Weighted Mean Calculator
A weighted mean is an average where some numbers count more than others, each scaled by a weight you assign. It is how grade point averages handle credit hours, how portfolios blend returns by dollars invested, and how surveys combine groups by population. This tool takes a list of values and a matching list of weights, then returns the weighted mean alongside the plain arithmetic mean for comparison and the total of the weights. Enter one number per line in each box, in the same order, so each value lines up with its weight.
Weighted mean formula
Weighted sum = sum of (value * weight)
Total weight = sum of weights
Weighted mean = weighted sum / total weight
Each value is multiplied by its weight, the products are added, and the total is divided by the sum of the weights. Equal weights reduce this to the ordinary arithmetic mean.
How the weighted mean works
- Each value is scaled by its weight, so larger weights pull the mean toward that value.
- The values and weights must form matching lists of the same length.
- Weights need not sum to one; the formula normalises by their total automatically.
- When all weights are equal the weighted mean equals the plain arithmetic mean.
- The total of the weights must be nonzero, so an all-zero weight list is invalid.
Weighted mean: frequently asked questions
What is a weighted mean?
A weighted mean, also called a weighted average, is an average in which some values count more than others according to a weight assigned to each. You multiply each value by its weight, add those products, and divide by the total of the weights. Values with larger weights pull the result toward themselves more strongly.
What is the formula for the weighted mean?
The weighted mean is the sum of each value times its weight, divided by the sum of the weights: weighted mean = sum(value * weight) / sum(weight). If every weight is equal, this reduces to the ordinary arithmetic mean, since each value then contributes the same amount.
Where is the weighted mean used?
Weighted means appear in grade point averages where courses carry different credit hours, in portfolio returns weighted by the amount invested, in survey results weighted by population, and in any setting where observations differ in importance or reliability. The weights encode how much each value should matter.
How do I enter values and weights?
Enter your values in the first box and the matching weights in the second box, one number per line, in the same order. The first value pairs with the first weight, the second with the second, and so on. The two lists must have the same number of entries for a valid result.
What if the weights do not add up to one?
The weights do not need to sum to one or to 100. The formula divides by the total of the weights, so any positive weights work and the relative sizes are what matter. Whether your weights are credit hours, dollars, or counts, the calculator normalises by their sum automatically.
Official sources
- National Institute of Standards and Technology: NIST/SEMATECH e-Handbook of Statistical Methods.
- U.S. Bureau of Labor Statistics: How weighted averages are used in price indexes.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.