Weighted Average Calculator
Calculate a weighted average of values and their weights, with the sum of weights and the unweighted mean for comparison.
Your inputs
Results
Weighted average
82
- Sum of weights
- 1
- Unweighted average (for comparison)
- 80
✓Exact calculation — rounded only for display
What this calculator does
When some values matter more than others — grades, portfolio returns, prices by quantity — a weighted average reflects their importance.
Formula and method
Weighted average = Σ(xᵢ × wᵢ) ÷ Σwᵢ
Worked example
Calculated by this tool with its default inputs:
Inputs
- Values: 80, 90, 70
- Weights (same count as values): 0.2, 0.5, 0.3
Results
- Weighted average: 82
- Sum of weights: 1
- Unweighted average (for comparison): 80
How to read the results
Weights need not add up to 1; they are normalised automatically.
Assumptions and limitations
- Values and weights must be listed in the same order.
Questions
Can a weight be zero?
Yes, that value is ignored, but at least one weight must be positive.
Methodology and verification
- Result type
- Exact mathematical calculation (rounded only for display)
- Formula version
- 1.0
- Automated verification
- 4 reference and validation test cases, checked against independently computed values. The site cannot be built if any of them fail.
- Editorial review
- Awaiting human editorial review. The explanation was drafted with AI assistance; the formula and examples are verified by the automated tests above.
Privacy
Everything you enter is calculated in this browser and is not sent to Numerith or anyone else. Inputs are added to a share link only if you choose to include them. Privacy policy