The weighted average calculator above handles the very common case where a plain average is simply the wrong answer: when some of your numbers deserve more influence than others. Enter a list of values and a matching list of weights, and it returns the weighted mean, the substituted arithmetic that produced it, each item's share of the total weight, and the ordinary unweighted average beside it so you can see exactly how much the weighting changed the outcome.
Arb Digital publishes this alongside its other statistics tools because weighting errors are quietly expensive. Averaging three monthly conversion rates without accounting for wildly different traffic volumes, or averaging unit prices across orders of different sizes, produces a number that looks authoritative and is wrong by whatever the volume differences happen to be. If your specific task is a course grade with weighted assessments, our weighted grade calculator is purpose-built for that; this page is the general-purpose version for any values and any weights.
What This Weighted Average Calculator Does
Give it two lists of the same length. The first holds your values, the second holds the weight attached to each. The headline result is the weighted mean: each value multiplied by its weight, all of those products added together, then divided by the total weight. Weights do not need to sum to 100 or to 1 — the division by total weight normalises whatever scale you use, so raw counts, percentages, hours, dollars or arbitrary importance scores all work.
The grid shows the weighted sum, the total weight, the ordinary unweighted mean, and the difference between the two averages. That last figure is the one worth watching. A large gap means the weighting is doing significant work, and it is a signal that anyone reporting the simple average of the same data is publishing a materially different number. The bar display underneath shows each item's share of the total weight, which makes it obvious when a single entry dominates.
Negative values are allowed; negative weights are not, because a negative weight has no coherent interpretation as a share of influence and can produce a total weight of zero, which makes the average undefined. If your lists are different lengths the calculator either trims to the shorter one or fills missing weights with 1, according to the option you pick.
How to Use It
- Enter your values in the first box, in any order, separated by commas, spaces or line breaks.
- Enter the matching weights in the second box in exactly the same order. The first weight applies to the first value.
- Pick any convenient weight scale. Percentages, raw counts and hours all give identical results because the weights are normalised.
- Read the working line to see the multiplication and division substituted with your own numbers.
- Compare against the unweighted mean to judge how much the weighting mattered.
The Formula and How It's Calculated
The formula is weighted mean = (w₁x₁ + w₂x₂ + … + wₙxₙ) ÷ (w₁ + w₂ + … + wₙ). Multiply each value by its weight, sum the products, and divide by the sum of the weights.
Using the default data — values of 85, 92 and 78 with weights of 20, 50 and 30 — the products are 85 × 20 = 1700, 92 × 50 = 4600 and 78 × 30 = 2340. Those sum to 8640. The weights total 100. So the weighted average is 8640 ÷ 100 = 86.4. The unweighted mean of the same three values is (85 + 92 + 78) ÷ 3 = 255 ÷ 3 = 85, so weighting has pulled the result up by 1.4 points, because the highest value happens to carry half of the total weight.
Notice what happens if every weight is equal: the weights cancel and the formula collapses to the ordinary arithmetic mean. That is the useful way to think about it — the arithmetic mean is just a weighted mean where every observation carries the same weight, as set out in MathWorld's definition of the weighted mean. Our mean, median and mode calculator covers that equal-weight case along with the other measures of centre.
The Averaging Trap That Costs Real Money
Here is the single most common weighting error in commercial reporting, and it is worth walking through in numbers. Suppose one campaign gets 1,000 visits and converts at 2%, and another gets 100 visits and converts at 10%. The simple average of 2% and 10% is 6%. The true combined rate is (20 + 10) conversions out of 1,100 visits, which is 2.7%.
The gap between 6% and 2.7% is not rounding. It is the difference between a metric that is defensible and one that will not survive contact with the finance team. Rates, percentages and ratios must always be weighted by the denominator they were calculated from — visits, impressions, units, headcount — because averaging the rates themselves silently gives a tiny sample the same voice as a large one. The correct approach is either to weight by volume, as this calculator does, or to recompute the rate from the raw totals. Our conversion rate calculator works from raw counts for exactly that reason.
Choosing the Right Weights
The weights are the analytical decision; the arithmetic is not. Reference texts such as the NIST/SEMATECH e-Handbook of Statistical Methods treat the choice of weighting as part of the study design rather than a computational detail. A weight should represent how much of the underlying quantity each value stands for. For an average price across orders, weight by units sold. For an average interest rate across accounts, weight by balance. For an average salary across departments, weight by headcount. For an average score across assessments, weight by the marks each assessment is worth.
