CalculateY
Quick Answer
Three assignments with grades 95%, 80%, and 70% at weights 20%, 30%, and 50% produce a weighted grade of 79.0%.
Common Examples
| Input | Result |
|---|---|
| 95% (20%), 80% (30%), 70% (50%) | Weighted grade: 78.00% |
| 88% (25%), 92% (25%), 76% (50%) | Weighted grade: 83.00% |
| 100% (10%), 85% (40%), 90% (50%) | Weighted grade: 89.00% |
| 70% (30%), 85% (30%), 95% (40%) | Weighted grade: 84.50% |
How It Works
The Formula
Weighted Grade = Sum(Grade x Weight) / Sum(Weight)
In a weighted grading system, different assignments contribute different amounts to the final grade. A final exam worth 40% of the grade has twice the impact of homework worth 20%. The weighted average accounts for these differences.
Step by step:
- Multiply each assignment’s grade by its weight
- Sum all those products
- Divide by the sum of all weights
When all weights add up to 100%, the formula simplifies to: Weighted Grade = Sum(Grade x Weight / 100). If weights do not add to 100%, the calculator still produces a valid weighted average by dividing by the actual total weight.
Worked Example
A course has three graded components: Homework (20% weight, grade 95%), Midterm (30% weight, grade 80%), and Final Exam (50% weight, grade 70%).
Weighted sum = (95 x 20) + (80 x 30) + (70 x 50) = 1,900 + 2,400 + 3,500 = 7,800
Total weight = 20 + 30 + 50 = 100
Weighted Grade = 7,800 / 100 = 78.00%
Notice that even though the student scored 95% on homework, the overall grade is 78% because the final exam (where the student scored 70%) carries the largest weight at 50%.
Weighted vs. Unweighted Averages
An unweighted (simple) average treats all assignments equally. If the same three grades above were averaged without weights, the result would be (95 + 80 + 70) / 3 = 81.67%. The weighted average of 78.00% is lower because the lowest grade carries the most weight. Understanding this difference is important for planning study time and prioritizing assignments that carry higher weights.