The weighted average formula
A weighted average answers one question: what's the typical value, once you account for the fact that some entries matter more than others? The formula isΣ(value × weight) ÷ Σ(weight) — multiply each value by its weight, add everything up, and divide by the total weight. With the defaults above: 90 × 50 + 80 × 30 + 85 × 20 = 4500 + 2400 + 1700 = 8600, and 8600 ÷ 100 gives a weighted average of 86 — noticeably closer to 90 than the simple average of 85, because 90 carries half the total weight.
Where weighted averages show up
| Use case | Values | Weights |
|---|---|---|
| Course grade | Category scores | Syllabus percentages |
| GPA | Grade points per class | Credit hours |
| Average purchase price | Price per lot | Shares or units bought |
| Survey results | Group means | Group sizes |
| Blended interest rate | Rate per loan | Loan balances |
The pattern is always the same: whenever the things being averaged represent different amounts of stuff — different shares of a course, different numbers of people, different dollar balances — weight by the amount of stuff. Averaging the raw numbers without weights treats a 1-credit lab like a 4-credit lecture, which is how GPA math most often goes wrong.
Reading the two averages this tool shows
The result panel shows both the weighted and the simple average, because the gap between them is informative. If they're nearly equal, your weights are close to uniform and don't change much. If they diverge, the heavily-weighted rows are pulling the result their way — and if that surprises you, check whether a weight is entered wrong. A classic error is typing a weight of 100 instead of 10, which silently drags the average toward one row.
Weights don't need to sum to 100 or to any particular number. Credit hours summing to 15, percentages summing to 100, and ratios like 5 : 3 : 2 all produce identical results as long as each row's weight is in the same unit. What you can't do is mix units — weighting two rows by percent and one by points makes the result meaningless.
Frequently asked questions
How do you calculate a weighted average?
Multiply each value by its weight, add the products, and divide by the sum of the weights. Example: grades of 90, 80 and 85 with weights 50, 30 and 20 → (90×50 + 80×30 + 85×20) ÷ 100 = 86.9.
Do the weights have to add up to 100?
No. Because the formula divides by the sum of the weights, any consistent units work — percentages, credit hours, points or counts. Weights of 5, 3, 2 give the same result as 50, 30, 20.
When should I use a weighted average instead of a regular average?
Whenever the items don't count equally: course categories with different weights, classes with different credit hours, survey responses with different group sizes, or prices with different purchase quantities. A regular average is just a weighted average where every weight is 1.
Why is my weighted average closer to one value than the others?
The average is pulled toward the values carrying the most weight. With weights of 50/30/20, the first value contributes half of the result by itself — that's the entire point of weighting.