Points versus percents: two averages, one gradebook
Ask "what is my average" and most people expect one answer. But a stack of graded assignments supports two defensible averages, courses genuinely use both, and the difference between them is not a rounding error — on the right gradebook it is fifteen points. This guide shows both formulas, when they disagree, and how to tell which one your course runs.
The two formulas
Total points treats the whole course as one big assignment: add everything you earned, divide by everything possible.
total points = Σearned ÷ Σpossible × 100
Average of percents scores each assignment on its own, then averages those percents with equal weight:
average of percents = mean(earnedᵢ ÷ possibleᵢ × 100)
Under total points, big assignments matter more automatically — a 50-point test carries five times the freight of a 10-point quiz. Under average of percents, every assignment is a full vote regardless of size. Same gradebook, different philosophies.
The worked example
Three assignments: 45/50, 8/10, and 27/30 — that is 90%, 80%, and 90% individually.
Total points: you earned 45 + 8 + 27 = 80 of a possible 50 + 10 + 30 = 90, and 80 ÷ 90 × 100 = 88.9.
Average of percents: (90 + 80 + 90) ÷ 3 = 86.7.
The 80% quiz is the whole story of the gap. By points it is 10 of 90 possible — about 11% of the course, so its weak score barely dents the total. By percents it is a full third of the average, and it drags the result down 2.2 points further. Which number is "your average"? Whichever one the syllabus computes. Both are correct arithmetic; only one is your grade.
How far apart can they get?
Make the sizes extreme and the gap gets dramatic. A 95/100 essay and a 3/5 pop quiz: total points gives 98 ÷ 105 × 100 = 93.3, while average of percents gives (95 + 60) ÷ 2 = 77.5 — a 15.8-point spread between an A and a C+ on a common scale, from one five-point quiz. Students on percent-averaged syllabi learn this the hard way: small assignments are not small. A pop quiz worth five points can carry the same weight as the midterm.
The reverse intuition holds on total-points syllabi: blowing a five-point quiz there is nearly free, and the rational study hour goes wherever the points are. Neither system is wrong. They just reward different behavior, which is exactly why you should know which one you are in before finals week.
How to tell which method your course uses
Read the syllabus grading section for one of these tells. "Your grade is total points earned divided by total points possible" is the points method. "Assignments are averaged" or a category table with weights (homework 20%, exams 40%) means percents are being averaged — inside categories, and then across them with weights, which is the weighted-grade math. When every assignment in a category is worth the same points, the two methods agree exactly and the question dissolves; the calculator notes when that happens with your numbers.
Fine print that actually matters
Extra credit fits both methods — a 12/10 quiz simply adds two bonus points to the numerator (points) or scores as 120% (percents), and the calculator accepts it. What neither formula covers is policy layered on top: dropped lowest scores (the test average calculator handles that transparently), replacement rules, or category caps. And a percent average feeding a letter grade still has to pass through your school's scale, which is the percent-to-letter converter's territory. The syllabus decides every one of these; it always wins.