Weighted Average Calculator
Add values and weights below. Results update as you type.
Last reviewed: May 2026| Label (optional) | Value | Weight (%) | Contribution |
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This weighted average calculator computes the weighted mean of any number of value-and-weight pairs using the standard formula Σ(value × weight) ÷ Σ(weight). The sections below explain exactly how that math differs from a simple average, walk through three concrete worked examples (a class grade, an investment return, and a survey response), cover the most common mistakes people make with weights, and point you toward the right variant — weighted median, geometric mean, or harmonic mean — when the plain weighted arithmetic mean isn't the tool for the job.
What This Calculator Does
Weighted Average vs. Simple Average
A weighted average — also called a weighted mean — is the right answer whenever the numbers you're combining are not equally important. The calculator above accepts any number of value-and-weight pairs, multiplies each value by its weight, sums those products, and divides by the sum of the weights. For comparison it also reports the simple (unweighted) average, computed by summing all the values and dividing by the count. The gap between the two figures is the size of the correction that weighting introduces, and seeing both side by side often makes the difference visceral in a way a single number never does.
Two Weight Modes: Percentage and Points
The calculator supports two weight modes. In percentage mode, weights are expected to sum to 100 (course-grade syllabi, survey design, and budget allocations almost always express weights this way), and the calculator will flash a soft warning if your weights drift away from 100. In points mode, weights are absolute — credit hours, dollar amounts, response counts, lab repetitions, or any other count-style measure. Both modes use the same underlying formula; the division by Σ(weight) normalizes everything automatically, so the choice between modes is purely about what's easier for you to enter. Switching modes mid-calculation does not lose your data; only the column header and the warning behavior change.
What the Three Result Tiles Tell You
The large center tile shows the weighted average — your headline number. The unweighted-average tile is the simple mean of the same values, ignoring weights. The total-weight tile shows the sum of the weights you've entered, useful as a sanity check (it should equal 100 in percentage mode, or your total credits / total dollars / total responses in points mode). Each individual row also displays its contribution: the percentage of the final weighted sum attributable to that single pair. When one row's contribution dominates the total — anything above 40% — it's worth double-checking that the weight was entered correctly, because the result is now largely a function of that single data point.
How to Use It
Entering Value/Weight Pairs
Each row of the table represents one observation: a label (optional), a numeric value, and a numeric weight. Type any of the three and results recompute instantly — there's no Calculate button to press. The default rows show a sample grade calculation (homework, midterm, final) to make the workflow concrete, but clicking Reset and overwriting them with your own data is the normal way to use the tool. Use the + Add Row button to extend the table when you have more than three observations; the cross icon on the right of any row removes it.
Reading the Results in Real Time
Below the table, four pieces of information update as you type: weighted average, unweighted average, total weight, and per-row contribution. The contribution column tells you how much of the final answer is coming from each individual pair — values displayed as percentages of the weighted sum. This is the fastest way to spot a weighting mistake: if you intended a homework category to count for 20% but its contribution shows 50%, your weight column has too high a number.
Sharing and Resetting
Every calculation produces a sharable URL containing your inputs. Copy the URL from the share input below the calculator and anyone who opens it sees the same scenario pre-filled — no signup, no account. The Reset button restores the three default rows and clears any custom rows you've added. The Print button generates a clean printable view of the results (without the calculator chrome) so you can drop it into a notebook, an email attachment, or a class submission. Both buttons sit in the small action row directly under the result tiles.
Worked Examples
Example 1: Class Grade — Midterm, Final, Homework
- Midterm score
- 84 (weight 30%)
- Final score
- 91 (weight 50%)
- Homework score
- 88 (weight 20%)
Simple average: (84 + 91 + 88) ÷ 3 = 263 ÷ 3 = 87.67. This is the wrong answer for a final course grade — it ignores the syllabus weighting entirely.
Weighted average: (84 × 0.30 + 91 × 0.50 + 88 × 0.20) ÷ (0.30 + 0.50 + 0.20). Numerator: 25.2 + 45.5 + 17.6 = 88.3. Denominator: 1.00. Weighted average = 88.3.
The official course grade is 88.3, but a student computing their average informally with the simple-mean shortcut would arrive at 87.67 — a 0.63-point gap that can be the difference between a B+ and an A-. The discrepancy comes from the fact that the final exam is weighted 2.5× more heavily than homework, so the high final score (91) pulls the weighted result above what the simple mean produces. Whenever a single category carries a heavier syllabus weight than the others, the simple average is reliably wrong; weights must be applied.
