Weighted Average Calculator
Calculate the average of values that count for different amounts, using weights you enter.
Weighted average
- Total weight
- Sum of value × weight
How we calculated this
Worked example
Inputs: values 80, 90, 70 with weights 20, 30, 50. Formula: the weighted average is the sum of each value times its weight, divided by the total weight. Substitution: (80 × 20 + 90 × 30 + 70 × 50) ÷ (20 + 30 + 50) = 7,800 ÷ 100. Result: 78.
How it works
Each value counts in proportion to its weight, so a value with a larger weight pulls the result towards itself. Weights are relative: only their proportions matter, so they need not add up to 100, and weights of 1 and 1 give the same answer as 50 and 50. A weight may be 0, in which case that value does not count. A weight may not be negative, and at least one weight must be greater than 0, because the total weight is what the result is divided by. Every value needs exactly one weight. A result that six decimal places do not capture exactly is shown with "≈".
What this result means
The weighted average is the sum of each value multiplied by its weight, divided by the total weight. A value with a larger weight pulls the result towards itself more than one with a smaller weight.
Common mistakes
- Assuming the weights must add up to 100. They need not: only their proportions matter, so weights of 1 and 1 give the same result as weights of 50 and 50.
- Entering the weights in a different order from the values. The first weight belongs to the first value, the second to the second, and so on.
Assumptions and limitations
- Every value needs exactly one weight. Weights must be zero or positive, and at least one must be greater than zero.
- This is the weighted arithmetic mean only. Weights are treated as relative amounts, not as percentages of a total.