Weighted average calculator
A weighted average (or weighted mean) gives some values more influence than others. Instead of treating every number equally, each value is multiplied by a weight that reflects its importance before everything is combined. It is how course grades work when an exam counts for more than a quiz, how a portfolio return blends holdings of different sizes, and how survey results account for sample sizes.
How it works
Multiply each value by its weight, sum those products, then divide by the sum of the weights:
weighted average = Σ(value × weight) ÷ Σ(weight)
The weights do not need to sum to 1 or 100 — dividing by their total normalises them automatically, so weights of 3, 2, 1 behave exactly like 50%, 33%, 17%. Add as many rows as you need and the result updates live in your browser.
Example
Say a course grade combines a quiz of 80 (weight 1), a midterm of 70 (weight 2), and a final of 90 (weight 3):
| Component | Value | Weight | Value × Weight |
|---|---|---|---|
| Quiz | 80 | 1 | 80 |
| Midterm | 70 | 2 | 140 |
| Final | 90 | 3 | 270 |
The weighted average is (80 + 140 + 270) ÷ (1 + 2 + 3) = 490 ÷ 6 = 81.67. A plain average of 80, 70 and 90 would be 80, so the heavier final pulls the result up.
Where weighted averages come up in practice
Course grades. The most common use: when a final exam counts for 40%, a midterm for 30%, and homework for 30%, a plain average of your scores on those three components would give the wrong answer. The weighted average gives the right one.
Investment portfolios. A portfolio with $80,000 in an asset returning 8% and $20,000 in an asset returning 3% does not have a 5.5% blended return. The weighted average of those returns by allocation gives (80,000 × 8 + 20,000 × 3) / 100,000 = 7%. That is the figure relevant for actual performance.
Survey results with unequal sample sizes. If one survey group has 1,200 respondents and another has 300, averaging the group averages directly overstates the smaller group. Weighting each group’s average by its sample size gives the correct combined average.
Price indexes. Consumer price indexes weight commodities by how much of household income they represent, so energy (a large share) moves the index more than postage stamps. The index is a weighted average of price changes.
Common mistakes
- Using weights that do not reflect the actual importance. If the homework weight in your calculator does not match what the syllabus says, the answer will be wrong. Double-check your source.
- Treating equal percentages as already normalized. Weights of 40%, 30%, and 30% do not need to add to 100 before you enter them — the calculator normalizes automatically — but it is still worth confirming they are the right proportions.
- Averaging percentages directly. Averaging two percentage returns or two group pass rates without weighting by the group sizes is a classic mistake that can reverse the real result (Simpson’s paradox).
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