What is a weighted average?
A weighted average is an average in which some values count for more than others. In an ordinary average, every number carries exactly the same importance: you add them up and divide by how many there are. In a weighted average, each number is first multiplied by a weight representing how much it should count, and the total is divided by the sum of those weights rather than by the count.
Weighted Average = (v₁w₁ + v₂w₂ + ... + vₙwₙ) ÷ (w₁ + w₂ + ... + wₙ) “Weighted mean” is the more formal, statistical name for the same thing. If a textbook asks for the weighted mean and a syllabus asks for the weighted average, they want the identical number — this calculator produces it either way.
Worked example: a weighted average of course grades
Course grades are the most common everyday use of a weighted average, because assessments rarely count equally. Suppose a course is graded like this:
- Grade 1: 90 — Weight: 20
- Grade 2: 80 — Weight: 30
- Final: 70 — Weight: 50
Multiply each value by its weight:
- 90 × 20 = 1,800
- 80 × 30 = 2,400
- 70 × 50 = 3,500
Add the weighted values, add the weights, then divide one by the other:
(1,800 + 2,400 + 3,500) ÷ (20 + 30 + 50) = 7,700 ÷ 100 = 77 So the weighted average is 77. A simple average of 90, 80 and 70 would have been 80 — the weighted figure is lower because the final exam, worth half the grade on its own, is also the lowest score, while the 90 counts for only a fifth.
Do the weights have to add up to 100?
No. Enter weights as plain numbers — for percentage weights, enter 20 for 20%, 30 for 30%, and so on. The calculator divides by whatever the weights actually total, so weights of 20, 30 and 50 produce exactly the same weighted average as 0.2, 0.3 and 0.5, or as 2, 3 and 5. What matters is the ratio between the weights, not the total they happen to sum to.
That’s what makes the weighted average work for units that were never percentages in the first place: credit hours in a GPA, share counts in a portfolio’s average cost, sample sizes when combining survey results, or quantities when averaging prices paid.
Common weighted average examples
- GPA: grade points weighted by credit hours, so a four-credit course moves your average twice as much as a two-credit one.
- Average cost per share: each purchase price weighted by the number of shares bought at that price.
- Average price paid: each unit price weighted by the quantity bought at it.
- Combining survey or test results: each group’s result weighted by how many people were in that group.
- Scoring and evaluation rubrics: each criterion’s score weighted by how much that criterion matters overall.
Reading the calculation steps
The results panel shows the whole calculation, not just the answer. Step 1 multiplies each value by its weight, so you can check any single row at a glance. Step 2 adds those products together — that total is also shown as Sum of Weighted Values. Step 3 adds the weights themselves, shown as Total Weight. Step 4 divides one by the other to give the weighted average.
Simple Average is shown alongside for comparison: it ignores the weights entirely and just divides by the number of values. The gap between the two tells you how much the weighting actually moved the result.
Frequently asked questions
Is a weighted mean the same as a weighted average?
Yes. They're two names for the same calculation. "Weighted mean" is the term you'll usually see in statistics; "weighted average" is the everyday phrasing used on syllabi, in spreadsheets and in finance. Both refer to the sum of value × weight divided by the sum of the weights.
What happens if my weights don't add up to 100%?
Nothing breaks — the calculator divides by the real total rather than assuming 100. This is correct behaviour for weights like credit hours or share counts, which have no reason to total 100. If you're working from a syllabus where the weights are supposed to total 100% and they don't, check the Total Weight figure in the results: it's the quickest way to spot a missing assignment.
What values and weights can I enter?
Values can be positive, zero, negative or decimal — a −10% return or a temperature below zero is perfectly valid. Weights can be zero, positive or decimal, but not negative. A weight describes how much a value counts, so it has to be zero or more; a negative weight could push the result outside the range of your own numbers entirely.
Can a weight be zero?
Yes. A weight of zero means the value contributes nothing to the weighted average, which is a convenient way to temporarily exclude a row without deleting it. If every weight is zero there's nothing left to average, so the calculator asks you to give at least one row a weight above zero rather than dividing by zero.
When is a weighted average the wrong tool?
When your numbers compound rather than add — investment returns across several years, or growth rates period over period. Averaging those arithmetically overstates the result, so use the Geometric Mean Calculator instead. If all your values count equally, you don't need weights at all; the Average Calculator.