Weighted Average Calculator
Solve weighted average problems step-by-step with our free calculator. See formulas, worked examples, and clear explanations.
Formula
Weighted Average = Sum(value_i * weight_i) / Sum(weight_i)
Multiply each value by its weight, sum all products, then divide by the total of all weights. When all weights are equal, this reduces to the simple arithmetic average.
Worked Examples
Example 1: GPA Calculation
Problem: Calculate the GPA for: Chemistry (4 credits, A = 4.0), English (3 credits, B+ = 3.3), Math (4 credits, A- = 3.7), PE (1 credit, A = 4.0).
Solution: Weighted products:\nChemistry: 4.0 x 4 = 16.0\nEnglish: 3.3 x 3 = 9.9\nMath: 3.7 x 4 = 14.8\nPE: 4.0 x 1 = 4.0\nSum of products: 16.0 + 9.9 + 14.8 + 4.0 = 44.7\nTotal credits: 4 + 3 + 4 + 1 = 12\nGPA = 44.7 / 12 = 3.725
Result: Weighted GPA = 3.725
Example 2: Portfolio Return
Problem: Calculate the portfolio return for: Stocks (60% allocation, 15% return), Bonds (30% allocation, 4% return), Cash (10% allocation, 2% return).
Solution: Weighted returns:\nStocks: 15 x 60 = 900\nBonds: 4 x 30 = 120\nCash: 2 x 10 = 20\nSum of products: 900 + 120 + 20 = 1040\nTotal weight: 60 + 30 + 10 = 100\nWeighted average return = 1040 / 100 = 10.4%
Result: Portfolio weighted return = 10.4%
Frequently Asked Questions
What is a weighted average and how does it differ from a regular average?
A weighted average is a calculation that gives different values different levels of importance (weights) when computing the average. Unlike a regular (arithmetic) average where all values contribute equally, a weighted average multiplies each value by its assigned weight before summing and dividing by the total weight. For example, if three test scores are 85, 92, and 78 with weights of 30%, 40%, and 30%, the weighted average is (85 times 0.3 plus 92 times 0.4 plus 78 times 0.3) equals 85.7, while the regular average would be (85 plus 92 plus 78) divided by 3 equals 85. The weighted average gives more influence to the score with higher weight (92 at 40%), producing a different result than equal weighting.
How do you calculate a weighted average step by step?
Calculating a weighted average involves four straightforward steps. First, multiply each value by its corresponding weight to create weighted products. Second, sum all the weighted products together. Third, sum all the weights together. Fourth, divide the sum of products by the sum of weights. For example, with grades of 90, 80, and 70 with weights 50, 30, and 20: Step 1 produces 4500, 2400, and 1400. Step 2 sums to 8300. Step 3 sums weights to 100. Step 4 divides 8300 by 100 to get 83. The formula is written as: weighted average equals the sum of (value times weight) divided by the sum of weights. Always verify that your weights represent meaningful relative importance.
When should you use a weighted average instead of a simple average?
Use a weighted average whenever the data points have different levels of importance, frequency, or reliability. Common scenarios include calculating GPA where courses have different credit hours, computing portfolio returns where investments have different allocation amounts, and averaging survey results where respondents have different demographic representation weights. In academics, a final grade might weight exams at 60%, homework at 25%, and participation at 15%. Using a simple average would incorrectly treat all components as equally important. Weighted averages are also essential in index calculations like the S&P 500 (weighted by market capitalization) and the Consumer Price Index (weighted by consumer spending patterns).
How is weighted average used in GPA calculations?
Grade Point Average (GPA) is one of the most common applications of weighted averages. Each course has a grade value (A equals 4.0, B equals 3.0, etc.) and a weight measured in credit hours. The GPA equals the sum of (grade points times credit hours) divided by the total credit hours. For example: Chemistry (4 credits, A equals 4.0), English (3 credits, B equals 3.0), and PE (1 credit, A equals 4.0). Weighted sum: 4 times 4.0 plus 3 times 3.0 plus 1 times 4.0 equals 16 plus 9 plus 4 equals 29. Total credits: 8. GPA equals 29 divided by 8 equals 3.625. Without weighting, the average would be (4.0 plus 3.0 plus 4.0) divided by 3 equals 3.667, which overstates the contribution of the 1-credit PE course.
How do portfolio returns use weighted averages?
Investment portfolio returns are calculated as the weighted average of individual asset returns, where weights are the proportion of total investment in each asset. If you have 50% in stocks returning 12%, 30% in bonds returning 5%, and 20% in cash returning 2%, the portfolio return is 0.50 times 12 plus 0.30 times 5 plus 0.20 times 2, which equals 6.0 plus 1.5 plus 0.4 equals 7.9%. This correctly reflects the greater impact of stocks on overall performance. Portfolio risk is also weighted, though not as a simple weighted average due to correlation effects between assets. Fund managers continuously monitor these weighted averages to ensure portfolio allocations match their investment strategy and risk tolerance targets.
What happens if all weights are equal in a weighted average?
When all weights are equal, the weighted average reduces exactly to the regular arithmetic average. This is because every value is multiplied by the same constant weight, and dividing by the sum of weights cancels out the common factor. For values 10, 20, 30 with equal weights of 5: weighted sum equals 10 times 5 plus 20 times 5 plus 30 times 5 equals 300, total weight equals 15, weighted average equals 20. Regular average equals (10 plus 20 plus 30) divided by 3 equals 20. They are identical. This makes the arithmetic mean a special case of the weighted average where uniform importance is assumed. In practice, if you discover all your weights should be equal, you can simplify by using the regular average formula instead.