Weighted Average Calculator
Enter a set of values and their corresponding weights to get the weighted average in one step. Weighted averages are used everywhere — course grades where exams count more than homework, portfolio returns where larger positions count more than smaller ones, and survey results where certain responses are given extra weight.
Enter values and weights
Enter at least one value–weight pair, then press Calculate.
The weighted average formula
weighted average = (v₁w₁ + v₂w₂ + … + vₙwₙ) / (w₁ + w₂ + … + wₙ)
Each value is multiplied by its weight, the products are summed, and the total is divided by the sum of all weights. Because the divisor is the sum of weights (not the count), weights do not need to add up to 100 or 1 — they only need to be proportional to the importance you want each value to have.
| Symbol | Meaning |
|---|---|
v₁ … vₙ | The values being averaged |
w₁ … wₙ | The weight assigned to each value |
Σ(vᵢwᵢ) | Sum of each value multiplied by its weight |
Σ(wᵢ) | Sum of all weights |
Any positive numbers will do. Course credit hours, portfolio dollar amounts, survey frequency counts, even relative "importance" scores — the weighted average is the same regardless of the scale of the weights, as long as their ratios are the same.
Worked examples
Example 1 — Course grade with weighted categories
Homework: 92 (weight 20%) · Quizzes: 85 (weight 30%) · Final exam: 78 (weight 50%)
Numerator: 92 × 20 + 85 × 30 + 78 × 50 = 1840 + 2550 + 3900 = 8290.
Denominator: 20 + 30 + 50 = 100.
Weighted average = 8290 / 100 = 82.9.
Weighted average = 82.9
Example 2 — GPA with credit hours
Math (grade 3.7, 4 credits) · History (grade 3.3, 3 credits) · Biology (grade 4.0, 5 credits)
Numerator: 3.7 × 4 + 3.3 × 3 + 4.0 × 5 = 14.8 + 9.9 + 20.0 = 44.7.
Denominator: 4 + 3 + 5 = 12.
Weighted GPA = 44.7 / 12 ≈ 3.725.
Weighted GPA ≈ 3.725
Example 3 — Portfolio return
Stock A returned 12% on £10,000 · Stock B returned 4% on £30,000 · Stock C returned 8% on £20,000
Numerator: 12 × 10000 + 4 × 30000 + 8 × 20000 = 120000 + 120000 + 160000 = 400000.
Denominator: 10000 + 30000 + 20000 = 60000.
Weighted return = 400000 / 60000 ≈ 6.67%.
Weighted return ≈ 6.67%
When to use a weighted average
Use a weighted average whenever the values you are combining are not equally important. Common cases:
- Grades and GPAs — different assessments, courses or credit hours carry different weight.
- Financial returns — a return on a £50,000 position should count more than the same return on a £500 position.
- Survey analysis — certain demographic groups may be over-sampled and need down-weighting to match the population.
- Composite scores — performance ratings that combine several metrics at different importance levels.
- Price indices — inflation measures weight goods by their share of a household budget.
If the values are naturally equal in importance, use the ordinary average calculator instead.
Common mistakes
- Dividing by the count instead of the sum of weights. In an ordinary average you divide by the number of values; in a weighted average you divide by the total weight.
- Assuming the weights must add to 100. They do not. Course credit hours, portfolio amounts and survey weights rarely sum to 100. The formula handles any positive weights.
- Using negative weights. Weighted averages are only defined for non-negative weights. If you need to down-weight something, use a small positive weight rather than a negative one.
- Forgetting that weighted averages can equal the simple average. This happens when all weights are equal — a useful sanity check when verifying your inputs.
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Frequently asked questions
A weighted average is an average where each value contributes in proportion to its weight. The formula is Σ(value × weight) ÷ Σ(weight).
No. The weights can be any positive numbers — course credits, dollar amounts, counts, or relative importance scores. The formula divides by the sum of weights, so the total can be anything.
In a plain average, every value contributes equally. In a weighted average, some values count more than others. If you set all weights equal to each other (for example, all 1), the weighted average reduces to the plain average.
No — weighted averages are only defined for non-negative weights. If a value should count less, give it a smaller positive weight rather than a negative one.
The calculator starts with three rows and lets you add as many as you need. Rows can be removed as long as at least one remains. Practical use is up to dozens of pairs without any slowdown.