Use the free Weighted Average Calculator below: your data never leaves your browser — all work happens on your device, and nothing is uploaded to any server.
Why Some Numbers Count More Than Others
An ordinary average treats every number equally, but life rarely does. A final exam worth 60% of your grade should count more than a quiz worth 10%. A fund that holds 80% of your money in one stock should move your portfolio more than a fund holding 5%. A weighted average handles this by multiplying each value by its weight, adding those products, and dividing by the total weight. The formula is short: weighted average = sum(value × weight) / sum(weight).
The difference from a plain average can be large. Scores of 90 and 80 average to 85 plainly. But if the 90 has weight 0.4 and the 80 has weight 0.6, the weighted average is (90 × 0.4 + 80 × 0.6) / 1 = 84. The lower score counted more, so the result sits closer to it. That pull towards the heavily weighted value is the whole idea.
How to Use This Calculator
Paste one pair per line, value first, then weight, separated by a comma or a space. For example, type “90, 0.4” on one line and “80, 0.6” on the next, then press Calculate weighted average. The tool shows every product, the sum of the products, the total weight, and the final division, plus the plain average for comparison. Seeing the plain average next to the weighted one is useful: if they differ a lot, the weights are doing a lot of work, and you should double-check them.
Weights do not have to add up to 1. They can be percentages, counts, credit hours, or money amounts. The tool divides by the actual total weight, so weights of 40 and 60 give the same answer as 0.4 and 0.6. Weights must not be negative, and their total must be above zero, or the division has no meaning.
A Worked Example: Course Grades
A course has homework worth 30%, a midterm worth 30%, and a final worth 40%. A student scores 70 on homework, 80 on the midterm, and 90 on the final. The weighted average is (70 × 0.3 + 80 × 0.3 + 90 × 0.4) / 1 = 21 + 24 + 36 = 81. The plain average would be 80, so the strong final lifts the grade by one point. Try it in the tool with three lines: “70, 0.3”, “80, 0.3”, “90, 0.4”.
Now change the final weight to 0.7 and the others to 0.15 each, keeping the same scores. The weighted average jumps to 84. Same scores, different weights, different grade. That sensitivity is why teachers publish their weightings: the weights are part of the grading policy, not a detail.
Where Weighted Averages Appear
Grade point averages weight courses by credit hours. Stock indices weight companies by market value. Consumer price indices weight goods by how much households actually buy. Sports ratings weight recent games more than old ones. In each case the weights encode a judgement about importance, and the weighted average is the honest way to combine numbers that do not deserve equal say.
One famous special case is the weighted average of a data set where the weights are counts. If 30 students score 70 and 10 students score 90, the class average is (30 × 70 + 10 × 90) / 40 = 75. That is just a weighted average with weights 30 and 10, and it is how group averages are combined without access to every individual score.
Common Mistakes
The most common mistake is forgetting to divide by the total weight, especially when weights do not sum to 1. Adding the products alone gives a number on the wrong scale. Another mistake is using weights that sum to 100 but entering them as 40 and 60 while also dividing by 100 again, which double-counts the scaling. The tool divides by the actual total, so enter weights as they are and let it handle the division.
A subtler mistake is choosing weights that hide a weak result. If a low score gets a tiny weight, the average barely moves, which may be the intent or may be manipulation. Always ask who chose the weights and why before trusting a weighted average someone else computed.
Try It Yourself
Compute your own course grade, your portfolio return from two holdings, or a restaurant rating where food counts double. Compare each weighted result with the plain average. The gap between them tells you how much the weights matter, and that gap is the most useful number on the screen after the answer itself.
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