Weighted Average Calculator

Weight shares and contributions to the mean

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.

How to use this calculator

1. Enter each value and its weight in the same row. Add or remove rows as needed; completely blank rows are ignored.
2. Use the same value units and the same weight interpretation throughout the list.
3. Inspect the normalized weights to confirm which entries drive the average.
4. For a larger list, open Paste or edit text and enter one value, weight pair per line. Use pasted data loads the rows; Calculate can also use the pasted text directly.

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.

Solving one additional value

Target mode holds every existing row fixed and solves one added value: required value = [target × (total existing weight + next weight) − weighted sum]/next weight. The next weight must be positive; current weights remain nonnegative and need not total 100. A mathematically required value can exceed the existing entry range or a real-world score cap, so assess whether it is feasible in your context. This solves one future value, not a redistribution of the existing weights.

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