Weighted Average Calculator
Calculate the weighted average (weighted mean) of values with different weights.
Useful for grades, investments, and surveys.
A weighted average is a mean calculated by giving different values different levels of importance (weights). Unlike a simple average where all values contribute equally, a weighted average reflects the fact that some data points matter more than others.
Core formula: Weighted Average = Σ(Value × Weight) ÷ Σ(Weights)
Or expanded: WA = (V₁×W₁ + V₂×W₂ + V₃×W₃ + … + Vₙ×Wₙ) ÷ (W₁ + W₂ + W₃ + … + Wₙ)
If weights already sum to 1 (or 100%): WA = Σ(Value × Weight Fraction)
What each variable means:
- Value (Vᵢ) — the individual data points (grades, prices, measurements, etc.).
- Weight (Wᵢ) — the relative importance or contribution of each value. Weights can be any positive numbers — they do not need to sum to 1 or 100 before the calculation.
- Σ(Weights) — the sum of all weights used as the denominator to normalize the result.
Common real-world applications:
| Application | Values | Weights |
|---|---|---|
| GPA calculation | Course grades | Credit hours per course |
| Investment portfolio return | Asset returns | Dollar amount in each asset |
| Exam final grade | Quiz, midterm, final scores | % contribution each carries |
| Average purchase price (cost basis) | Price per unit bought | Units bought at each price |
| Weather forecast | Daily temperature readings | Recency (recent = higher weight) |
Worked example 1 — Final Course Grade: A student has these scores and weights:
- Homework: 82/100 → 20% weight
- Midterm: 74/100 → 30% weight
- Final Exam: 91/100 → 50% weight
Weighted Average = (82 × 0.20) + (74 × 0.30) + (91 × 0.50) = 16.4 + 22.2 + 45.5 = 84.1 (Final grade: 84.1%)
Simple average (incorrect): (82 + 74 + 91) ÷ 3 = 82.3 — understates the final exam importance.
Worked example 2 — Portfolio Return:
- Stock A: 12% return, $15,000 invested
- Stock B: −3% return, $5,000 invested
- Stock C: 8% return, $30,000 invested
WA return = (0.12×15,000 + (−0.03)×5,000 + 0.08×30,000) ÷ 50,000 = (1,800 − 150 + 2,400) ÷ 50,000 = 4,050 ÷ 50,000 = 8.1% portfolio return
Simple average: (12 − 3 + 8) ÷ 3 = 5.67% — significantly misleading because it ignores allocation sizes.