Weighted Average Calculator
Calculate a weighted mean from values and their weights, with each item's contribution shown and a comparison against the plain average.
How to use this calculator
- 1Enter the values you want to average, separated by commas, spaces or new lines.
- 2Enter one weight for each value, in the same order. They can be percentages, raw counts or any consistent scale — they do not have to total 100.
- 3Optionally name each item so the contribution table is easier to read.
How the calculation works
Weighted mean = Σ(wᵢ × xᵢ) ÷ Σ(wᵢ)- xᵢ
- Each value being averaged
- wᵢ
- The weight attached to that value — how much it counts
- Σ
- Sum across every item
Dividing by the sum of the weights is what normalises them, which is why they never need to add up to 100 or to 1. Weights of 10/15/25/50 and 0.1/0.15/0.25/0.5 give exactly the same answer, and so do raw counts like 200/300/500.
When every weight is the same, the formula collapses to the ordinary mean: Σ(w·x)/Σ(w) becomes w·Σx / (n·w), and the w cancels. The plain average is just the special case where nothing is weighted more than anything else.
Each item's contribution to the final figure is (wᵢ × xᵢ) ÷ Σw, and those contributions add up to the weighted mean — which is what the table below shows.
Worked example
A course grade with weighted categories
- 1.Multiply each score by its weight: 95×10 = 950, 88×15 = 1,320, 72×25 = 1,800, 80×50 = 4,000.
- 2.Sum those products: 950 + 1,320 + 1,800 + 4,000 = 8,070.
- 3.Sum the weights: 10 + 15 + 25 + 50 = 100.
- 4.Weighted average: 8,070 ÷ 100 = 80.7.
- 5.The plain average of 95, 88, 72 and 80 is 335 ÷ 4 = 83.75 — a full 3.05 points higher, because the plain average treats the 50%-weighted final exam as no more important than the 10%-weighted homework.
Result: 80.7 — versus a plain average of 83.75
When a plain average misleads
An ordinary average treats every number as equally important. That is the right assumption surprisingly rarely. A student whose final exam counts for half the grade, an investor whose portfolio holds far more of one asset than another, a shop averaging review scores where one product has ten thousand ratings and another has three — in each case the plain mean quietly asserts that all the items matter the same, and produces a number that describes nothing real.
The weighted mean fixes this by attaching an explicit weight to each value and dividing by the total weight rather than the count. The arithmetic is barely more complex; what changes is that the assumption about importance becomes visible and adjustable instead of hidden.
Weights do not have to be percentages
A persistent misconception is that weights must add up to 100, or to 1, before the formula works. They do not. Because the final step divides by the sum of the weights, any consistent scale normalises itself: weights of 10, 15, 25 and 50 give exactly the same answer as 0.1, 0.15, 0.25 and 0.5, or as 200, 300, 500 and 1,000. What matters is the ratio between the weights, never their absolute size.
This is what makes the weighted mean so flexible in practice. You can weight by raw counts (how many students sat each exam), by declared percentages (a syllabus saying the final is worth 50%), or by an arbitrary judgement of importance ("this criterion matters three times as much"), and the formula handles all three identically without any conversion step.
Where weighted averages turn up
The same calculation appears under many different names across fields.
- Course grades — a syllabus assigning percentages to homework, quizzes, a midterm and a final is defining exactly this calculation. GPA is a weighted average too, with course credit hours as the weights.
- Portfolio return — the return on a portfolio is the weighted average of its holdings' returns, weighted by how much money sits in each — which is why a large position's performance dominates the total.
- Weighted average cost of capital — a company's overall cost of financing, blending the cost of debt and equity in proportion to how much of each it uses.
- Inventory and unit costing — when identical goods are bought at different prices, the weighted average cost per unit uses quantities purchased as the weights.
- Survey and poll aggregation — combining results from samples of different sizes weights each by its sample size, so a poll of 2,000 people counts for more than one of 200.
Common mistakes
Three errors account for most wrong weighted averages.
- 1Dividing by the count instead of the total weight — the single most common slip. Σ(w·x) must be divided by Σw, not by n. Dividing by n gives a number with no meaningful interpretation at all unless the weights happen to average to 1.
- 2Misaligning the two lists — values and weights are paired by position, so a missing or extra entry in either list silently shifts every subsequent pairing. This calculator refuses to run when the lengths differ, precisely because the result would look plausible and be wrong.
- 3Averaging averages — taking the plain mean of several group averages ignores that the groups may be different sizes. Combining a 30-student class averaging 70 with a 10-student class averaging 90 gives 75, not 80 — the group sizes are the weights.
What this assumes, and where it stops
Assumptions
- Values and weights are paired by position — the first weight belongs to the first value, and so on.
- Weights are non-negative. A zero weight is allowed and simply excludes that item from the result.
Limitations
- Handles a one-dimensional weighted mean. Weighted medians, weighted standard deviations and multi-level (nested) weighting schemes are out of scope.
- Does not check that your weights are the right ones — it applies whatever you enter. If a syllabus or fund factsheet states the weights, take them from there rather than estimating.
Common questions
Do my weights need to add up to 100?
No. The formula divides by the sum of the weights, which normalises whatever scale you use. Weights of 10, 15, 25 and 50 give the same answer as 0.1, 0.15, 0.25 and 0.5, or as raw counts like 200, 300, 500 and 1,000. Only the ratios between weights matter.
Why is my weighted average different from the normal average?
Because the weights are not all equal, so some values count for more. The result is pulled toward whichever values carry the heavier weights. If every weight were the same, the two averages would be identical — the plain mean is simply the equally-weighted case.
How do I combine averages from groups of different sizes?
Use the group averages as the values and the group sizes as the weights. Averaging a 30-student class scoring 70 with a 10-student class scoring 90 gives (70×30 + 90×10) ÷ 40 = 75, not the 80 you would get by averaging 70 and 90 directly.
Formula and content last reviewed on .
Results are estimates for information only, not professional advice.
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