Example 2: Investment Portfolio Return
- $10,000 in Bond Fund
- 7% return (weight: $10,000)
- $25,000 in Index Fund
- 4% return (weight: $25,000)
- $5,000 in Growth Fund
- 12% return (weight: $5,000)
Total invested: $10,000 + $25,000 + $5,000 = $40,000.
Weighted return: (10000 × 7 + 25000 × 4 + 5000 × 12) ÷ 40000. Numerator: 70,000 + 100,000 + 60,000 = 230,000. Denominator: 40,000. Weighted return = 230,000 ÷ 40,000 = 5.75%.
The simple-mean approach — averaging 7%, 4%, and 12% to get 7.67% — overstates the portfolio's actual performance by nearly two full percentage points. The 12% Growth Fund return looks impressive in isolation, but it sits on only $5,000 of the total $40,000 portfolio, so its real contribution to the blended return is far smaller than its raw number suggests. Conversely the modest 4% return on the $25,000 Index Fund position dominates the result because that's where most of the money sits. This is the right way to think about portfolio return whenever positions are unequally sized.
Example 3: Customer Survey Mean Score
- Premium tier customers
- 200 responses, mean score 4.2 (weight: 200)
- Standard tier customers
- 150 responses, mean score 3.8 (weight: 150)
- Free tier customers
- 350 responses, mean score 4.5 (weight: 350)
Total responses: 200 + 150 + 350 = 700.
Weighted mean satisfaction: (200 × 4.2 + 150 × 3.8 + 350 × 4.5) ÷ 700. Numerator: 840 + 570 + 1575 = 2985. Denominator: 700. Weighted mean = 2985 ÷ 700 = 4.26.
A simple-mean of the three tier scores (4.2, 3.8, 4.5) gives 4.17, but this treats the Free tier's 350-respondent sample as equally informative as Standard tier's 150-respondent sample — it isn't. Weighting by response count produces 4.26, the answer you'd get by averaging all 700 individual responses one at a time. For any survey result reported by segment, the segment-level means must be reweighted by their sample sizes before they can be combined into a single headline figure.
Common Use Cases
GPA Calculation
Cumulative grade-point average is the canonical weighted mean. Each course's grade-point value (A = 4.0, B = 3.0, and so on) is weighted by the credit hours assigned to it. A 5-credit chemistry sequence with lab represents far more academic effort than a 1-credit PE elective, so a simple average of letter grades is unreliable. The right calculation is GPA = Σ(grade-points × credits) ÷ Σ(credits). Most universities use this formula automatically; if you're projecting forward to a target GPA, this calculator gives you the same number the registrar's transcript engine produces.
Portfolio Returns and Asset Allocation
Blended portfolio returns are weighted by the dollar value of each position. The same principle extends to expected return calculations under modern portfolio theory: each asset's expected return is weighted by its target allocation. When rebalancing, this calculator can help you sanity-check whether a proposed allocation produces the blended return you actually want — particularly useful when reading prospectus return figures that may be reported at the position level rather than the portfolio level.
Customer Satisfaction Scores
Net Promoter Score and customer satisfaction metrics are often reported by customer segment (enterprise, mid-market, SMB; or premium, standard, free), but the headline company-wide figure needs to weight each segment by something — typically respondent count for unbiased estimation, or revenue / lifetime value when satisfaction matters more for higher-value customers. The right weighting choice depends on the question being asked. Always document which weights you used; "average CSAT" without a weighting basis is ambiguous.
Election Polling and Demographic Weighting
Survey responses are weighted by demographic factors to correct for sampling skew — if young men are underrepresented in raw responses, their answers are upweighted to match census demographic shares before reporting top-line numbers. This is mechanically the same formula this calculator implements; only the source of the weights (population proportions from census data) differs from the simpler cases. Mishandled weighting is the single largest source of polling miss controversies, which is why methodology documents always disclose the weighting variables and source proportions.
Grade Tracking and Final-Grade Projection
Mid-semester, students often ask "what do I need on the final to get an A?". Set the final's row to weight 50% and value as the unknown, fill in everything else from your gradebook, and solve algebraically: needed_final = (target_grade − sum_of_other_contributions) ÷ final_weight. This calculator gives you the current weighted average so far, which is the starting point for that projection.
