Weighted Average Calculator
Calculate the weighted average of a set of values and their corresponding weights. Useful for grade calculations, financial analysis, and statistical measurements where not all data points contribute equally.
How to Use This Weighted Average Calculator
Follow these simple steps to calculate a weighted average:
- Enter each value and its corresponding weight in the row fields.
- Click "Add Row" to add more value-weight pairs, or click the X button to remove a row.
- Click the "Calculate" button to compute the weighted average.
- Compare the weighted average with the simple (unweighted) average in the results.
Weighted Average Formula
The weighted average is calculated by multiplying each value by its weight, summing those products, and dividing by the sum of all weights:
The simple average treats all weights equally (each weight = 1):
The difference shows how much the weighting changes the result compared to a simple average.
Examples
Homework: 95 (weight 30%), Midterm: 85 (weight 30%), Final: 78 (weight 40%)
Weighted Avg = (95×0.30 + 85×0.30 + 78×0.40) / (0.30+0.30+0.40)
= (28.5 + 25.5 + 31.2) / 1.0 = 85.2
Stock A returned 12% (invested $5000), Stock B returned 6% (invested $15000):
Weighted Avg = (12×5000 + 6×15000) / (5000+15000)
= (60000 + 90000) / 20000 = 7.5%
Values: 100 (weight 1), 50 (weight 4)
Weighted Avg = (100×1 + 50×4) / 5 = 300/5 = 60
Simple Avg = (100 + 50) / 2 = 75
Difference = 75 - 60 = 15
Frequently Asked Questions
What is a weighted average?
A weighted average is a type of average where each value contributes proportionally to the final result based on its assigned weight. Unlike a simple average where every value counts equally, a weighted average gives more importance to values with higher weights. It is widely used in grading systems, portfolio analysis, and survey data.
When should I use a weighted average instead of a simple average?
Use a weighted average when different data points have different levels of importance or frequency. For example, in a college course, the final exam might count for 40% while homework counts for 20%. In finance, you would weight returns by the amount invested in each asset. A simple average is appropriate only when all data points are equally significant.
How do I calculate a weighted grade?
To calculate a weighted grade: (1) Multiply each grade by its weight (as a decimal). (2) Sum all the weighted scores. (3) Divide by the sum of all weights. For example, if your quiz score is 90 with weight 0.2 and exam score is 80 with weight 0.8: weighted grade = (90×0.2 + 80×0.8) / (0.2+0.8) = 82.
Can weights be negative or zero?
Mathematically, zero weights are allowed (that value is simply excluded), but negative weights are unusual and can produce misleading results. In most real-world applications, weights represent proportions, counts, or importance and should be non-negative. Our calculator requires weights to be zero or greater.