Weighted Average Calculator
Calculate weighted average scores ($\bar{x}_w = \frac{\sum w \cdot x}{\sum w}$) for school grades, inventory unit costs, financial investments, and weighted survey responses.
Calculate Weighted Average Score & Totals
Enter score and weight on each line (format: Value, Weight).
Calculation Results
Calculated using weighted average equations: \text{Weighted Avg} = \frac{\sum (w \cdot x)}{\sum w}
Quick Summary
The Weighted Average Calculator computes weighted overall averages ($\bar{x}_w = \frac{\sum w \cdot x}{\sum w}$), weight totals, and normalized scores.
Formula Explanation
\text{Weighted Average} = \frac{(w_1 \cdot x_1) + (w_2 \cdot x_2) + \dots + (w_n \cdot x_n)}{w_1 + w_2 + \dots + w_n}How It Works
A weighted average accounts for the relative proportion or importance of each item. The Weighted Average Calculator multiplies each number by its corresponding weight, sums the weighted products, and divides by total weight.
Step-by-Step Worked Example
Practical Problem: An investor buys 40 shares of stock at $90/share and 60 shares at $80/share. Calculate average cost per share.
- Step 1: Calculate total cost of first lot: $40 \text{ shares} \times \$90 = \mathbf{\$3,600}$.
- Step 2: Calculate total cost of second lot: $60 \text{ shares} \times \$80 = \mathbf{\$4,800}$.
- Step 3: Calculate total invested capital ($\sum w \cdot x$): $\$3,600 + \$4,800 = \mathbf{\$8,400}$.
- Step 4: Calculate total share count ($\sum w$): $40 + 60 = \mathbf{100\text{ shares}}$.
- Step 5: Calculate weighted average share cost: $\$8,400 / 100 = \mathbf{\$84.00\text{ per share}}$.
Real-World Calculation Examples
Scenario 1: Stock Purchase Average Cost
Parameters: $90 (40 shares), $80 (60 shares)
Result: $84.00 Average Share Price.
Scenario 2: Weighted Test Scores (40% Midterm, 60% Final)
Parameters: 88 (40%), 94 (60%)
Result: 91.60 Weighted Exam Score.
Scenario 3: Product Rating Reviews
Parameters: 5 stars (80 reviews), 1 star (20 reviews)
Result: 4.20 Star Average Rating.
Scenario 4: Mixed Gasoline Blending Cost
Parameters: $3.50 (500 gal), $4.00 (500 gal)
Result: $3.75 Average Fuel Price.
Key Benefits of Using This Calculator
Stock Dollar Cost Averaging
Calculates average purchase price per share across multiple trade orders.
Academic & Survey Weighting
Weights survey responses by sample subgroup demographic proportions.
Multi-Format Input Support
Accepts spaces, commas, or tab delimiters for quick data entry.
100% Free & Client-Side
Executes locally in your browser with zero latency or web server transmission.
Frequently Asked Questions (FAQ)
What is weighted average?
Weighted average is an average that gives different degrees of importance or weight to numbers in a dataset.
How is weighted average used in Dollar Cost Averaging (DCA)?
DCA investors calculate weighted average share cost by dividing total dollars spent by total shares acquired.
What is weighted average inventory method (AVCO)?
AVCO calculates cost of goods sold and inventory value based on the weighted average cost per unit of inventory purchased during a period.
Is weighted average the same as weighted mean?
Yes — weighted average and weighted mean refer to the exact same mathematical formula ($\frac{\sum w \cdot x}{\sum w}$).
What happens if a weight is zero?
A zero weight means that specific value is excluded from contributing to the weighted average result.
How do I calculate weighted average in Excel?
Use formula =SUMPRODUCT(values, weights) / SUM(weights).
What is volume-weighted average price (VWAP)?
VWAP is a financial trading benchmark calculating the average stock price weighted by trading volume throughout a trading day.
How do I calculate weighted average of percentages?
Multiply each percentage by its base sample count or weight, sum products, and divide by total base count.
What is weighted average duration in bonds?
Macaulay duration weights the timing of cash flows by their present value proportion.
Can values be negative in weighted average calculations?
Yes — values $x$ (such as negative profit margins or portfolio losses) can be negative.