7CC - 6CD - 5DD - 4FR - 0Again, these might be different for every institute.Calculating the SPINow, let's talk about how the SPI for a semester is calculated. Suppose you have taken 9 courses (T1, T2, T3, T4, T5, T6, L1, L2, L3) in a particular semester. Each course has associated with it the number of credits for that course. Assume that T1 has 4 credits, T2 through T6 have 3 credits each, and L1 through L3 have 1.5 credits each. (I have deliberately chosen an example which is slightly complicated, but is actually real.) Thus, the total number of credits for this semester is 23.5. Note this down. We'll need this later.Once you have your results for the semester, you will be assigned a grade for each course you have taken. Now, it's a simple matter of calculating your grade points for the semester to get to your SPI. But how do you do that? "You just add the grade points corresponding to the grades received in each course!", you say? Well, almost, not really. This is where the course weightage (credits) comes in. For each course, you multiply your grade points for that course (eg. 8 if you got a BB) by the credits for that course (4 if the course is T1) to get a number. Calculate this number for all the courses. Now, add this number for all courses, and then divide this sum with the total number of credits for that semester (23.5 in our example). So basically, you just took a weighted average of your grade points for each course with the course credits as the weights. The result is your SPI.Continuing our aforementioned example, assume you get the following grades in each course:Course (credits) - Grade (grade points)T1 (4) - BB (8)T2 (3) - AA (10)T3 (3) - CD (5)T4 (3) - DD (4)T5 (3) - AB (9)T6 (3) - CC (6)L1 (1.5) - BC (7)L2 (1.5) - AA (10)L3 (1.5) - DD (4)Now your SPI is simply$\frac{4*8 + 3*10 + 3*5 + 3*4 + 3*9 + 3*6 + 1.5*7 + 1.5*10 + 1.5*4}{4 + 3 + 3 + 3 +3 + 3 + 1.5 + 1.5 + 1.5}$$&= \frac{165.5}{23.5}$$&= 7.04$Calculating the CPICalculation of the CPI is quite similar to calculation of the SPI, in that it is also a weighted average. This time, you take a weighted average of (guess what?) your SPI for each semester upto that point. But what would the weights be? The weight for a particular semester would be the weight of all the courses in that semester combined, i.e. the sum of the credits for all the courses in that semester. For example, the weight of the semester in our SPI calculation example was 23.5.Again, an SPI of 8.0 in a 23.5-weighted semester is more valuable than an SPI of 8.0 in a 21.5-weighted semester. Miscalculation of the semester weightage can cause serious damage to your CPI. (Something like this happened in our institute, affecting the CPI of all the students. Thankfully, the issue was finally resolved.)Thus, in conclusion, the CPI (or CGPA) is just a weighted average of your performance in each semester (your SPI), which in turn is a weighted average of your performance in each course (your grade points). The weights are determined by the course credits.I have omitted situations where a student fails a course in a particular semester (FR grade) and repeats it in the next, or is not allowed to give the exam due to attendance issues (XX grade) and repeats it in the next etc. But the basic principle remains the same. After every semester, you calculate your SPI for that semester, using which you update your overall CPI. (The CPI after the first semester is the same as the SPI of the first semester.)Any further questions, let me know in the comments.P.S. Having trouble with LaTeX markup. Can someone please correct that?

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