Employee Performance Reviews
Multi-factor performance reviews score employees across categories (technical work, collaboration, leadership, project delivery), with each category weighted by its strategic importance for the role. The overall review score is the weighted mean. Calibration sessions across teams often hinge on whether managers agree on the weights; once weights are fixed and applied consistently, comparisons across employees become meaningful.
Common Mistakes
Mistake 1: Using a Simple Average When Weights Should Apply
This is by far the most common error and the one with the largest practical impact. Whenever observations have different importance — different sample sizes, different dollar amounts, different credit hours, different syllabus weights — the simple mean is the wrong tool. The size of the error depends on how unequal the weights are and how correlated the values are with the weights. In the class-grade example above, the gap is only 0.63 points; in a survey where the largest segment also has the most extreme view, the gap can be several full points on a 5-point scale.
Mistake 2: Forgetting That Weights Don't Have to Sum to 1
Many people learn the weighted-mean formula in a context where weights are presented as probabilities summing to 1.00, and then assume the formula breaks if their weights don't add up that way. They don't. The denominator Σ(weight) in the formula handles normalization automatically, so weights of 30, 50, 20 produce the same result as weights of 0.30, 0.50, 0.20 or 3, 5, 2. You should normalize manually only if you want the intermediate steps to be cleaner to read.
Mistake 3: Confusing Weighted Average with Weighted Moving Average
The names overlap, but the two operations answer different questions. A weighted average collapses a fixed dataset into one number. A weighted moving average is a smoothing transformation applied to a time series — at each time step, it computes a weighted average over a sliding window of recent observations, typically giving more weight to more recent data (exponential smoothing is the most common variant). Stock-chart software defaults to the moving-average flavor; this calculator handles the static summary flavor. They share the same kernel formula but produce very different outputs.
Mistake 4: Mishandling Missing Data
If one row in your dataset is incomplete, you have a choice to make and the choice matters. Dropping the pair entirely (listwise deletion) gives you an unbiased weighted average over the remaining observations, but with reduced precision. Treating the missing value as zero pulls the weighted average downward, sometimes drastically — which is correct if zero is what "missing" means (a student who skipped an assignment) and incorrect if missing just means unknown (a student whose grade hasn't been entered yet). The worst case is to leave the row in place with weight > 0 but value blank or NaN; many implementations will then either crash, treat the value as zero silently, or produce a misleading result. The calculator above filters incomplete rows from the weighted-mean computation but still shows them in the table, making the omission explicit.
The Formula
The Standard Weighted Mean
weighted_mean = Σ(value_i × weight_i) / Σ(weight_i)Each value is multiplied by its weight, the products are summed, and that sum is divided by the sum of the weights. The denominator does double duty: it normalizes the result so the units of "weight" cancel out, and it ensures the answer falls between the smallest and largest input value (a property called the convex combination guarantee, which only holds when all weights are non-negative — see the final FAQ on negative weights for why that matters).
Derivation: Why the Denominator Is What It Is
Start with the special case where weights sum to exactly 1. The formula collapses to weighted_mean = Σ(value_i × weight_i) — the denominator is 1 and disappears. In this case the weights are interpretable as probabilities, and the weighted mean is identical to the expected value of a discrete random variable. Now generalize: if weights don't sum to 1, divide every weight by Σ(weight) to renormalize them. The new weights sum to 1, and the formula still works. Algebraically, you can pull the 1 ÷ Σ(weight) factor out of the sum, and what's left is the familiar Σ(v × w) ÷ Σ(w) shape. This is why the formula handles arbitrary weight scales transparently.
Connection to Expected Value
The expected value E[X] of a discrete random variable X taking values v_1, v_2, … v_n with probabilities p_1, p_2, … p_n is exactly E[X] = Σ(v_i × p_i). The probabilities are weights that sum to 1 by construction, so the weighted-mean formula collapses to the expected-value formula. This is the bridge between weighted averages and probability theory: every probability-weighted forecast is a weighted average where the weights happen to be normalized probabilities.
Special Cases
Equal weights: If every weight is the same value (call it w), the formula simplifies to Σ(value × w) ÷ (n × w) = Σ(value) ÷ n, which is the simple arithmetic mean. The simple mean is therefore a special case of the weighted mean, not a different formula. Counts as weights: When weights represent counts (number of responses per group, frequency per bucket), the weighted mean is mathematically equivalent to computing the simple mean across the ungrouped data. This is sometimes called the grouped data mean — useful when raw data is unavailable but summary statistics by group are reported.
