Weighted Mean Calculator
Add as many value/weight pairs as you need — the calculator returns the weighted mean, contrasts it with the simple average, shows every product in the sum, and draws a bar of each weight's share.
What is a weighted mean?
A weighted mean is an average where each value carries an importance — a weight — instead of every value counting equally. The classic classroom setting is course grades: assignments, quizzes and the final exam are usually worth different percentages of the overall grade. If you take the plain average of your scores you get the wrong answer, because the 40%-weighted final exam should influence your grade far more than a 5%-weighted homework.
Formally, given values x₁, x₂, …, xₙ with matching weights w₁, w₂, …, wₙ, the weighted mean is the sum of value × weight, divided by the sum of the weights. The next section walks through exactly what that formula does, with a diagram and worked example for every idea.
Weighted mean explained, idea by idea
Each card below pairs a plain-English definition with the formula (and what every symbol means), a small diagram, and a worked example — so you can see the concept and the arithmetic side by side.
The weighted mean formula
Multiply each value by its weight, add those products up, then divide by the sum of the weights. Values with bigger weights pull the answer toward themselves — which is exactly what you want when some numbers matter more than others.
Weight share (why raw numbers still work)
You don't have to convert your weights into percentages first. The Σw in the denominator normalises them for you, so weights of 20/30/50 give the exact same answer as 20%/30%/50% or 2/3/5. The picture below shows how each weight becomes a share of the whole.
When all weights are equal
If every weight is the same, the weights cancel out and the weighted mean collapses to the plain arithmetic mean. That's why the simple average is really a special case of the weighted average — the case where every value is equally important.
Common places weighted means show up
- Grades and GPA — assignments carry different percentages, courses carry different credit hours.
- Portfolio returns — a 5% gain on a small holding should not count the same as a 5% gain on a huge one.
- Product ratings — a 4.5-star rating from 200 reviews is more trustworthy than 5.0 from 3 reviews; sites weight by review count.
- Survey data — respondents from under-represented groups get up-weighted so the sample matches the target population.
- Inventory costing — weighted-average cost methods value stock using the total cost divided by total units received.
Features of this calculator
- Dynamic row list — add or remove value/weight pairs as your dataset grows
- Shows both the weighted mean and the plain arithmetic mean so you can see the impact of the weights
- Show/hide step-by-step working — every value × weight product, both totals, and the final division
- Weight-share bar plus per-row contribution bars — spot which entries dominate the average
- Bar chart with height = value and width = weight, and a dashed line marking the weighted mean
- Weights work at any scale (raw counts, percentages, dollars, hours) — the formula normalises internally
- Guards against empty inputs and all-zero weights, which would divide by zero
Frequently asked questions
+How is a weighted mean different from a simple average?
A simple (arithmetic) mean divides the sum by the count, treating every value equally. A weighted mean divides the sum of (value × weight) by the sum of weights, so values with larger weights pull the answer more than values with smaller weights.
+What if all the weights are equal?
Then the weighted mean equals the simple mean exactly. That's why the simple average is really a special case of the weighted average — the case where every value is equally important.
+Can weights be zero?
Yes. A weight of zero effectively drops that value from the calculation. What can't happen is every weight being zero — that would divide by zero. The calculator flags this case.
+Can weights be negative?
In this calculator, no — negative weights don't have a natural "importance" interpretation and can flip the answer in unexpected ways. If you're doing something like a hedge fund short position where a negative weight makes sense, model it as a positive weight on a sign-flipped value.
+Do the weights need to sum to 1 or 100%?
No. Any positive scale works — 1/2/3, 10/20/30, or dollar amounts. The Σw denominator normalises them for you. Sums of 1 or 100 just make each weight feel like a share, which is easier to read at a glance.