Weighted Average Calculator
The average where not every value counts the same: sum(wx)/sum(w) with the simple mean printed BESIDE it — because the divergence between the two is the finding, and the weights are the whole question.
Weighted Average Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Non-negative weights only — survey estimators with negative weights are out of scope
- Item weights, not time weights — moving windows live on the moving-average page
In short: Scores 92, 85, 78 carrying weights 20, 30, 50: the weighted average is (92×20 + 85×30 + 78×50)/100 = 82.9 — nearly three points below the simple mean of 85, because the 78 carries half the freight. That gap IS the finding: weights decide whose voice the average hears. The page refuses what the algebra cannot honor — a zero weight-sum has no denominator, negative weights would let a value count against itself — and prints the weight share of each row so the divergence can be traced item by item.
Formula
x̄w = Σ(wᵢxᵢ)/Σwᵢ · simple mean = Σxᵢ/n
Weights need not sum to 1 — the denominator Σw normalizes whatever you type. Equal weights collapse the formula to the plain mean, which is why both are printed: the gap between them is how much the weighting decided.
Worked Example
- Paste the values and the weights — same count, weights non-negative, not all zero.
- Read the weighted average, then the work card: every wᵢxᵢ product shown.
- Compare the simple mean beside it — the gap is the weighting’s fingerprint.
- Use the share card to see each row’s percent hold on the answer.
Defaults: 82.9 weighted vs 85 simple — the 78’s 50% share drags the average down. Equal weights give 85 exactly; Σw = 0 and negative weights are refused with the rule named.
Strengths & Limits Of This Model
Where this engine is strong
- Simple mean printed beside so the weighting’s fingerprint is a number, not a shrug
- Per-row weight shares shown — the contested input made auditable
Where it stops
- No trimmed or winsorized weighting
- No time-weighted variants (moving-average territory)
Practical Use Cases
Gradebook
scores against credit hours or percentages
Portfolio
positions against their sizes
Survey
responses against their sample counts
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Weighted Average Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why is the weighted average 82.9 and not 85?
Because weights decide whose voice the average hears: the 78 carries 50% of the total weight, so it drags the result to 82.9 even though it is the smallest value on the smallest share of rows. The simple mean (85) is the equal-weights special case — printed beside so the fingerprint of your weighting is visible, not hidden.
Do the weights have to sum to 100?
No — the formula divides by Σw whatever it is: 20/30/50, 2/3/5, and 0.2/0.3/0.5 all give 82.9. Percent-style weights are a display convention, not a mathematical requirement. What the page does require is Σw > 0: weights summing to zero leave nothing to divide by.
Why refuse negative weights?
Because a weight is “how much this value counts”, and a negative count would let a value argue against itself — the average could be pushed outside the range of the data, which no honest average permits. (Specialized finite-population estimators do use negative weights; they are estimators, not averages, and out of scope here.)
What is the difference between this and the mean page’s weighted mode?
Question size. The mean page computes a weighted mean as one MODE of a general average tool; this page makes the weights the entire question — shares per row, the divergence from the simple mean, and the gradebook/survey framing. Same arithmetic, opposite emphasis; use whichever frame matches your problem.
How is this different from a moving average?
Time. Here the weights attach to ITEMS (scores, positions, responses); a moving average attaches them to TIME WINDOWS — recent rows heavy, old rows light. The moving-average page owns that machinery; the two share the word “average” and little else.
What if my weights are sample sizes?
That is the survey use case, and it is the most honest one: averaging group means weighted by group sizes reconstructs the pooled mean exactly. Weighting by anything else — budget, convenience, loudness — is a modeling decision the share card makes visible.
Can weights be percentages?
Yes — percent weights are just weights; the denominator normalizes them. The share card then prints each row’s actual hold on the answer, which for percent inputs equals the typed number only when they sum to 100 — the card shows the true shares either way.
Why does the work card show every product?
Because the weighted average is the one statistic whose inputs are almost always contested: show wᵢxᵢ for every row and the argument moves from the answer to the weights, where it belongs. The number is bookkeeping; the weights are the decision.