Beyond Weighted Average
Weighted Median — Robust to Outliers
The weighted mean is sensitive to extreme values: one row with a very large value and a non-trivial weight can drag the result far in its direction. The weighted median solves this by reporting the middle value (in the sense of half-weight on each side) rather than the weighted average. It's slower to compute but far more robust when your dataset contains outliers — house-price averages, income distributions, and any other heavy-tailed quantity benefit from the median treatment over the mean. The formula doesn't have a clean closed form; you sort the values by their underlying value, accumulate weights, and find the point where cumulative weight crosses half of Σ(weight).
Weighted Variance — Measuring Spread
The weighted mean tells you the center of your weighted dataset; the weighted variance tells you the spread. The standard formula is weighted_variance = Σ(weight_i × (value_i − weighted_mean)²) ÷ Σ(weight_i), but this is biased downward when the weights are sample frequencies. The Bessel-corrected unbiased version divides by Σ(weight) − Σ(weight²) ÷ Σ(weight) instead. Statistical software (R's weighted.mean / cov.wt, Python's statsmodels.stats.weightstats.DescrStatsW) implements both variants; choose based on whether weights represent reliability (use the biased form) or sampling frequency (use the Bessel correction).
Weighted Geometric Mean — Multiplicative Quantities
When values compound multiplicatively — yearly returns chained over time, index components combined by ratio, growth rates over multiple periods — the arithmetic weighted mean overstates the true center. The weighted geometric mean fixes this: GM = ∏(value_i ^ (weight_i / Σweight)). For three returns of 1.20, 0.90, 1.15 with equal weights, the arithmetic mean is 1.0833 (8.33% annualized), but the geometric mean is (1.20 × 0.90 × 1.15)^(1/3) = 1.0740 (7.40% annualized). The geometric version is the compound annual growth rate (CAGR), which is what actually matters when projecting future portfolio value.
Weighted Harmonic Mean — Rates Averaged by Different Quantities
The classic example: you drive 60 miles at 30 MPG, then 120 miles at 40 MPG. What's your average MPG over the whole trip? The simple mean of 30 and 40 is 35, but that's wrong — you used more gallons on the first segment, so it counts more heavily. The right answer uses the harmonic mean weighted by distance: HM = Σ(distance) ÷ Σ(distance ÷ MPG) = (60 + 120) ÷ (60 ÷ 30 + 120 ÷ 40) = 180 ÷ 5 = 36 MPG. The harmonic mean is always less than or equal to the arithmetic mean, with the gap growing as the input values spread further apart. Use it whenever you're averaging rates (miles per gallon, prices per share, p/e ratios) over quantities denominated in the rate's denominator.
FAQ: Weighted Average Questions
How is weighted average different from a regular average?
A regular (arithmetic) average treats every value as equally important — sum all values, divide by count. A weighted average lets each value carry a different importance through its weight, then divides by the sum of weights rather than the count. The formula is Σ(value × weight) ÷ Σ(weight). For three test scores of 84, 91, and 88, the simple average is (84 + 91 + 88) ÷ 3 = 87.67. But if those carry weights of 30%, 50%, and 20%, the weighted average becomes (84 × 0.30 + 91 × 0.50 + 88 × 0.20) ÷ (0.30 + 0.50 + 0.20) = 88.7. The 1.03-point difference comes entirely from the higher weight assigned to the strongest score. Use the simple average only when all observations truly are equally important; otherwise weights are required to get the right answer.
Do weights have to add up to 1 or 100%?
No — the weighted-average formula handles normalization automatically by dividing the weighted sum by the sum of weights. You can enter 30, 50, and 20 (summing to 100), or 3, 5, and 2 (summing to 10), or even credit hours like 4, 3, 5 — all three produce the correct weighted average for the same underlying values. The reason weights are often presented as percentages summing to 1.00 or 100 is convention, not mathematical requirement. The calculator on this page will flash a warning if your percentage-mode weights drift away from 100 because that often signals a data-entry error, but the math underneath remains correct either way. The takeaway: weights express relative importance, and the formula's denominator (Σ weight) makes their absolute scale irrelevant.
Why isn't simple average appropriate for GPA?
