When a class uses category weights, your course grade is a weighted sum: each category average is multiplied by how much that category counts. This page focuses on the weighted grade formula — the equation, the algebra and worked examples you can copy.
All numbers below are made-up for teaching the math. Always use the weights on your own syllabus.
The formula in one line
If every category you include has a score, and you write weights as decimals (30% → 0.30):
- Weighted grade = (score₁ × weight₁) + (score₂ × weight₂) + … + (scoreₙ × weightₙ)
When the weights you used add up to 1 (that is, 100%), that sum is your course percentage.
If the weights you used add up to something other than 1 — for example mid-semester, when some categories are still empty — divide by the sum of those weights:
- Weighted grade = (score₁ × weight₁ + … + scoreₖ × weightₖ) ÷ (weight₁ + … + weightₖ)
Same idea in percent form (weights as 20, 30, … instead of 0.20, 0.30):
- Weighted grade = (score₁ × w₁ + … + scoreₖ × wₖ) ÷ (w₁ + … + wₖ)
where each w is the weight percent. Dividing by the total of the w values scales the result back to a percentage.
Why the formula works
Think of each weight as a share of the course. A 20% homework category is one-fifth of the grade; a 40% final is two-fifths. Multiplying a category average by its weight converts "how you did in that pile of work" into "how many grade points that pile contributes."
Adding those contributions rebuilds the whole grade. Dividing by the total weight used is only needed when you are looking at a partial set of categories, so the shares still add up correctly among the work that exists so far.
A step-by-step walkthrough with mid-semester tables also appears in how to calculate a weighted grade. This article stays close to the equation and the algebra.
Worked example: all categories finished
Suppose a course uses these weights and you already have every category average:
| Category | Weight | Score | Contribution (score × decimal weight) |
|---|---|---|---|
| Homework | 15% | 94% | 94 × 0.15 = 14.10 |
| Quizzes | 20% | 86% | 86 × 0.20 = 17.20 |
| Midterm | 25% | 78% | 78 × 0.25 = 19.50 |
| Final | 40% | 88% | 88 × 0.40 = 35.20 |
Weights total 15 + 20 + 25 + 40 = 100% (or 1.00 as a decimal).
- Sum of contributions: 14.10 + 17.20 + 19.50 + 35.20 = 86.00
- Weighted grade = 86%
Using the percent form of the formula gives the same result: (94×15 + 86×20 + 78×25 + 88×40) ÷ 100 = (1410 + 1720 + 1950 + 3520) ÷ 100 = 8600 ÷ 100 = 86.
Check your weighted grade or what you need on the final — free, in your browser.
Open the free grade calculator →Worked example: mid-semester (weights do not total 100% yet)
Same syllabus, but the final has not happened, and you want your current grade from graded work only:
| Category | Weight | Score | Contribution |
|---|---|---|---|
| Homework | 15% | 94% | 14.10 |
| Quizzes | 20% | 86% | 17.20 |
| Midterm | 25% | 78% | 19.50 |
- Contributions: 14.10 + 17.20 + 19.50 = 50.80
- Weights used: 0.15 + 0.20 + 0.25 = 0.60
- Current weighted grade = 50.80 ÷ 0.60 = 84.67% (about 84.7%)
If you forgot to divide by 0.60 and treated 50.80 as a finished grade, it would look like a failing score. It is not: you have only completed 60% of the weighted work. Leave empty categories out of both the numerator and the denominator. Do not enter them as zero unless you actually scored zero.
Algebra: solving for a missing score
Often you know the weights and every score except one — usually the final — and you want that missing score. Start from the full formula and rearrange.
Let:
G= target course grade (as a percent)F= unknown final scorew_f= final weight as a decimalC= sum of (score × weight) for every other categoryW= sum of those other weights (as decimals)
Then:
- G = C + (F × w_f) when all weights total 1
- So F = (G − C) ÷ w_f
Numeric example
Using the table above, homework + quizzes + midterm already contribute C = 50.80, and w_f = 0.40. You want a course grade of at least G = 85.
- F = (85 − 50.80) ÷ 0.40 = 34.20 ÷ 0.40 = 85.5
You need about 85.5% on the final to land an 85% in the course (assuming nothing else changes). For more "what do I need" scenarios, see what do I need on my final.