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Mathematical Proof & Formula

Grade Point Average (GPA) Formula

Calculates semester or collegiate GPA by weighting letter grade quality points with course credit hours.

Mathematically Verified Proof
•Standard Curricular Mathematics•Peer-Reviewed Formulas
\text{GPA} = \frac{\sum_{i=1}^{n} (P_i \times C_i)}{\sum_{i=1}^{n} C_i}

Variable Definitions

Variable SymbolMathematical Meaning
P_iGrade quality points for course i (e.g. 4.0 for A, 3.0 for B)
C_iCredit hours assigned to course i

Calculation Steps

  1. Convert each letter grade to numeric grade points.
  2. Multiply grade points by credit hours to find quality points.
  3. Sum all course quality points.
  4. Divide by total attempted credit hours.

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Authoritative References & Academic Standards

Vetted against official government, institutional, and collegiate guidelines

.org sourceOfficial Source
Collegiate Grading Systems & Transcript Evaluation
AACRAO (American Association of Collegiate Registrars and Admissions Officers)

National academic standards for undergraduate 4.0 quality points, credit-hour weighting, and transcript calculations.

.org sourceOfficial Source
AP Course Rigor and 5.0 Weighted Grading Framework
College Board AP Central

Official standards for Advanced Placement course difficulty, AP exam grading scales, and high school weighted point bonuses.

.org sourceOfficial Source
Grade Point Average (GPA) & Quality Points
Wikipedia (Educational Assessment)

Overview of secondary and higher education grading metrics, honors multipliers, and collegiate Latin honors thresholds.