GPA reflects how well you performed across all coursework, and not every course carries the same load. A 5-credit chemistry sequence with a lab represents far more academic effort than a 1-credit physical-education course, so a simple average of letter grades would let an easy A in PE artificially inflate (or a tough B in chemistry artificially deflate) the cumulative figure. The correct calculation weights each grade-point value by its credit hours: GPA = Σ(grade-point × credits) ÷ Σ(credits). For a semester with A (4.0) in 3-credit English, B (3.0) in 4-credit chemistry, and A (4.0) in 1-credit PE, the simple average is (4 + 3 + 4) ÷ 3 = 3.67. The weighted GPA is (4 × 3 + 3 × 4 + 4 × 1) ÷ 8 = 3.50 — a meaningful difference for class rank, scholarships, and graduate-school applications.
Can I use this calculator for investment portfolio return?
Yes — portfolio return is one of the cleanest applications of the weighted-average formula. Enter each holding's return as the value and the dollar amount allocated as the weight. The calculator will divide the weighted sum by the total dollars invested to give you the weighted average return, which is the figure most investors actually want when they ask "what did my portfolio do this year?". For example, $10,000 returning 7%, $25,000 returning 4%, and $5,000 returning 12% produces a weighted return of (10000 × 7 + 25000 × 4 + 5000 × 12) ÷ 40000 = 230000 ÷ 40000 = 5.75%. Note this is the time-weighted approximation for a single period; if your positions changed mid-period you'll want a money-weighted or internal-rate-of-return calculation instead, which accounts for the timing of deposits and withdrawals.
What's the difference between weighted average and weighted moving average?
They look similar but answer different questions. A weighted average collapses a fixed set of value/weight pairs into a single number, treating the weights as fixed importance scores. A weighted moving average is a smoothing technique applied to a time series — at each point in time, it computes a weighted average over a sliding window of recent observations, typically giving more weight to recent data than to older data. So a 5-day weighted moving average of stock prices recomputes daily as the window slides forward and the old observation drops off the end. The math at any single instant is the same Σ(v × w) ÷ Σ(w) formula, but the moving variant produces a sequence of values rather than one summary number. Use this calculator for the static summary case; for time-series smoothing, a charting tool with built-in moving-average overlays is the better fit.
When should I use the weighted geometric mean instead?
Use a weighted geometric mean when your values are multiplicative — that is, they chain together by multiplication rather than addition. The two most common cases are compounding returns over multiple periods and ratios used in index construction. The arithmetic weighted mean of yearly returns of +20%, −10%, and +15% is +8.33%, but that overstates the true compound annual growth rate: (1.20 × 0.90 × 1.15)^(1/3) − 1 = 7.40%. For weighted geometric mean, raise each value to the power of its normalized weight and multiply: GM = ∏(value_i ^ (weight_i / Σweight)). When in doubt, ask whether averaging your numbers makes sense by addition or by multiplication. Returns, growth rates, and inflation factors are multiplicative; test scores, temperatures, and dollar amounts are additive.
How do I handle missing data?
There is no universally correct answer — it depends on what the missing observation means. If a value is genuinely unknown and unmeasured, the safest approach is to drop both the value and its weight from the calculation; this is called listwise deletion and produces an unbiased weighted average over the remaining observations. If the value is missing because the underlying quantity was zero (a student who skipped an assignment, a survey respondent who declined to answer), substituting zero may be appropriate — but be explicit about that choice because it can pull the weighted average down significantly. Avoid the common mistake of leaving the weight in place while setting the value to zero unintentionally; that treats unknown as zero and biases the result. For more sophisticated cases, imputation methods like mean substitution or regression imputation can preserve sample size while reducing bias, but those go beyond what a calculator can decide for you.
Can I weight by negative numbers?
Mathematically yes — the formula Σ(value × weight) ÷ Σ(weight) does not break on negative weights, and you'll get a defined result as long as the denominator is non-zero. But negative weights almost never have a meaningful interpretation in real applications. A weight represents importance or share, and "negative importance" doesn't correspond to anything physical. Negative weights can also produce surprising and counterintuitive results: a single small negative weight can flip the sign of the weighted sum or push the result outside the range of the input values, which violates one of the basic guarantees of the simple weighted mean. The calculator on this page guards against this by requiring weights ≥ 0. The one legitimate use case is in regression contexts where "weight" is actually a coefficient on a linear combination — but that's a different formula being computed, not a weighted average.