Weighted Average Calculator
Calculate the weighted mean from up to 10 values and their weights.
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How to Calculate a Weighted Average
A weighted average (or weighted mean) gives different values different levels of importance. Unlike a simple average where all values contribute equally, a weighted average multiplies each value by its weight before summing, then divides by the total weight.
The Weighted Average Formula
Weighted Average = (v₁×w₁ + v₂×w₂ + ... + vₙ×wₙ) / (w₁ + w₂ + ... + wₙ)
Where vᵢ are the values and wᵢ are the corresponding weights. The weights do not need to sum to 1 or 100 — they can be any positive numbers that represent relative importance.
Common Applications
GPA calculation: A 3-credit A (4.0) and a 4-credit B (3.0) have a weighted GPA of (4.0×3 + 3.0×4)/(3+4) = (12+12)/7 = 3.43, not the simple average of 3.5. Course credits are the weights.
Investment portfolio returns: Different positions have different sizes (weights). A $10,000 position returning 10% and a $40,000 position returning 5% give a weighted return of ($1,000+$2,000)/$50,000 = 6%, not the simple average of 7.5%.
Grade calculations: Exams worth 60% of the grade and homework worth 40% require weighting the scores accordingly.
Weights as Percentages
When weights are percentages that sum to 100%, the formula simplifies to just the sum of (value × weight/100). This is common in grading rubrics where each component has a defined percentage contribution to the final grade.
Worked Example: Course Grade Calculation
A course has three graded components. Homework is worth 20% and a student scored 88. Midterm is worth 30% and the student scored 75. Final exam is worth 50% and the student scored 82. Weighted grade = (88×20 + 75×30 + 82×50) / (20+30+50) = (1760 + 2250 + 4100) / 100 = 8110 / 100 = 81.1. The simple average would be (88+75+82)/3 = 81.67 — close here, but they diverge significantly when weights are unequal.
| Component | Score | Weight | Score × Weight |
|---|---|---|---|
| Homework | 88 | 20% | 1,760 |
| Midterm | 75 | 30% | 2,250 |
| Final Exam | 82 | 50% | 4,100 |
| Total | — | 100% | 8,110 → 81.1 |
Frequently Asked Questions
A simple average treats all values equally. A weighted average gives some values more influence based on their weight. Use weighted average when items differ in importance, size, or frequency.
Multiply each grade (grade points) by the course credit hours, sum the products, then divide by total credit hours. A (4.0) in a 3-credit class + B (3.0) in a 4-credit class = (12+12)/7 = 3.43 GPA.
No. Weights can be any positive numbers representing relative importance. The formula divides by the sum of all weights, so the scale doesn't matter.
Use weighted average when data points have different levels of importance, different sample sizes, or different frequencies. Examples: GPA (credits as weights), stock portfolio returns (position sizes as weights), survey results (sample sizes as weights).
If all weights are the same, the weighted average equals the simple arithmetic mean. Equal weights mean each value contributes the same amount.
Market-cap-weighted indices like the S&P 500 weight each company by its market capitalization. A company worth $2 trillion influences the index more than a company worth $10 billion. The index return is the weighted average of individual stock returns, weighted by their market caps.
No. A weighted average always falls between the minimum and maximum input values. It is a weighted mean — it represents a central tendency, not a value outside the input range. If your result seems too high or low, check that weights are entered correctly.