Weighted Average Calculator
Compute a weighted mean from lines of value,weight pairs, with total weight, the difference from a simple average and a worked example that gives 87.25.
Results
Weighted average
- Total weight
- 12
You might also need
Educational estimates · not financial advice · free, no signup
Formula / how it works
Weighted average = Σ(value × weight) ÷ Σ(weight). With equal weights this reduces to the ordinary mean.
Detailed guide
What it is, how to use it, how to read the numbers, common mistakes, a worked example, formulas, and FAQs.
What this calculator is
A weighted average gives more influence to some values than others. Instead of treating every number equally, each value is multiplied by its weight, the products are added and the total is divided by the sum of the weights. It is the right tool whenever the importance, size or frequency of items differs. Typical uses include course grades with different credit weights, portfolio returns weighted by position size, average prices weighted by quantity and survey scores weighted by group size. Enter one value,weight pair per line. The weights do not need to sum to 100 or 1 because the calculation divides by the total weight.
When to use / who it helps
- You are calculating an overall grade from items with different weights.
- You need an average price across purchases of different quantities.
- You are averaging scores across groups of different sizes.
- You are computing a portfolio's weighted return.
- You want to see how weights change the result.
How to use
Steps
- Enter one value,weight pair per line.
- Use positive weights.
- Read the weighted average.
- Read the total weight.
- Compare with the simple average of the values.
- Convert percentages to the same scale first.
How to interpret results
- The result lies between the smallest and largest values.
- Larger weights pull the average toward their values.
- Equal weights give the simple mean.
- Total weight is shown for checking.
- Weights need not sum to 1 or 100.
Common mistakes & gotchas
- Averaging the values without weights.
- Swapping value and weight in a pair.
- Using percentage weights that do not apply to the same base.
- Entering negative weights.
- Forgetting to include every item.
Worked example
Worked example — four scores with weights 3, 4, 2, 3
- Products: 85 × 3 = 255, 90 × 4 = 360, 78 × 2 = 156, 92 × 3 = 276.
- Sum of products: 255 + 360 + 156 + 276 = 1,047.
- Total weight: 3 + 4 + 2 + 3 = 12.
- Weighted average: 1,047 ÷ 12 = 87.25. The simple average (85 + 90 + 78 + 92) ÷ 4 = 86.25, a full point lower.
Result: The weighted average is 87.25 with a total weight of 12.
To load the form's own demo values, tap Try example above the Calculate button.
How to calculate / formula
Weighted average = Σ(value × weight) ÷ Σ(weight). With equal weights this reduces to the ordinary mean.
Frequently asked questions
What is a weighted average?
An average where each value counts in proportion to its weight.
How do I calculate a weighted average?
Multiply each value by its weight, add the products and divide by the sum of weights.
Do weights have to add up to 100?
No.
How does it differ from the simple average?
A simple average gives every value equal weight.
Where is it used?
Grades, portfolio returns, average prices and survey data.
Can weights be zero?
Yes, but the value then has no influence.