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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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