Weighted grade:
why 80, 90 and 70 do not average to 80
Work out an overall mark from components with different weights, and find the exam score you need for a target grade.
Calcylator Editorial Team
Updated · 4 min read
Why the simple average gives the wrong answer
A course rarely treats all assessments equally. A weekly quiz might be worth a fifth of the grade, a project a third and the final exam a half. If you average the three percentages without regard for weight, you are treating a quiz as important as an exam, and the result tells you nothing reliable about where you stand.
Take scores of 80, 90 and 70. Their simple average is 80. Weighted by what they are actually worth, the overall mark is 78. The 2-point gap seems small, but near a grade boundary it can be the difference between a B and an A-minus, and it grows when the weights are more unequal.
Weights also reflect how the course designer expects learning to be shown. A project that takes weeks to complete earns more than a quick quiz, and a final exam that covers everything earns more than either. The weights are a statement of priorities, which is why a strong result in a heavy component is worth much more than a perfect score in a light one.
The formula
- Score:
- Mark in one component, as a percentage
- Weight:
- Share of the course grade that component carries
- Σ:
- Sum over all components
Quizzes
80% × 20% = 16.0
Project
90% × 30% = 27.0
Exam
70% × 50% = 35.0
Total of products
16 + 27 + 35 = 78
Sum of weights
20 + 30 + 50 = 100
Overall grade
78%
78 ÷ 100 = 78%; the weights add to 100%, so no further scaling is needed.
The mental model is that the exam supplies 35 of the 78 points, the project 27 and the quizzes 16. Seeing each component's contribution as points rather than percentages makes it easy to spot where marks were lost.
A quick check protects against slips. The overall grade must fall between the lowest and highest component scores, and it should sit closer to the components with the most weight. If a result of 70 or 90 appears for the example above, an input was entered wrongly or a weight was applied twice.
Spreadsheets make this routine. A SUMPRODUCT of the score column and the weight column, divided by the SUM of the weights, reproduces the formula exactly and updates itself each time a new mark is typed in.
When only some marks are in
Midway through a course, the weights of finished components do not add to 100. In that case divide by the sum of the weights you have, which re-scales the result to the work done so far.
Quizzes
80% × 20% = 16
Project
90% × 30% = 27
Sum of weights so far
50
Working
(16 + 27) ÷ 50
Grade so far
86%
The final exam, worth the remaining 50%, is still to come.
This is a snapshot of the completed work and not a forecast. The remaining weight is large and can move the overall grade a long way, in either direction.
Working out the score you need on the exam
Rearrange the formula to solve for the missing component. Subtract the points already earned from the target, then divide by the weight of the remaining piece.
- Target:
- Overall grade you want
- Points earned:
- Sum of score × weight so far
- Weight:
- As a decimal, 0.5 for a 50% component
Points so far
16 + 27 = 43
Target overall
85%
Exam weight
0.5
Working
(85 − 43) ÷ 0.5
Exam score needed
84%
For a 90% target the exam would need (90 − 43) ÷ 0.5 = 94%.
| Exam score | Overall grade |
|---|---|
| 60% | 73% |
| 70% | 78% |
| 80% | 83% |
| 90% | 88% |
| 100% | 93% |
The table has a ceiling. With 43 points banked and 50 on offer, the highest possible overall mark is 93%, so a target above that is out of reach whatever the exam score. Knowing this early helps you choose where to put effort.
Be careful when a course has a minimum pass mark on the final in addition to the overall grade. Some departments require, say, 40 per cent on the exam itself regardless of the course total, and the required score in the formula is then the larger of the two figures. Check the syllabus for these gate rules before you plan your effort.
When components are scored in points
Many courses report raw points instead of percentages. In that case, the weight of a component is built into its maximum points, and the overall grade is just total points earned divided by total points possible.
| Component | Points earned | Points possible | Equivalent weight |
|---|---|---|---|
| Homework | 42 | 50 | 10% |
| Midterm | 68 | 100 | 20% |
| Lab reports | 110 | 150 | 30% |
| Final exam | 74 | 100 | 40% |
Because the points possible differ, you cannot add the percentages directly. The weighted method keeps things consistent: convert each component to a percentage, multiply by its weight and add.
Homework
42 ÷ 50 = 84% × 10% = 8.4
Midterm
68 ÷ 100 = 68% × 20% = 13.6
Lab reports
110 ÷ 150 = 73.3% × 30% = 22.0
Final exam
74 ÷ 100 = 74% × 40% = 29.6
Sum
8.4 + 13.6 + 22.0 + 29.6
Overall grade
73.6%
Lab reports: 73.33% × 0.30 = 22.0; the total is 73.6%.
If the course simply pooled its points instead, the total would be 294 ÷ 400 = 73.5%. That is close to 73.6% but not identical, because the point shares of 12.5%, 25%, 37.5% and 25% differ from the stated weights of 10%, 20%, 30% and 40%. Always use whichever scheme the syllabus names, and ask the instructor if it is not clear.
Credits, GPA and rounding
The same arithmetic runs university credit systems. Each course grade point is weighted by its credits. Courses worth 4, 3 and 2 credits with grade points of 8, 9 and 7 give (32 + 27 + 14) ÷ 9 = 8.11, not the simple mean of 8. Scales differ by institution, so use the one your own university publishes.
- Check whether the instructor drops the lowest quiz or caps a component, as that changes the inputs before you weight them.
- Round only at the end, since rounding each component first can shift the final figure by a point or more.
- Use the weights from the syllabus, as percentages sometimes get revised in a term.
- Treat extra credit as an added score on the component it belongs to, rather than as a separate weight.
- If a component was marked out of points, not percent, convert it to a percentage before weighting.
Common questions
How do you calculate a weighted grade?
Multiply each score by its weight, add the products, and divide by the sum of the weights. With 80% × 20%, 90% × 30% and 70% × 50%, the products are 16, 27 and 35, and the total is 78%.
What if my weights do not add up to 100%?
Divide the sum of score × weight by the sum of the weights you have. For weights of 20 and 30 with scores of 80 and 90, the total is 43 divided by 50, which gives an 86% grade so far.
How do I find what I need on the final exam?
Subtract your earned points from the target overall grade and divide by the exam's weight as a decimal. With 43 points earned, a target of 85% and a 50% exam, the answer is (85 − 43) ÷ 0.5 = 84%.
Why is my weighted grade lower than my average score?
Because the lower marks sit in the heavier components. Marks of 80, 90 and 70 average 80, but the 70 carries half the weight, so the weighted result is 78. The weights decide how much each score matters.
Is a weighted grade the same as GPA?
They use the same idea of weighting, but GPA applies credit hours to grade points across courses, while a weighted course grade applies assessment weights within one course. Your institution's scale and rounding rules govern the official figures.
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