Understanding your result
The mean uses each value in proportion to its weight. The normalized share column expresses each weight as a percentage of the total, and the contribution column shows how much that row adds to the final average. Zero-weight rows have no effect.
For course scores with percentage weights or points earned and possible, use the Grade Calculator to apply the grading conventions documented on that page.
The formula
Weights may be frequencies, quantities, percentages, or arbitrary relative importance scores, but use one interpretation consistently. They need not sum to one or one hundred. Values may be negative; weights must be nonnegative and at least one must be positive.
Three values with unequal influence
Values 10, 20, and 30 with weights 2, 3, and 5 produce products of 20, 60, and 150. Their sum is 230 and total weight is 10, so the weighted average is 23. The simple unweighted mean would be 20.
How to use this calculator
- Enter one value and its weight on each line, separated by a comma.
- Use the same value units and the same weight interpretation throughout the list.
- Inspect the normalized weights to confirm which entries drive the average.
Use the denominator that matches the data
For average purchase price, quantities can serve as weights and the result is total purchase value divided by total quantity, before costs not entered. For a frequency table, each count is the number of observations at that value. Relative-importance weights answer a different question and should not be mixed with frequencies in the same list.
A weighted average does not describe spread or uncertainty. Two datasets can have the same weighted mean while containing very different individual values. For nonnegative weights, the mean must lie between the smallest and largest values that have positive weight, which is a useful reasonableness check.
Assumptions & limitations
What this calculation assumes
- Every row has exactly one numeric value and one numeric weight.
- Weights describe comparable influence on the same quantity.
- Zero-weight rows are retained in the table but excluded from the effective row count.
What to keep in mind
- This tool does not calculate weighted variance, uncertainty, or survey design corrections.
- Use decimal points without thousands separators so commas can separate the two fields.
Common questions
Must weights add to 100?
No. The calculation divides by their actual sum. Multiplying every weight by the same positive constant leaves the mean unchanged.
Can I calculate course grades here?
The arithmetic works for weighted scores, but the grade calculator includes course-specific conventions. This tool does not apply grade letters or incomplete-course rules.