Weighted Average Calculator
Mean with per value weights plus plain mean for contrast.
What it does
Weighted averages give some values louder voices than others: finals count more than quizzes, expensive holdings move portfolios more than small ones. Each value multiplies by its weight before the total divides by all weights.
The tool above takes two matching lists: values with weights. It returns the weighted mean with the plain mean beside it for contrast, plus the total weight.
The default grades 90, 80, 70 at weights 0.3, 0.5, 0.2 read 27 + 40 + 14 = 81 against a plain mean of 80. The middle grade dominates through its half weight.
Definitions follow Khan Academy average units with the same weight normalization in LibreTexts math references. Both divide by the weight sum, so weights need no pre scaling to percentages.
How to use
- Type the values with commas or spaces.
- Type exactly as many weights in the same order.
- Read weighted mean first for the real answer.
- Compare plain mean to see the weight effect.
- Rescale weights freely; only shares matter.
Formula
- value x weight
- Each contribution scaled by importance.
- sum weights
- Normalizer, any scale works.
- plain
- Equal voice baseline for contrast.
Weights cannot go negative and must add above zero. Counts must match exactly or the page refuses instead of pairing wrongly.
Worked example
Example: 90, 80, 70 at 0.3, 0.5, 0.2
Defaults: values 90, 80, 70; weights 0.3, 0.5, 0.2.
- Products: 90x0.3 = 27, 80x0.5 = 40, 70x0.2 = 14.
- Sum: 27 + 40 + 14 = 81. Weights add to 1.
- Weighted: 81 / 1 = 81.
- Plain: (90+80+70)/3 = 80.
- Tool shows 81, 80, total weight 1.
Reference table
| Weights | Weighted | Plain |
|---|---|---|
| Equal thirds | 80 | 80 |
| 0.3, 0.5, 0.2 | 81 | 80 |
| 0.5, 0.3, 0.2 | 83 | 80 |
| 0, 0, 1 | 70 | 80 |
Limits
- Weights model importance, not accuracy.
- Negative weights rejected outright.
- Lists cap at 50 pairs.
- Outliers still pull through heavy weights.
Common mistakes
- Mismatching value and weight order.
- Forgetting to divide by weight sum.
- Normalizing weights to 100 first unnecessarily.
- Averaging the weights themselves into grades.
- Using plain mean where weights apply.
Try it yourself
Quick checks. Answers sit tucked under each question.
100, 50 at 1, 1?
Weighted 75, plain 75, weight 2.
90, 70 at 3, 1?
(270+70)/4 = 85.
Weights 30, 50, 20 instead?
Same 81: shares match 0.3, 0.5, 0.2.
Questions
How do you calculate weighted average?
Sum of value times weight over sum of weights: 81 here.
Must weights add to 100?
No. Division normalizes any scale; 30/50/20 matches 0.3/0.5/0.2.
Weighted vs plain mean?
Weighted voices values unequally; plain voices all alike.
Can weights be zero?
Yes for ignored values, but the total must stay above zero.
Negative weights?
Rejected here; they model offsets needing different math.
Where is this used?
Grades, portfolios, GPA credits, shipping blends, survey scores.