How this calculator works
A weighted average gives some values more influence over the result than others, unlike a plain average which treats every value equally. It's the right tool whenever some inputs matter more than others: a final exam usually counts for more of a course grade than a weekly quiz, and a large investment position moves a portfolio's return more than a small one.
Enter your values and their matching weights in the same order — for example, exam scores in one list and their percentage weights in the other. The weights don't need to add up to 1 or 100; the calculator normalizes them automatically by dividing by their total.
The formula
Weighted average = (Σ value × weight) ÷ (Σ weight)When every weight is equal, this formula reduces exactly to the plain arithmetic mean — a useful way to check that the weights are set up correctly.
Worked example: course grade weighting
- Exam: 90, weighted 50%. Midterm: 80, weighted 30%. Homework: 70, weighted 20%.
- Multiply each score by its weight: 90 × 0.5 = 45, 80 × 0.3 = 24, 70 × 0.2 = 14.
- Add the weighted scores: 45 + 24 + 14 = 83. Add the weights: 0.5 + 0.3 + 0.2 = 1.
- Divide: 83 ÷ 1 = 83 — the final course grade, three points above the plain average of 80.
Frequently asked questions
Do the weights need to add up to 100% or 1?
No. This calculator divides by the total weight automatically, so entering 5, 3, 2 gives the same result as entering 50%, 30%, 20% — both normalize to the same proportions.
What happens if I enter a different number of values than weights?
The calculation can't pair them up correctly, so the calculator won't return a result until both lists have the same number of entries, in matching order.
How is this different from a simple average?
A simple average treats every value as equally important. A weighted average lets some values count more — useful whenever the underlying quantities aren't of equal size or importance, like exam categories or portfolio holdings of different sizes.
Can weights be zero?
Yes for an individual item — it simply contributes nothing to the result. But the total of all weights can't be zero, since that would mean dividing by zero.
Can the weighted average be higher than the highest individual value?
No — as long as every weight is zero or positive, a weighted average always falls somewhere between the lowest and highest value in the list, just like a simple average. In this page's own course-grade example, the weighted average of 83 sits between the lowest score (70) and the highest score (90), never above or below either one.