Weighted Average Calculator
Calculate a general weighted average from values and relative or percentage weights.
Calculate a weighted average
Enter values and non-negative weights. Weights may be relative numbers or percentages and do not need to total 100.
Result
What is a weighted average?
A weighted average combines values while allowing some observations to count more than others. Each value is multiplied by its weight, the products are added, and that weighted sum is divided by the total weight.
Weighted average formula
Weighted average = Σ(value × weight) ÷ Σ(weight)
The weights describe relative influence. They do not need to be percentages and they do not need to total 100.
Worked example
For values 10, 20, and 30 with weights 1, 2, and 3, the weighted sum is 10 + 40 + 90 = 140. The total weight is 6, so the weighted average is 23.33.
Weighted vs. arithmetic mean
An arithmetic mean gives every value equal influence. A weighted average changes that influence according to the weights. When all weights are equal and positive, the weighted average is the same as the arithmetic mean.
Relative weights
Relative weights such as 1, 2, and 3 mean the second value counts twice as much as the first and the third counts three times as much. Multiplying every weight by the same positive factor does not change the weighted average.
Percentage weights
You can also enter percentage-style weights such as 20, 30, and 50. They happen to total 100, but that is not required by the mathematical formula because the calculation divides by the actual total weight.
Zero weights
A row with weight zero contributes nothing to the weighted sum and does not affect the result. Zero weights are valid, but at least one entered weight must be greater than zero.
Common uses
Weighted averages are used in statistics, finance, composite scores, survey summaries, index calculations, inventory costing, performance metrics, and many other situations where observations have unequal importance or frequency.
Common mistakes
- Dividing by the number of values instead of the total weight.
- Assuming weights must total 100.
- Using negative weights when the intended model requires non-negative influence.
- Forgetting that a zero-weight row has no effect on the result.
Frequently asked questions
Do weights have to add to 100?
No. Any non-negative relative weights are valid as long as their total is greater than zero.
Can values be negative?
Yes. Values may be negative, zero, or positive finite numbers.
Can a weight be zero?
Yes. That row simply has no influence on the weighted average.
Is this only for grades?
No. This is a general mathematical weighted-average calculator rather than a course-grade tool.