How to use this weighted average calculator
Enter one value and one nonnegative weight in every row. Weights may be percentages, decimal proportions, credits, quantities, frequencies, or any other consistent scale. Use Add another row for more pairs and Remove to delete an unneeded pair. The weights do not have to total 100 because the calculator divides the weighted sum by the actual total weight.
How the calculation works
A regular arithmetic mean gives every value equal influence. A weighted average multiplies each value by a weight that represents its relative importance, then divides the sum of those products by the sum of all weights. A value with twice the weight of another value contributes twice as much to the result.
Weights must use one consistent interpretation across the data set. Percentages may total 100, decimal proportions may total 1, and course credits or frequencies may total another positive number. Scaling every weight by the same factor does not change the weighted average. Zero-weight rows have no effect, while negative weights are excluded from this general-purpose calculator because they require specialized interpretation.
Formulas
Weighted average
Weighted sum
Worked examples
Weighted course grade
An exam score of 70 weighted 60 and a project score of 90 weighted 40 give (70 × 60 + 90 × 40) ÷ 100 = 78.
Average price per item
Ten items cost $4 each and five items cost $7 each. The quantity-weighted average is (4 × 10 + 7 × 5) ÷ 15 = $5 per item.
Common uses
Course grades
Combine assignments, exams, and projects when each category contributes a different share of the final grade. Enter weights on one consistent scale, such as percentages or decimal proportions.
Prices and portfolios
Find an average purchase price, rate, or return when quantities or invested amounts differ. The weight should represent the amount that actually contributes to the combined result.
Composite metrics
Build a summary from criteria with different importance levels. Document why each weight was chosen so the result remains interpretable and can be reproduced later.
Accuracy and limitations
The calculator multiplies each value by its weight, sums those products, and divides by the sum of the weights. Weights do not need to total 100, but they must use the same scale.
A mathematically correct weighted mean can still mislead if weights are arbitrary or observations are not comparable. Verify the weighting method required by the course, index, contract, or analysis.
Frequently asked questions
Do the weights have to add up to 100?
No. They may total 100, 1, a number of credits, a frequency count, or any other positive total. The calculator normalizes them by dividing by their sum.
Can I use percentage weights?
Yes. Enter percentages as ordinary numbers, such as 60 and 40. You may also enter decimal proportions such as 0.6 and 0.4; both scales produce the same answer.
What happens when a weight is zero?
A zero-weight value contributes nothing to the weighted sum or result. At least one row must have a positive weight.
Can weights be negative?
This calculator accepts nonnegative weights only. Negative weights occur in some specialized financial and statistical models and should be interpreted within the rules of that model.
Is a weighted average the same as an arithmetic average?
Only when every value has the same weight. Unequal weights make some observations contribute more strongly than others.
Can I add more value and weight pairs?
Yes. Use Add another row to expand the calculator and Remove to delete a row. At least one row remains available.
Is the weighted average calculator free to use?
Yes. NumUtility is free, requires no account, and places no limit on ordinary calculations.
Are my entries stored?
No. The calculation runs in your browser. Values entered into the tool are not sent to NumUtility or saved by us.