Guide · The formula
How to Calculate a Weighted Average
Updated: June 2026
A weighted average is what you reach for whenever some numbers deserve to count more than others — a final exam that matters more than a quiz, a large purchase that should outweigh a tiny one. It is barely harder than an ordinary average, but the one extra step trips a surprising number of people. Here is the formula, two worked examples, and the mistakes worth avoiding.
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The formula in one line
Every weighted average follows the same recipe. Each value carries a weight that says how much it counts. You multiply, add, and divide:
The symbol Σ just means "add up". So you walk down your list multiplying each value by its weight, total those products, and then divide by the total of the weights. That final division is the step people forget — without it you only have a weighted sum, not an average.
Step by step
- List your pairs. Write each value next to its weight. The weight can be a coefficient, a percentage, a number of credits, or a quantity.
- Multiply each pair. value × weight gives that item's contribution.
- Add the contributions. This is Σ(value × weight).
- Add the weights. This is Σ(weight).
- Divide. Contributions ÷ weights is your answer.
Example 1 — student grades
Suppose a course grades a midterm at coefficient 2, a final exam at coefficient 3, and homework at coefficient 1. A student scores 14, 11 and 17 respectively. Lay it out:
| Item | Value | Weight | value × weight |
|---|---|---|---|
| Midterm | 14 | 2 | 28 |
| Final | 11 | 3 | 33 |
| Homework | 17 | 1 | 17 |
| Total | 6 | 78 |
The weighted average is 78 ÷ 6 = 13. Notice the plain average of 14, 11 and 17 is 14 — higher — because the weighted version gives the strong homework score less say and the weaker final more.
Example 2 — average price
You buy 10 units at $4 and 30 units at $6. The simple average of 4 and 6 is 5, but that ignores how many you bought of each. Weighting by quantity: (4×10 + 6×30) ÷ (10 + 30) = (40 + 180) ÷ 40 = 220 ÷ 40 = $5.50. Because most units cost $6, the true average price sits much closer to 6 than to 5.
Common mistakes
- Forgetting to divide by the total weight. The single most common error — it leaves you with an inflated number.
- Assuming weights must total 100. They don't. Coefficients of 1, 2, 3 work perfectly because only their ratio matters.
- Mixing percentages and counts. Pick one kind of weight per calculation and stay consistent.
- Averaging the averages. You can't take a plain average of two group means unless the groups are the same size — that's exactly what the weighted version fixes.
Frequently asked questions
What is the weighted average formula?
Multiply each value by its weight, sum the products, then divide by the sum of the weights: Σ(value × weight) ÷ Σ(weight).
Do weights need to sum to 1 or 100?
No. Any positive numbers work because the formula divides by their total, so only the ratio between them affects the result.
What if all the weights are equal?
Then the weighted average equals the ordinary simple average — the equal weights cancel out in the division.
Can a weighted average sit outside the range of my values?
No. It always lands between the smallest and largest value, just like a simple average.