GPA Formula – Grade Point Average Calculation

The complete GPA formula with variable definitions, a grade-point conversion table, step-by-step usage, and fully worked examples for semester and cumulative GPA.

Formula

GPA = \frac{\sum ( GP \times C R )}{\sum C R}

GPA is the weighted mean of grade points (GP) earned in each course, weighted by the number of credit hours (CR) per course. Quality points for a course = GP × CR.

Variables

Symbol	Name	Description	Unit
GPA	Grade Point Average	The final weighted average on the 0.0 – 4.0 scale	—
GP	Grade Points	The numeric value assigned to a letter grade (e.g., A = 4.0, B = 3.0)	—
CR	Credit Hours	The number of credit hours (units) a course is worth	—
QP	Quality Points	Quality points for one course: QP = GP × CR	—
n	Number of courses	The total number of courses included in the GPA calculation	—

How to Use

Look up the grade point value for each letter grade using the 4.0 scale (A = 4.0, B = 3.0, C = 2.0, D = 1.0, F = 0.0, with ± adjustments).
Multiply the grade point value by the credit hours for each course to get quality points (QP = GP × CR).
Add all quality points together: ΣQP.
Add all credit hours together: ΣCR.
Divide total quality points by total credit hours: GPA = ΣQP / ΣCR.

Examples

1. Semester GPA — three courses

A student takes three courses in one semester:

Course	Credits (CR)	Grade	GP	QP = GP × CR
Mathematics	3	A	4.0	12.0
English	3	B+	3.3	9.9
Physics	4	B	3.0	12.0

GPA = \frac{12.0 + 9.9 + 12.0}{3 + 3 + 4} = \frac{33.9}{10} = 3.39

ℹSemester GPA = 3.39 — Good Standing.

2. Impact of one failing grade

The same student retakes Physics but also fails a new 2-credit elective.

Course	Credits	Grade	GP	QP
Mathematics	3	A	4.0	12.0
English	3	B+	3.3	9.9
Physics	4	A−	3.7	14.8
Art Elective	2	F	0.0	0.0

GPA = \frac{12.0 + 9.9 + 14.8 + 0.0}{3 + 3 + 4 + 2} = \frac{36.7}{12} = 3.06

⚠One F in a 2-credit course dropped the GPA from 3.39 to 3.06. The F contributes 0 quality points but still adds to total credit hours.

3. Cumulative GPA across two semesters

Calculate cumulative GPA by pooling all quality points and all credit hours — do NOT average the semester GPAs.

Semester	ΣQP	ΣCR	Semester GPA
Fall	33.9	10	3.39
Spring	42.3	12	3.53

Cumulative GPA = \frac{33.9 + 42.3}{10 + 12} = \frac{76.2}{22} \approx 3.46

ℹCumulative GPA = 3.46. Note: averaging the semester GPAs ((3.39 + 3.53) / 2 = 3.46 here, but will differ when credit totals are unequal).

4. GPA needed to reach a target

A student has 60 credit hours completed with a cumulative 2.80 GPA and wants to reach 3.0 by the end of next semester (15 additional credits). What GPA is needed next semester?

Current QP = 2.80 \times 60 = 168.0

Target QP = 3.00 \times (60 + 15) = 3.00 \times 75 = 225.0

QP Needed Next Semester = 225.0 - 168.0 = 57.0

Required Semester GPA = \frac{57.0}{15} = 3.80

⚠The student needs a 3.80 semester GPA — mostly A grades — to reach a 3.0 cumulative from a 2.80 starting point with only 15 remaining credits.

Use the Calculator — Interactive calculator for this formula
Read the Notes — Step-by-step explanation with worked examples