Weighted Average Calculator
Enter values and weights — get the weighted mean for grades, GPA, portfolio returns, or any weighted dataset with a full step-by-step breakdown.
Calculating...
Add values and weights, then click Calculate.
What Is a Weighted Average?
A weighted average (also called a weighted mean) is a type of average where each value contributes a different amount to the final result based on its assigned importance, or weight. Unlike a simple arithmetic mean — which treats every value equally — a weighted average lets you reflect real-world priorities such as credit hours, portfolio allocations, or survey response counts.
Weighted averages appear in almost every quantitative field: your GPA uses course credit-hours as weights, a stock portfolio uses dollar allocations, and a customer survey report weights responses by the number of respondents in each category.
Weighted Average Formula
Core formula
x̄_w = Σ(xᵢ × wᵢ) / Σ(wᵢ)
x̄_w is the weighted mean; xᵢ is each value; wᵢ is each weight.
Normalised weight (share)
ŵᵢ = wᵢ / Σ(wᵢ)
Each item's fraction of the total weight. Sums to exactly 1 (100%).
Item contribution to mean
cᵢ = xᵢ × ŵᵢ
How much each item shifts the final mean. Sum of all cᵢ equals the weighted mean.
Worked Example — Grade Calculator
Homework 92 (weight 20%), Midterm 78 (weight 30%), Final 85 (weight 50%):
Weighted sum = (92 × 20) + (78 × 30) + (85 × 50) = 1840 + 2340 + 4250 = 8430
Total weight = 20 + 30 + 50 = 100
Weighted mean = 8430 / 100 = 84.3
Weighted vs Simple Average — When to Use Each
| Situation | Simple Average | Weighted Average |
|---|---|---|
| GPA with equal credit courses | ✓ | – |
| GPA with mixed credit hours | ✗ | ✓ |
| Portfolio return (equal positions) | ✓ | – |
| Portfolio return (unequal allocations) | ✗ | ✓ |
| Survey Likert scale (unequal response counts) | ✗ | ✓ |
| Test scores with equal worth | ✓ | – |
When all weights are equal, the weighted average equals the simple arithmetic mean — our calculator detects this and shows an "Equal weights" notice.
Common Use Cases
Grade & GPA Calculator
Weight each assignment or exam by its percentage of the total grade. For GPA, use credit hours as weights so a 4-credit Chemistry course influences your GPA more than a 1-credit elective.
Portfolio Return
If 60% of your portfolio is in US stocks returning 12.4%, 25% in bonds at 3.2%, and 15% in real estate at 8.7%, the weighted return is 9.545% — not the simple average of 8.1%.
Survey Analysis
Likert-scale surveys have unequal response counts per option. Weight each score (1–5) by the number of respondents who chose it to get the true average sentiment score — not the mean of the five score labels.
Business KPI Scoring
Composite performance scores weight metrics by strategic importance. A company might weight revenue growth at 40%, customer retention at 35%, and NPS at 25% to produce a single performance index.
Frequently Asked Questions
Do my weights need to add up to 100%?
No. The formula divides the weighted sum by the total weight, so any consistent unit works. You can use percentages (summing to 100), credit hours (summing to 12), or raw counts — the result normalises automatically. Our calculator shows a green "= 100%" badge as a convenience indicator when weights sum to 100, but it will compute correctly regardless.
What is the difference between a weighted mean and an arithmetic mean?
An arithmetic mean gives every value equal weight (implicitly weight = 1). A weighted mean lets each value contribute a different amount. When all weights are identical the two are mathematically equivalent — our calculator flags this with an "Equal weights" notice to let you know a simple average would give the same result.
How do I calculate a weighted GPA?
Enter each course grade as the Value and its credit hours as the Weight. For example: Calculus (3.7, 3 credits), History (4.0, 3 credits), Chemistry (3.3, 4 credits), English (4.0, 2 credits). The weighted GPA = (3.7×3 + 4.0×3 + 3.3×4 + 4.0×2) / (3+3+4+2) = 44.3 / 12 ≈ 3.69. Use the "GPA Calculator" preset to see this worked automatically.
Can I use negative weights?
No — weights must be positive numbers greater than zero. A weight represents importance or frequency, and a negative importance has no mathematical meaning in this context. The calculator will show an error if any weight is zero or negative.
What does the "Share" column mean in the breakdown table?
Share (or normalised weight) is each item's weight expressed as a percentage of the total weight. It shows how much influence each item has over the final result. If an item has a 50% share it contributes exactly half of the weighted mean — the "Contribution" column multiplies the value by this share to show the exact additive amount.
How many items can I calculate at once?
The calculator supports 2 to 20 items per calculation. The minimum of two ensures the weighted average is meaningful (a single value trivially equals itself). The upper limit of twenty keeps the step-by-step breakdown readable. For larger datasets, consider a spreadsheet formula: SUMPRODUCT(values, weights) / SUM(weights).
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