A weighted grade is a course grade built from categories that count for different shares: homework a fifth, tests two fifths, the final a fifth, in whatever split the syllabus sets. The arithmetic is one line, but three things trip people: weights that do not add to 100, categories with nothing in them yet, and the difference between a weighted system and a points system. This page has the calculator, the formula, the worked example and a what-if table, with a printable worksheet.
Download the weighted grade worksheet (PDF) (the formula, a worked example, a blank table for your own categories, the letter scales and the what-if table for each weight; two pages, free).
The calculator
The formula
Course grade = (w1 x s1 + w2 x s2 + ... + wn x sn) / (w1 + w2 + ... + wn)
where w is each category's weight and s is your score in it. When the weights add to 100 the denominator is 100, and the grade is just the sum of weight x score / 100. Each product is the category's contribution in percentage points.
Worked example. A course graded 20 percent homework, 20 percent quizzes, 40 percent tests, 20 percent final exam:
| Category | Weight | Score | Contribution (weight x score / 100) |
|---|---|---|---|
| Homework | 20% | 95% | 19.00 points |
| Quizzes | 20% | 82% | 16.40 points |
| Tests | 40% | 78% | 31.20 points |
| Final exam | 20% | 85% | 17.00 points |
| Course grade | 100% | 83.60% |
83.60 percent is a B on the plus-minus scale and a B on the 10-point scale. The tests category, at 40 percent, contributed 31.20 of the 83.60 points; the student's 78 there cost more than the 82 in quizzes, because it was weighted twice as heavily.
Weights that do not add to 100
Divide by the real total. Three categories weighted 30, 30 and 30 give (30a + 30b + 30c) / 90, which is the plain average. The calculator does this automatically and says so. The same rule explains what gradebooks do before a category has any marks: a course with a 20 percent final that has not happened yet is graded on the other 80, so the displayed grade is (20 x 95 + 20 x 82 + 40 x 78) / 80 = 83.25 in the example above, and it drops to 83.60 the moment the 85 on the final is entered. A grade that "fell for no reason" on the day a new category opened fell for this reason.
Percentage systems and points systems
Two kinds of gradebook, which look alike and are not:
| Weighted (percentage) system | Points system | |
|---|---|---|
| What is fixed | Each category's share of the grade | Each assignment's point value |
| One 10-point quiz in a 20% quiz category with four quizzes | Worth 5% of the course grade | Worth 10 points out of whatever the course total is |
| Adding an extra assignment to a category | Dilutes the others in that category; the category's share is unchanged | Raises the course total; every other assignment's share shrinks a little |
| How to compute the grade | This page's formula | Total points earned / total points possible |
| Where it says which | The syllabus: "categories" and "weights" | The syllabus: "points" and a total |
A points course converts to this calculator by using each category's total possible points as its weight.
What moves the grade most: the what-if table
How much the course grade moves for five more points in a category, by the category's weight:
| Category weight | 5 more points in it moves the grade by | 10 more points |
|---|---|---|
| 10% | 0.50 | 1.00 |
| 15% | 0.75 | 1.50 |
| 20% | 1.00 | 2.00 |
| 25% | 1.25 | 2.50 |
| 30% | 1.50 | 3.00 |
| 40% | 2.00 | 4.00 |
| 50% | 2.50 | 5.00 |
| 60% | 3.00 | 6.00 |
Which is the whole strategy of a weighted course: a student at 83 with tests at 40 percent and homework at 10 percent raises the grade four times as fast per point on tests as on homework. The calculator reports this for your own heaviest category.
The letter scales
| Percentage | Plus-minus letter (Buffalo Public Schools) | 4.0 points | 10-point letter (North Carolina) | 4.0 points |
|---|---|---|---|---|
| 97-100 | A+ | 4.0 | A | 4.0 |
| 93-96 | A | 4.0 | A | 4.0 |
| 90-92 | A- | 3.7 | A | 4.0 |
| 87-89 | B+ | 3.3 | B | 3.0 |
| 83-86 | B | 3.0 | B | 3.0 |
| 80-82 | B- | 2.7 | B | 3.0 |
| 77-79 | C+ | 2.3 | C | 2.0 |
| 73-76 | C | 2.0 | C | 2.0 |
| 70-72 | C- | 1.7 | C | 2.0 |
| 67-69 | D+ | 1.3 | D | 1.0 |
| 65-66 | D | 1.0 | D | 1.0 |
| 60-64 | F | 0.0 | D | 1.0 |
| below 60 | F | 0.0 | F | 0.0 |
Both scales are real published scales (Buffalo Public Schools; the North Carolina state scale); yours may set an A at 94 or round 89.5 up. The percentage is the number; the letter is the school's reading of it.
What the number is for
Run it in week six, not week eighteen. A weighted grade at mid-term tells a student three things: the category carrying the grade, the category dragging it, and how many points in the heavy category separate the current letter from the next. For what you need on the final specifically, the final grade calculator; for two quarters and an exam, the semester grade calculator; for a single test's percentage and letter, the test grade calculator.
Download the weighted grade worksheet (PDF) (the formula, the worked example, a blank category table, the letter scales and the what-if table; two pages, free).
Where to get help
A 1-on-1 online class with a tutor who holds a master's in mathematics and teaches the US curriculum, Algebra 1 to AP Calculus, chemistry and physics, at 7 am before school, after 4 pm and on weekend mornings, US time, for US$10 to $13 an hour: the grade worked out above read together in the free 30-minute first class, the category or the course where five more points cost least found, and the term spent on exactly that. How online tutoring from India to the USA works, or the 1-on-1 online tutoring page.
Questions parents ask
1How do you calculate a weighted grade?
2What if the weights do not add up to 100?
3What is the difference between a weighted and a points-based grade?
4How much does one category move the grade?
5Can I use this as a final grade calculator?
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