What Is a Weighted Average?
A weighted average (also called the weighted arithmetic mean) is a type of average where each value contributes to the final result proportionally to its assigned weight. In a regular (unweighted) average every value counts equally — but in real life some values matter more than others.
Weighted Average Formula
Given n values x₁, x₂, …, xₙ with corresponding weights w₁, w₂, …, wₙ:
x̄ = (x₁·w₁ + x₂·w₂ + … + xₙ·wₙ) / (w₁ + w₂ + … + wₙ) = Σ(xᵢ · wᵢ) / Σwᵢ
If all weights are equal, the weighted average equals the plain arithmetic mean.
Weighted Average vs. Arithmetic Mean
The arithmetic mean treats every data point equally. The weighted mean lets you say "this value is twice as important" by assigning it a weight of 2 instead of 1. Typical use cases:
- GPA / Academic grades — a final exam worth 40% of your grade vs. a quiz worth 10%.
- Financial portfolio — stocks with different amounts invested.
- Survey results — responses from demographic groups of different sizes.
- Manufacturing quality — defect rates across production batches of different sizes.
- Physics & engineering — center of mass, average density, mean free path.
How to Use This Calculator
- Choose the number of items (2 – 10).
- Select the unit type: plain numbers, percentage, any of 13 world currencies (USD, RUB, EUR, GBP, JPY, CNY, CAD, AUD, CHF, BRL, INR, MXN, KRW), metric length/mass/volume, or US imperial length/mass/volume.
- Enter an optional label for each row (e.g., "Exam", "Quiz", "Homework").
- Enter the value and weight for each item.
- Click Calculate.
The calculator shows the weighted mean, the arithmetic mean for comparison, total weight, the full formula, and a per-item breakdown table with weight percentages.
Example: Weighted GPA
| Subject | Grade (0–4) | Credit hours |
|---|---|---|
| Mathematics | 3.7 | 4 |
| History | 3.3 | 3 |
| Physics | 4.0 | 4 |
| English | 3.0 | 2 |
Weighted GPA = (3.7×4 + 3.3×3 + 4.0×4 + 3.0×2) / (4+3+4+2) = (14.8+9.9+16.0+6.0) / 13 = 46.7 / 13 ≈ 3.592
Arithmetic mean = (3.7+3.3+4.0+3.0) / 4 = 3.500 — a difference of 0.092 points.
Different Types of Averages
- Arithmetic mean — sum divided by count. Most common average.
- Weighted mean — each value multiplied by its weight before summing.
- Geometric mean — nth root of the product of n values. Used for growth rates.
- Harmonic mean — reciprocal of the arithmetic mean of reciprocals. Used for rates (speed, price-to-earnings ratios).
Measurement Systems Supported
This calculator supports both the metric system (mm, cm, m, km, g, kg, mL, L) and the US customary (imperial) system (in, ft, yd, mi, oz, lb, fl oz, gal), as well as 13 major world currencies.
Frequently Asked Questions
- Can weights be decimals?
- Yes. Weights can be any positive number — integers (1, 2, 3), percentages (0.40, 0.30), credit hours (4.5), or any other positive value.
- Do weights need to sum to 1 or 100?
- No. The calculator automatically normalizes weights by dividing by their sum. You can use any positive values.
- Can values be negative?
- Yes. The calculator handles negative values (e.g., temperature in Celsius, financial losses).
- What is the weighted average used for in high school GPA?
- In the US, weighted GPA accounts for course difficulty. Honors or AP courses get extra weight (e.g., a 4.0 scale becomes a 5.0 scale), so an "A" in an AP class adds more to the GPA than an "A" in a standard class.