About the Weighted Average Calculator
A simple average pretends every number matters equally. Reality rarely works that way: your final exam counts 50% of the course, the homework 20%; the big warehouse order dominates your average unit cost; the large survey group outweighs the small one. A weighted average fixes this by letting each value pull on the result in proportion to its importance.
This calculator takes any number of value-weight pairs — grades and their percentages, prices and their quantities, scores and their credits — and returns the weighted mean, alongside the simple average so you can see exactly what the weighting changed.
Just need the plain mean, median, and mode? That's our Average Calculator.
The Weighted Average Formula
One line, universally applicable:
Weighted Average = (v₁×w₁ + v₂×w₂ + … + vₙ×wₙ) ÷ (w₁ + w₂ + … + wₙ)
Two properties worth knowing: if all weights are equal, this collapses to the simple average — and weights don't need to sum to 100 or 1, because the division normalizes them. Grade weights of 20/30/50 and 2/3/5 give the identical answer.
Worked Example: A Course Grade
A typical syllabus weighting, computed step by step:
| Component | Score | Weight | Score × Weight |
|---|---|---|---|
| Homework | 90 | 20% | 18.0 |
| Midterm exam | 78 | 30% | 23.4 |
| Final exam | 85 | 50% | 42.5 |
| Total | — | 100% | 83.9 |
Weighted average: 83.9 — versus a simple average of 84.3. Small gap here, but shift the final-exam score to 70 and the weighted grade drops to 76.4 while the simple average only falls to 79.3: the 50% weight makes the final worth 2.5 homework units per point. That's the number to know before exam week.
Where Weighted Averages Appear
The same formula under different names:
- Course grades — components weighted by syllabus percentages.
- GPA — grade points weighted by credit hours (a 4-credit A moves you 4× a 1-credit A).
- Inventory cost — unit prices weighted by quantities purchased (the accountant's 'weighted average cost method').
- Stock portfolios — returns weighted by position sizes.
- Survey data — responses weighted to match population demographics.
- GPS and sensors — readings weighted by their reliability.
The pattern in every case: when observations differ in importance, size, or reliability, the weighted mean is the honest summary and the simple mean is a distortion.