Weighted Average Calculator (With Step-by-Step Work)
Solve weighted average problems by entering values and their weights, and see each multiplication step shown before the total.
Reviewed by Manoj Kumar, Mathematics Educator
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.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy