Weighted Average Calculator
Compute the weighted mean when different values contribute unequally to the overall average. Compare it to the simple average to see how weighting changes the result.
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Formula
x̄_w = (v₁w₁ + v₂w₂ + v₃w₃) / (w₁ + w₂ + w₃)
Multiply each value by its corresponding weight, sum the products, then divide by the total weight. The weights do not need to sum to any particular value (like 100 or 1) — the formula normalizes automatically. When all weights are equal, the weighted average equals the simple arithmetic mean.
How to use the Weighted Average Calculator
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Enter your value 1
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Enter your weight 1
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Enter your value 2
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Enter your weight 2
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Enter your value 3
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Enter your weight 3
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Read your results instantly
Results update in real time as you type.
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When to use a weighted average
Use a weighted average whenever different items contribute unequally to the total. Grade point averages weight courses by credit hours — a 4-credit chemistry course matters more than a 1-credit seminar. Stock portfolio returns weight each asset by its dollar value. Inflation indices weight price changes by how much consumers typically spend on each category.
A simple average implicitly assumes all items are equally important. When that assumption is wrong, the simple average is misleading. Weights make the importance of each component explicit and adjustable.
Weights do not need to sum to 100
Weights can be raw frequencies, dollar amounts, percentages, credit hours, or any positive number. The formula divides by the sum of all weights, so the scale cancels out. Weights of (30, 40, 30) produce the same weighted average as weights of (3, 4, 3) or (0.3, 0.4, 0.3).
However, if your weights do sum to 100%, you can interpret each weight directly as the percentage contribution of that component to the final average.
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Weighted average vs. simple average
For the default values {80 with weight 30, 90 with weight 40, 70 with weight 30}, the weighted average is 82.0 while the simple average is 80.0. The difference arises because value 2 (90) receives 40% of the total weight rather than the 33% it would get in a simple average.
This calculator shows both side by side so you can immediately see the impact of unequal weighting. If the two are close, weighting has little effect on your result.
Tips & Insights
GPA calculation
For a GPA, each course grade is the value and the credit hours are the weight. A B (3.0) in a 4-credit class contributes more than an A (4.0) in a 1-credit seminar.
Zero weight excludes a value
Setting a weight to 0 effectively removes that value from the average. This lets you quickly test what the average would be without a particular data point.
Weights must be non-negative
Negative weights are not meaningful in standard weighted average calculations. All weights should be zero or positive.
Worked Examples
Course grade calculation
Weighted average: 85.5. Simple average: 87.0. The final exam's 50% weight pulls the grade closer to the final score than the simple average would suggest.
Investment portfolio return
Weighted average return: 7.60%. Simple average: 7.33%. The larger stock allocation shifts the result toward Stock B's return.
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Frequently Asked Questions
What is a weighted average?
A weighted average gives different items different levels of importance. Each value is multiplied by its weight before averaging, so items with higher weights have more influence on the result.
Do weights have to add up to 100?
No. Weights can be any positive numbers. The formula divides by the total weight, so the scale does not matter. Using 100 as the total is convenient but not required.
What happens when all weights are equal?
When all weights are the same, the weighted average equals the simple (arithmetic) mean. Equal weights imply equal importance.
Can weights be decimals?
Yes. Weights of 0.3, 0.4, and 0.3 work exactly the same as weights of 30, 40, and 30. Use whatever scale is natural for your application.
How is weighted average used in GPAs?
Each course grade (4.0 scale) is multiplied by its credit hours (the weight). The sum is divided by total credit hours to get the GPA. A 3-credit A contributes three times as much as a 1-credit A.
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