Weighted Average Calculator
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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.
Frequently Asked Questions
How do you calculate a weighted average?
Multiply each value by its weight, add those products up, and divide by the sum of the weights. Example: grades of 90 (weight 20), 78 (weight 30), and 85 (weight 50): (90×20 + 78×30 + 85×50) ÷ (20+30+50) = 8,390 ÷ 100 = 83.9.
How do I calculate a weighted average in Excel?
Use SUMPRODUCT divided by SUM: =SUMPRODUCT(A2:A10, B2:B10)/SUM(B2:B10), where column A holds values and column B holds weights. SUMPRODUCT does the multiply-and-add in one step. This calculator gives the same result without the spreadsheet.
What is the formula for the weighted average method?
Weighted average = Σ(value × weight) ÷ Σ(weights). In inventory accounting specifically, the 'weighted average cost method' applies this to purchases: total cost of goods available ÷ total units available, which weights each purchase price by its quantity automatically.
How do you calculate a weighted average mark?
Convert each assessment's weight from the syllabus (e.g., final 50%, midterm 30%, homework 20%), multiply each mark by its weight, and add: a 85 final, 78 midterm, 90 homework gives 0.5×85 + 0.3×78 + 0.2×90 = 83.9. If the weights already sum to 100%, no division step is needed.
Do the weights have to add up to 100?
No — the formula divides by the total weight, which normalizes any scale. Weights of 20/30/50, 2/3/5, or 0.2/0.3/0.5 all produce the identical answer. Use whatever units are natural: percentages, credit hours, quantities, or plain counts.
What's the difference between weighted and simple average?
A simple average gives every value equal influence (add them, divide by the count). A weighted average lets each value pull proportionally to its weight. They agree only when all weights are equal — and this calculator shows both, so the gap itself tells you how lopsided your weights are.
Can a weighted average be higher than the highest value?
No. With positive weights, a weighted average always lands between the minimum and maximum value — weights redistribute influence, they can't manufacture a result outside the data. If your calculation lands outside that range, a weight went in as a value or vice versa.
How is weighted average used for GPA?
GPA is a weighted average where the values are grade points (A = 4.0, B = 3.0…) and the weights are credit hours: Σ(grade points × credits) ÷ Σ(credits). That's why heavy-credit courses move a GPA fastest — a 4-credit course has four times the pull of a 1-credit one at the same grade.
Sources & References
- [1]Weisstein, E.W. Weighted mean — Wolfram MathWorld
Methodology. This calculator uses standard, peer-reviewed mathematical formulas. It is reviewed and maintained by the Vast Calculators editorial team.
Last updated · July 2026
Results are estimates for general use; verify critical figures independently.