How CGPA & SGPA Calculation Works
An authoritative mathematical explanation of the credit-weighted grading system used across universities.
1. Understanding SGPA (Semester Grade Point Average)
SGPA measures your academic achievement in a specific semester. Because courses have varying credit weights, SGPA is calculated as a weighted average rather than a simple arithmetic mean.
The Official SGPA Formula
SGPA = Σ(Ci × Gi) ÷ Σ(Ci)
- Ci = Credit value assigned to subject i
- Gi = Grade point secured in subject i
- ΣCi = Total credits registered in the semester
Worked Example for a 4-Subject Semester
| Subject | Credits (C) | Grade Point (G) | Credit Points (C × G) |
|---|---|---|---|
| Data Structures | 4 | 9 (A+) | 36 |
| Discrete Mathematics | 4 | 8 (A) | 32 |
| Operating Systems | 3 | 10 (O) | 30 |
| Programming Lab | 2 | 7 (B+) | 14 |
| Total | 13 Credits | - | 112 Points |
Calculated SGPA: 112 ÷ 13 = 8.62
2. Understanding CGPA (Cumulative Grade Point Average)
CGPA represents your overall cumulative performance from the start of your program across all completed semesters.
The Official Cumulative CGPA Formula
CGPA = Σ(SGPAj × TotalCreditsj) ÷ Σ(TotalCreditsj)
Equivalently, it is the sum of all earned credit points across all completed semesters divided by all completed credits.
3. Converting CGPA to Percentage
Different universities specify distinct official formulas to calculate percentage equivalence from CGPA:
- UGC / AICTE / DTU Standard Formula:
Percentage (%) = CGPA × 10 - VTU (Visvesvaraya Technological University) Formula:
Percentage (%) = [CGPA - 0.75] × 10 - CBSE / Traditional Engineering Multiplier:
Percentage (%) = CGPA × 9.5
Frequently Asked Questions
Why are credits multiplied with grade points?
Credits represent the academic depth and contact hours of a course (e.g. a 4-credit Core Algorithm course carries twice the weight of a 2-credit lab). Credit-weighting ensures that performance in major subjects accurately reflects overall academic standing.
How do backlogs or failed subjects affect CGPA?
A failed subject typically earns 0 grade points. When included, its credit value still adds to total registered credits, lowering the overall average until cleared in a supplementary or re-evaluation exam.
Are non-credit or audit courses included in CGPA?
Non-credit courses (0 credits) require a passing grade for degree eligibility but carry 0 weight in the mathematical denominator, so they do not alter your numerical CGPA.