Weighted Average Calculator
Calculate weighted averages from values and their weights. Perfect for grades, investments, surveys, and any data where different items have different importance.
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All calculations happen entirely in your browser. No data is sent to any server.
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Values and Weights
| # | Value | Weight | Actions |
|---|---|---|---|
| 1 | |||
| 2 |
Enter values and their corresponding weights. The weighted average is calculated automatically as you type.
Table of Contents
What is a Weighted Average?
A **weighted average** (also called a weighted mean) is a type of average where different values contribute differently to the final result based on their assigned weights. Unlike a simple average where all values are treated equally, a weighted average recognizes that some values are more important or significant than others.
The key difference is that in a weighted average, each value is multiplied by its weight before being summed, and the total is divided by the sum of all weights rather than by the number of values.
Weighted averages are commonly used in:
- Academic grading — Final exams worth more than homework assignments
- Investment portfolios — Different stocks with different portfolio weights
- Survey analysis — Responses weighted by population size or importance
- Price indices — Different goods weighted by their economic importance
- Performance evaluation — Different metrics weighted by their significance
Formula and Calculation
The weighted average is calculated using the following formula:
Weighted Average = (Σ(value × weight)) / (Σweight)
Where Σ (sigma) means "sum of"
Step-by-step calculation:
- Multiply each value by its weight — For each value-weight pair, calculate value × weight
- Sum all weighted values — Add up all the products from step 1
- Sum all weights — Add up all the weights
- Divide — Divide the sum of weighted values by the sum of weights
Example: Calculate the weighted average of 85 (weight: 3), 90 (weight: 2), and 80 (weight: 5)
- Step 1: (85 × 3) + (90 × 2) + (80 × 5) = 255 + 180 + 400 = 835
- Step 2: 3 + 2 + 5 = 10
- Step 3: 835 ÷ 10 = 83.5
Result: Weighted Average = 83.5
Examples
Example 1: Course Grades
Calculate final course grade with weighted components:
- Homework: 92% (weight: 20%)
- Quizzes: 88% (weight: 30%)
- Midterm: 85% (weight: 25%)
- Final Exam: 90% (weight: 25%)
Calculation:
Weighted Average = (92×20 + 88×30 + 85×25 + 90×25) / 100
= (1840 + 2640 + 2125 + 2250) / 100
= 8855 / 100 = 88.55%
Result: Final Course Grade = 88.55%
Example 2: Investment Portfolio
Calculate average return of an investment portfolio:
- Stock A: 12% return (weight: 40% of portfolio)
- Stock B: 8% return (weight: 35% of portfolio)
- Stock C: 15% return (weight: 25% of portfolio)
Calculation:
Weighted Average = (12×40 + 8×35 + 15×25) / 100
= (480 + 280 + 375) / 100
= 1135 / 100 = 11.35%
Result: Portfolio Average Return = 11.35%
Example 3: Survey Results
Calculate weighted average satisfaction score from survey responses:
- Rating 5: 120 responses (weight: 120)
- Rating 4: 80 responses (weight: 80)
- Rating 3: 30 responses (weight: 30)
- Rating 2: 15 responses (weight: 15)
- Rating 1: 5 responses (weight: 5)
Calculation:
Weighted Average = (5×120 + 4×80 + 3×30 + 2×15 + 1×5) / 250
= (600 + 320 + 90 + 30 + 5) / 250
= 1045 / 250 = 4.18
Result: Average Satisfaction Score = 4.18 out of 5
Common Use Cases
- Academic Grading: Calculate final course grades when different assignments, tests, and exams have different weights
- Investment Analysis: Calculate average portfolio returns when different investments have different portfolio weights
- Survey Analysis: Calculate weighted averages from survey responses when different groups have different sample sizes or importance
- Price Indexes: Calculate consumer price indexes (CPI) where different goods are weighted by their economic importance
- Performance Evaluation: Calculate overall performance scores when different metrics or KPIs have different importance
- Financial Analysis: Calculate weighted average cost of capital (WACC) when different sources of financing have different costs and weights
- Statistical Analysis: Calculate weighted means when different data points have different reliability or significance
- Quality Control: Calculate average quality scores when different quality metrics have different importance
- Research: Calculate weighted averages in research studies when different observations have different sample sizes or reliability
- Business Metrics: Calculate overall business performance when different departments or products have different importance
Weighted Average vs. Simple Average
Understanding when to use a weighted average versus a simple average is important for accurate calculations:
Simple Average (Arithmetic Mean)
A simple average treats all values equally:
Simple Average = (Sum of all values) / (Number of values)
Use when:
- All values are equally important
- Each value represents the same unit or quantity
- You want a straightforward average with no special weighting
Example: Average of 85, 90, 80 = (85 + 90 + 80) / 3 = 85
Weighted Average
A weighted average recognizes that different values have different importance:
Weighted Average = (Σ(value × weight)) / (Σweight)
Use when:
- Different values have different importance or significance
- Values represent different quantities (e.g., portfolio percentages)
- You need to account for varying sample sizes or frequencies
- Some items should contribute more to the final result than others
Example: Weighted average of 85 (weight: 3), 90 (weight: 2), 80 (weight: 5) = (85×3 + 90×2 + 80×5) / 10 = 83.5
When Weights are Equal
If all weights are equal, the weighted average equals the simple average. For example, if all weights are 1, the weighted average formula simplifies to the simple average formula.
This is why weighted averages are more flexible — they can handle both equal and unequal weights, while simple averages assume equal weights for all values.
Frequently Asked Questions
A simple average treats all values equally: you sum all values and divide by the count. A weighted average multiplies each value by its weight before summing, then divides by the sum of weights. Weighted averages are used when different values have different importance or significance.
Yes! Weights can be expressed as percentages (e.g., 20%, 30%, 50%) or as absolute values (e.g., 2, 3, 5). The calculator works with any positive numbers. If you use percentages, make sure they sum to 100% for the most intuitive interpretation, though the calculator will work with any positive weights.
The calculator works perfectly fine even if weights don't sum to 100. The formula divides by the sum of weights, so it automatically normalizes. However, using weights that sum to 100 (percentages) makes the result easier to interpret and understand.
No. Weights must be non-negative (zero or positive). Negative weights don't have a meaningful interpretation in most weighted average calculations and would produce counterintuitive results.
If all weights are equal, you can use either a simple average or weighted average — both will give the same result. For example, if all weights are 1, the weighted average equals the simple average. The weighted average calculator will work correctly with equal weights.
Yes! The calculator supports decimal values and weights. You can enter values like 85.5, 92.75, or any decimal number. Similarly, weights can be decimals like 0.25, 0.3, 1.5, etc.
No. All calculations happen entirely in your browser using JavaScript. Your values, weights, and results are never sent to any server. This ensures complete privacy and security for your data.
A weight of zero means that value doesn't contribute to the weighted average (since value × 0 = 0). However, make sure your total weight (sum of all weights) is not zero, as dividing by zero is undefined. The calculator will warn you if the total weight is zero.