A test or quiz score
Percent = points earned ÷ points possible × 100
17.5 of 20 points: 17.5 ÷ 20 × 100 = 87.5%.
Grade and GPA formulas on one page
Most grade questions come down to one of thirteen formulas. A class grade is each score times its weight, divided by the weights that have a score; a GPA is grade points times credits, divided by credits; the score you need on a final is your goal minus what your grade so far already gives, divided by the final’s weight. Each formula below has one worked example and a link to the calculator that does it for you.
It fits on one page.
Download the grade and GPA workbook An Excel file with these formulas for a class grade, the score a final needs, a term GPA, a cumulative GPA and a GPA goal; type your own numbers over the example.
Each formula is also an image, with its worked example, for a slide or a class page: use “Download as an image” under it. The image carries this page’s address.
Class grades
A weighted class grade
Grade = (score × weight + score × weight + …) ÷ the weights of the categories with a score
Homework 92 at 40%, tests 85 at 40%, final project 78 at 20%: (92 × 40 + 85 × 40 + 78 × 20) ÷ 100 = 86.4%. A category with no score yet is left out, not counted as zero: 80 at 60% with the final still blank is 80% so far.
A class graded in points
Grade = all points earned ÷ all points possible × 100
9 of 10 on a quiz and 20 of 40 on a test: 29 ÷ 50 × 100 = 58%. The bigger test counts more, as its points say.
An average of grades that count the same
Average = sum of the grades ÷ number of grades
92, 85, 78 and 88: 343 ÷ 4 = 85.75%.
The score you need on the final
Needed = (goal − grade now × (1 − final weight)) ÷ final weight
87% now, a 90% goal, a final worth 30%: (90 − 87 × 0.7) ÷ 0.3 = 97%.
A semester grade
Semester = quarter 1 × its weight + quarter 2 × its weight + final × its weight
92 and 86 at 40% each and a 90 final at 20%: 36.8 + 34.4 + 18 = 89.2%. Before the final, a 90% semester needs (90 − 71.2) ÷ 0.2 = 94% on it.
The letter for a percentage
Letter = the highest cutoff your percentage reaches on your class scale
89.5% on the common US plus/minus scale: B+, because 89.5 is under the 90 cutoff. Only if your teacher rounds to whole percents first does it become 90, an A-.
GPA
A GPA
GPA = (grade points × credits, added for every course) ÷ all credits
An A (4) in a 3-credit course, a B (3) in a 3-credit course, a C (2) in a 2-credit course: (12 + 9 + 4) ÷ 8 = 25 ÷ 8 = 3.125, shown as 3.13.
A weighted high school GPA
Weighted GPA = (grade points + the school’s Honors or AP bonus, for every class) ÷ number of classes
A in a regular class, B in Honors, A in AP, with a school that adds 0.5 for Honors and 1 for AP: unweighted (4 + 3 + 4) ÷ 3 = 3.67; weighted (4 + 3.5 + 5) ÷ 3 = 4.17. The bonus is your school’s rule, not a national one.
A cumulative GPA from terms
Cumulative = (term GPA × term credits, added for every term) ÷ all credits
2.60 over 15 credits, 3.40 over 15 and 3.80 over 6: (39 + 51 + 22.8) ÷ 36 = 3.13. A plain average of the three GPAs would give 3.27, too high, because it counts the 6-credit term as much as each 15-credit one.
The GPA you need to reach a goal
Needed = (goal × (credits done + credits to come) − GPA now × credits done) ÷ credits to come
A 3.20 over 60 credits and a 3.40 goal after 30 more: (3.4 × 90 − 3.2 × 60) ÷ 30 = (306 − 192) ÷ 30 = 3.8.
Marking and curves
A test marked by questions wrong
Score = (questions − questions wrong) ÷ questions × 100
25 questions, 3 wrong: 22 ÷ 25 × 100 = 88%.
A flat curve
Curved score = score + the same points for everyone, at most 100
Scores of 50, 60 and 70 with 10 points added: 60, 70, 80. The class mean moves from 60 to 70.
The examples are worked by the same code the calculators run. Your school’s own rules come first: its weights, its grade points, whether it rounds, and what a blank or a retake does. The published scales and policies the calculators use are listed under Sources, at the foot of the page.
classgradecalculator.com/grade-formulas