Weighted Average Calculator

How it works

The weighted mean is Σ(value × weight) / Σ(weight). Values may be positive, zero or negative. Weights must be nonnegative, and at least one must be positive. A zero-weight row contributes zero and has no effect on the mean. The result lies within the range of positive-weight values in exact arithmetic. A negative weight is rejected because it changes the interpretation and can place the result outside that range. Frequency, percentage and relative weights all use the same formula; multiplying every weight by the same positive constant leaves the mathematical average unchanged. Input rounding and range limits still apply.

Each row's normalized share is weight / total weight. Its contribution is value × weight / total weight. Contributions add to the weighted mean before rounding. The table rounds values for readability; separately rounded contributions may not sum to the displayed answer, especially when large positive and negative terms cancel. Use the exported numerical audit rather than inferring an exact identity from rounded columns. A weighted average is not automatically a weighted median, a pooled variance, a financial return, or an appropriate combination of percentages that have different denominators. Choose weights that match the question.

The implementation decodes accepted IEEE 754 binary64 numbers as integers times powers of two. Weight totals and value×weight products are accumulated as bounded exact integers, and division is performed before the rounded result is reported. This avoids first overflowing a raw product or losing a small term through mixed-sign cancellation in an ordinary floating sum. It is exact accumulation of the accepted browser numbers, not exact arithmetic on original decimal strings. Reported ratios, normalized shares and contributions are rounded browser numbers. JSON includes the integer sums and their binary exponents to support independent reconstruction; it does not contain a hidden model or a prediction.

Both tools use decimal-point numbers, optionally in e notation, with at most 200 characters per numeric token. Nonzero magnitudes must be from 1e−100 to 1e100. Infinity, NaN, arithmetic expressions, units and grouping marks are rejected. A decimal whose normalized spelling cannot survive a round trip through a browser number is rejected rather than silently losing input digits. This does not make numbers exact decimals: 0.1 still has a binary approximation. Input is limited to 1 MiB of valid UTF-8, 10,000 list values or pairs, or 10,000 CSV records including the header, under shared 200-column and 200,000-cell guards. Local files must be nonempty. CSV needs a header row with unique, nonblank names and consistent field counts. Choose comma, semicolon or tab explicitly, select the numeric columns, and decide whether blank selected cells must be rejected or omitted. Non-numeric selected cells are always rejected with a source record number. Omitted CSV records are counted; unrelated text columns are not analyzed. In pair mode, use exactly two numbers per nonblank line, value first and weight second, separated by a comma or whitespace. One pair is sufficient when its weight is positive. Blank lines are ignored. In CSV mode, choose different columns for value and weight. Under the explicit omit policy, an incomplete pair is omitted as a whole, so values are never accidentally matched with weights from another record.

The main result shows the mean, total weight, accepted rows, positive-weight rows and zero-weight rows. The table previews up to 20 records. Row CSV includes every record's value, weight, normalized share and contribution. Analysis JSON includes every row, source mapping, omitted count, method and exact binary64 sum audit. Changing any input or setting clears the old result.

Inputs stay in browser-tab memory: no dataset upload, stored history or data in the URL. Editing data or calculation settings removes stale results and exports. Optional analytics uses fixed action labels and input mode, never numeric values, filenames or column names. JSON downloads deliberately contain the accepted input observations and calculation settings so you can retain an audit locally; share them only when appropriate.

Common use cases

• Combine measurements that represent different numbers of observations using frequency weights.
• Compare values with explicit nonnegative importance weights without forcing them to total 100.
• Audit a CSV calculation with original source record numbers and per-row contributions.
• Check a mixed-sign dataset without losing a small term in an ordinary floating-point sum.

Frequently asked questions

Standards and limitations

• NumPy: weighted-average formula and weight sum