Where weights are subjective — importance scores in a vendor evaluation, for instance — write down the reasoning before you assign them, because a weighted average built on undocumented weights is unauditable. Anyone can change the ranking by adjusting a weight from 3 to 5, and if nobody recorded why it was 3, there is no basis on which to object. Stating the weights and their justification alongside the result is what turns a weighted average from a number into evidence.
Weighted Averages in Portfolios and Inventory
Two specific applications are worth naming because they use this exact calculation under different labels. Portfolio return is a weighted average of holding returns, weighted by the value of each holding rather than by the number of positions. Owning ten small positions and one very large one produces a portfolio return dominated by the large one, whatever the simple average of the eleven returns says. Our portfolio rebalancing calculator works with those same value weights.
Inventory costing is the other. The weighted average cost method values stock at the average purchase price weighted by quantity bought at each price, rather than by how many separate purchase events occurred. Buying 1,000 units at $4 and 10 units at $9 gives a weighted average cost of $4.05, not $6.50. Any stock valuation using the simple average of purchase prices will be materially wrong whenever purchase quantities vary, which in practice is always.
When a Weighted Average Is Still the Wrong Tool
Weighting fixes unequal influence. It does not fix the wrong kind of average. If you are averaging growth rates or investment returns across successive periods, the correct answer is the geometric mean, because those quantities compound rather than add — our geometric mean calculator covers that. If you are averaging rates defined as something-per-something over a fixed distance or quantity, such as speeds over equal legs of a journey, the harmonic mean is correct, and our harmonic mean calculator handles it.
Weighting also does nothing about outliers. A single extreme value with a large weight can drag the result somewhere no individual item sits, and the average will look perfectly reasonable while representing nothing. Check the spread with our standard deviation calculator before quoting any average, weighted or not, and consider reporting the median alongside it when the distribution is skewed.
Arb Digital maintains a large free library of calculators and converters. Browse the collection, or tell us which one you keep wishing existed.
Browse All Free Tools Suggest a ToolCommon Mistakes to Avoid
- Averaging percentages without weighting by volume. This is the single most common error and it can be off by a factor of two or more.
- Mismatched list order. The third weight must belong to the third value. A single misalignment silently changes the answer.
- Assuming weights must total 100. They do not. Any consistent scale works because the calculation divides by the total weight.
- Using negative weights. A negative weight has no interpretation as a share of influence and can make the total weight zero, leaving the average undefined.
- Weighting when you should be compounding. Growth rates over successive periods need a geometric mean, not a weighted arithmetic one.
Related Free Tools From Arb Digital
For course grades with weighted components, use the weighted grade calculator or the GPA calculator, both of which apply this maths in an academic format. For equal-weight averages, use the mean, median and mode calculator. For compounding growth use the geometric mean calculator, and for rates and speeds use the harmonic mean calculator. Check the spread with the standard deviation calculator, and browse the full free online tools hub for more.
Frequently Asked Questions
Multiply each value by its weight, add all those products together, then divide by the sum of the weights. With values of 85, 92 and 78 carrying weights of 20, 50 and 30, the products total 8640 and the weights total 100, giving a weighted average of 86.4.
No. The formula divides by the total weight, so any consistent scale gives the same answer. Weights of 2, 5 and 3 produce exactly the same result as weights of 20, 50 and 30.
A normal average gives every value the same influence. A weighted average lets some values count for more, so the result moves toward whichever values carry the larger weights. They agree only when every weight is equal.
Only when they come from equal-sized groups. Otherwise weight each percentage by the volume it was calculated from, or recompute from the raw totals. A 2 percent rate on 1,000 visits combined with a 10 percent rate on 100 visits gives 2.7 percent overall, not 6 percent.
A weight of zero is allowed and simply removes that value from the calculation. Negative weights are not meaningful, because a weight represents a share of influence, and they can make the total weight zero, which leaves the average undefined.
You can either trim to the shorter list or treat the missing weights as 1, and this calculator offers both. Treating them as 1 gives those values a small equal influence rather than dropping them entirely.
Use a geometric mean for growth rates and investment returns that compound across periods, and a harmonic mean for rates such as speeds measured over equal distances. A weighted arithmetic mean is right when values add rather than multiply.
