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Weighted Average Calculator

Computes the weighted arithmetic mean Σ(w·x) / Σw of a list of values and a matching list of weights, along with the total weight and the unweighted mean for comparison.

When to use

Values contribute unequally to an average: course grades with credit weights, portfolio returns by allocation, survey answers with sampling weights, average price over different quantities.

Do not use when: All items count equally (use descriptive-statistics for the plain mean), or the weights are probabilities of outcomes (use expected-value, which also gives the variance).

Formula

weighted_average = Σ(values_i × weights_i) / Σ weights_i

Inputs

Parameter	Type	Unit	Required	Description
`values`	number_list		yes	The values to average.
`weights`	number_list		yes	Non-negative weight for each value, in the same order (percentages, credits, quantities); they need not sum to 1.

Outputs

Output	Type	Description
`weighted_average`	number	Σ(values × weights) / Σweights.
`total_weight`	number	Sum of the weights.
`weighted_sum`	number	Σ(values × weights) before dividing by the total weight.
`simple_average`	number	Plain arithmetic mean of the values, for comparison.
`count`	integer	Number of value/weight pairs.

Example

Grades 90, 80, 70 weighted 50/30/20 %: {"values":[90,80,70],"weights":[0.5,0.3,0.2]} → {"weighted_average":83,"total_weight":1,"weighted_sum":83,"simple_average":80,"count":3}

4, 8, 15 with weights 2, 1, 1: {"values":[4,8,15],"weights":[2,1,1]} → {"weighted_average":7.75,"total_weight":4,"weighted_sum":31,"simple_average":9}

GET https://tttkmbb.com/api/v1/calculate/weighted-average?values=90%2C80%2C70&weights=0.5%2C0.3%2C0.2

Machine access

API: GET https://tttkmbb.com/api/v1/calculate/weighted-average (query parameters) or POST with a JSON body {"inputs": {...}}
Schema: https://tttkmbb.com/api/v1/calculators/weighted-average · Markdown: https://tttkmbb.com/statistics/weighted-average.md · JSON definition: https://tttkmbb.com/statistics/weighted-average.json
MCP: server https://tttkmbb.com/mcp, tool run_calculator with calculator_id="weighted-average"
OpenAPI operationId: calculate_weighted_average
Freshness: static. Authentication: none. Rate limit: fair use (see rate limits).

Sources

Wikipedia – Weighted arithmetic mean (reference)
NIST/SEMATECH e-Handbook of Statistical Methods, 1.3.5.1 Measures of Location (government)

FAQ

Do the weights have to add up to 1 or 100?

No. The result is divided by the total weight, so 50/30/20, 5/3/2 and 0.5/0.3/0.2 all give the same average.

What if a weight is zero?

That value is ignored. At least one weight must be positive; negative weights are rejected.

Related calculators

Descriptive Statistics Calculator — Unweighted mean, median and spread of a list.
Expected Value Calculator — Probability-weighted mean and variance of outcomes.
GPA Calculator — Credit-weighted grade point average.