What this weighted grade calculator does
This tool computes a weighted average of any number of assessments. Each row is one assessment — a quiz, an assignment, a midterm, a final exam — with its own grade and its own weight. Unlike a simple average, which treats every assessment as equally important, a weighted average gives larger influence to assessments with larger weights. A 40-mark final and a 5-mark quiz should not count the same, and this calculator ensures they don't. It also shows the arithmetic behind the result: the numerator (Σ grade × weight), the denominator (Σ weight), and each row's individual contribution, so you can see exactly where your average is coming from.
Formula
Variable definitions
- gi — grade of assessment i, entered as a percentage (0–100).
- wi — weight of assessment i, any positive number (marks, percentage, credit hours, or arbitrary units).
- Σ — sum over all assessments from i = 1 to n.
Because the denominator is the sum of weights, the formula works whether your weights total 100, 40, or 250. Percentages, raw marks, and credit hours all produce the same weighted average as long as every weight is on the same scale.
Worked examples
Example 1: Weights that add to 100
- Σ (grade × weight) = 70×10 + 85×10 + 90×20 + 65×25 + 75×35 = 700 + 850 + 1800 + 1625 + 2625 = 7600.
- Σ weight = 10 + 10 + 20 + 25 + 35 = 100.
- Weighted grade = 7600 / 100 = 76.00%.
- Because the weights sum to 100, the weighted grade looks like a normal percentage average of the assessed marks.
Example 2: Weights that add to 40 (not 100)
- Σ (grade × weight) = 80×5 + 92×15 + 78×20 = 400 + 1380 + 1560 = 3340.
- Σ weight = 5 + 15 + 20 = 40.
- Weighted grade = 3340 / 40 = 83.50%.
- Even though the weights sum to 40, the division by 40 normalises the result. The answer is a valid percentage grade.
Example 3: Credit-hour weights (university style)
- Σ (grade × credit) = 75×3 + 82×4 + 68×3 + 88×2 = 225 + 328 + 204 + 176 = 933.
- Σ credits = 3 + 4 + 3 + 2 = 12.
- Weighted grade = 933 / 12 = 77.75%.
- Physics had the largest influence because it carried the most credit hours, not because 82 was the highest mark.
Example 4: Raw marks as weights
- Σ (grade × weight) = 90×20 + 60×50 + 75×100 = 1800 + 3000 + 7500 = 12300.
- Σ weight = 20 + 50 + 100 = 170.
- Weighted grade = 12300 / 170 = 72.35%.
- Notice Test 2's low score drags the average down hardest, because it carried the second-largest weight.
Example 5: All weights equal
- Σ (grade × weight) = 88 + 76 + 92 + 80 = 336.
- Σ weight = 4.
- Weighted grade = 336 / 4 = 84.00%.
- When every weight is equal, the weighted average equals the simple arithmetic mean — a useful sanity check.
Example 6: Zero weight (an ungraded practice quiz)
- Σ (grade × weight) = 40×0 + 85×10 + 78×40 = 0 + 850 + 3120 = 3970.
- Σ weight = 0 + 10 + 40 = 50.
- Weighted grade = 3970 / 50 = 79.40%.
- The practice quiz contributed nothing — its weight of 0 means it was ignored entirely, regardless of the 40% score.
Why the denominator is Σ weight, not 100
Many students learn the weighted average formula with an implicit assumption that all weights add to 100. That assumption is convenient but not necessary. The correct denominator is the sum of the weights you actually used. If you entered weights totalling 100, the two are the same. If you entered weights totalling 40, dividing by 100 would give a wrong answer that understates the grade by a factor of 2.5.
- Weights as percentages: total 100 → divide by 100.
- Weights as raw marks: total might be 170 → divide by 170.
- Weights as credit hours: total might be 12 → divide by 12.
- Weights as arbitrary importance scores: total might be 30 → divide by 30.
The formula is scale-invariant: multiplying every weight by 2 does not change the result, because both the numerator and denominator double. This is what makes the weighted average usable with any consistent weight scheme.
Common mistakes to avoid
- Forcing weights to add to 100. If you only know relative weights (1, 2, 3), use them as-is. There is no need to scale them.
- Dividing by 100 instead of by the sum of weights. This is the single most common error. If your weights don't total 100, dividing by 100 gives a wrong answer.
- Mixing percentages and raw marks in the grade column. Grades should all be percentages. Convert 17/20 to 85% before entering it.
- Averaging the grades first, then applying weights. The weights must be applied to each grade before summing, not after.
- Treating a weight of 0 as an error. A weight of 0 is valid — it means the assessment does not count. Only when every weight is 0 does the calculation become undefined.
- Forgetting to include every assessment. A missing row means a missing contribution. If a quiz counted toward your grade, it should be in the list, even if its weight is small.
- Assuming a weighted grade is bounded by 0 and 100 automatically. If any grade is outside 0–100, the weighted average can also fall outside. The calculator validates each grade for you.
FAQ
What is a weighted grade?
A weighted grade is an average where each assessment counts for a different amount. A test worth 30% of your grade pulls the average three times as much as an assignment worth 10%. The weighted grade is calculated by multiplying each grade by its weight and dividing the total by the sum of all weights.
Do the weights have to add up to 100?
No. The weighted average formula divides by the sum of weights, so any set of positive weights gives a correct result. If your weights happen to sum to 100, the result is the same as treating them as percentages. If they sum to something else (say 20 or 250), the calculation still works because the division by the total weight normalises the result.
How is the weighted grade different from a simple average?
A simple average treats every assessment equally. A weighted average gives more influence to assessments with larger weights. If your exam is worth 50% and a quiz is worth 5%, a low exam score hurts your weighted grade far more than a low quiz score would.
Can a weighted grade be higher than all the individual grades?
No. A weighted average is always between the smallest and largest of the individual grades. It can be equal to one of them if all other grades match it, but it can never exceed the highest grade or fall below the lowest.
What happens if I enter a weight of 0?
A weight of 0 means the assessment does not count toward your grade. The calculator allows it — the term contributes nothing to the numerator or the denominator. If every weight is 0, the calculation is undefined, and the calculator flags this as a domain error.
Can I mix percentages and marks out of different totals?
Yes, as long as each grade is entered as a percentage. If your assignment is scored out of 20 and you got 17, convert it to 85% first. The weighted average works on percentages regardless of what each individual assessment was scored out of.
Related tools
Related Hira Academy resources
Track your term progress with the free Student Portal, and revise subject content with our Class 9 notes and Class 10 notes.