A weighted average multiplies each value by its weight, adds the products, then divides by the sum of the weights. Use it when some results represent a larger share of the whole—for example, an exam worth more than a quiz, or a class with more students.
You can check the arithmetic with CheckMatter’s Scientific Calculator. This guide works through percentage weights, unequal group sizes, incomplete grades and a target-score calculation. All examples are invented, and the scores use the same 0–100 scale.
Method and examples checked on 20 October 2026 under our editorial policy. For an official grade, follow the assessment rules set by your school or course. These examples do not convert a percentage into an institutional GPA.
The weighted average formula
Weighted average = sum of (value × weight) ÷ sum of weights.
A simple average treats every entry equally. For values 80, 70 and 90, it is (80 + 70 + 90) ÷ 3 = 80. A weighted average can give a different answer because the entries contribute different amounts.
Weights can be percentages, credit counts, quantities or relative shares. Use one consistent basis and a positive total weight. The examples here use non-negative weights; negative weights do not have the ordinary interpretation of shares or counts.
Microsoft’s official guide to averages demonstrates a weighted average by dividing a sum of value–weight products by the total weight. The same arithmetic works without a spreadsheet.
Worked example: an exam carries more weight than a quiz
Suppose a course has three components, each already expressed as a score out of 100:
| Component | Score | Weight | Score × weight |
|---|---|---|---|
| Quiz | 80 | 20 | 1,600 |
| Project | 70 | 30 | 2,100 |
| Exam | 90 | 50 | 4,500 |
| Total | — | 100 | 8,200 |
The weighted result is 8,200 ÷ 100 = 82, or 82% on this score scale. The simple average was 80. The exam’s higher score influences the weighted result more because it accounts for half of the final grade.
You can also use decimal weights: 80 × 0.20 + 70 × 0.30 + 90 × 0.50 = 82. Because those weights add to 1, division by their total does not change the answer. Do not mix 20 with 0.30 and 0.50 in one calculation.
Check the result in two calculator steps
- Open the Scientific Calculator and press AC.
- Enter
80 × 20 + 70 × 30 + 90 × 50using the keypad, then press =. Check that the result is 8200. - Note the result, press AC, and enter
8200 ÷ 100. Press = to obtain 82.
This separates the numerator from the final division and makes the calculation easy to audit in the history. It also avoids relying on bracket entry. Enter percentage weights as ordinary numbers for this method; you do not need the calculator’s % key.
For larger lists in Excel, put values in A2:A4 and weights in B2:B4, then use =SUMPRODUCT(A2:A4,B2:B4)/SUM(B2:B4). Keep the corresponding values and weights on the same rows.
Why averaging two class averages can be wrong
Imagine Class A has 10 students with an average score of 60, while Class B has 30 students with an average of 80. Their combined student average is:
(60 × 10 + 80 × 30) ÷ (10 + 30) = 3,000 ÷ 40 = 75.
The simple average of the two class averages is 70, but that gives a class of 10 students the same influence as a class of 30. To find an average across all students, weight each class average by the number of students represented.
This works when the classes use comparable score definitions, the groups do not overlap and each class mean represents the stated count. If the reported class averages were rounded, the combined figure is also approximate.
What if only some assessments are complete?
Return to the quiz and project above, before the exam has been taken. The completed weighted products total 1,600 + 2,100 = 3,700, and their weights total 50.
Completed-work average = 3,700 ÷ 50 = 74. Separately, those completed components contribute 37 percentage points toward the full-course total: 3,700 ÷ 100 = 37.
These are different quantities. A completed-work average of 74 is not a final grade of 74, and treating the unfinished exam as zero would produce 37 for the full-course calculation. Whether a gradebook excludes, estimates or assigns zero to missing work depends on the course rules. Label the result you are reporting.
Find the score needed on the remaining exam
Suppose the same student wants an overall 85 and the exam is worth 50%. The completed assessments contribute 37 percentage points:
Required exam score = (85 − 37) ÷ 0.50 = 96.
Check it by substitution: 80 × 0.20 + 70 × 0.30 + 96 × 0.50 = 85. If the required result exceeded the allowed maximum of 100, that target would be unattainable under these assumptions. Extra credit, dropped assessments or other rules would need a different model.
Checks that catch common mistakes
- Check the score scale. A quiz score of 18 out of 20 is 90%, while 70 out of 100 is 70%. With equal assessment weights, their average percentage is 80%, not the average of the raw numbers 18 and 70. Total-points grading is a different rule.
- Check the denominator. Divide by total weight, not by the number of rows. Weights 2, 3 and 5 are equivalent to 20, 30 and 50 because all are scaled by the same factor.
- Check the range. With non-negative weights and a positive total, the answer must lie between the smallest and largest values that have positive weight.
- Keep zero values distinct from zero weights. A score of zero with a 20% weight affects the result. A zero-weight item does not contribute. An all-zero weight total makes the weighted average undefined.
- Round at the end. Keep the full products and denominator until the final division, then apply the rounding rule required for the task.
If you need help turning a raw score into a percentage first, use the Percentage Calculator. For grouping arithmetic safely, our order of operations guide explains why division must apply to the whole weighted total.
Choose weights that match the question, keep the values comparable, and show both totals. That makes a weighted average easier to check and harder to confuse with a simple mean.