80, 90, 100 with weights 20, 30, 50
Weighted average = Σ(value × weight) ÷ Σweight
The weighted sum is 80 × 20 + 90 × 30 + 100 × 50 = 9,300. The total weight is 100, so the average is 9,300 ÷ 100 = 93.
Statistics
Weighted Average Calculator
Find an average when some values count more than others.
Enter values and their weights
Weighted average
Enter each value and its weight, then select Calculate.
- Total weight
- Weighted sum
| Row: value × weight | Normalized weight | Contribution to mean |
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Your values and weights are calculated in your browser. Only successful calculations are added to this tab's recent history.
Formula and worked examples
The same values with weights 2, 3, 5
(80 × 2 + 90 × 3 + 100 × 5) ÷ 10
The weighted sum is now 930 and the total weight is 10. The average is still 93. Scaling every weight by the same positive factor does not change the answer.
Group means 10 and 20, with 2 and 3 items
(10 × 2 + 20 × 3) ÷ (2 + 3)
Use group sizes as weights when the values are means of comparable items. The combined mean is 80 ÷ 5 = 16. Taking an unweighted average of the two means would give 15.
Normalization, contributions, and rounding
For each row, multiply the value by its weight. Add these products to get the weighted sum, then divide by the total weight. The calculator does not assume the weights sum to 1 or 100.
A row's normalized share is weight ÷ total weight × 100%. Its contribution to the mean is value × weight ÷ total weight. In the first example, the shares are 20%, 30%, and 50%, and the contributions are 16, 27, and 50. Those contributions add up to 93.
Products and sums are kept exact within the input limits using 100 significant digits internally. Display rounding uses the exact weighted sum and total weight, rather than an already rounded average. Choose any number of decimal places from 0 through 10; the default is 2. Exact halfway values round away from zero, so 1.005 becomes 1.01 and −1.005 becomes −1.01 at two places.
The ≈ mark identifies a rounded display. Each share and contribution is rounded independently, so the displayed shares may not total exactly 100%, and displayed contributions may not sum exactly to the displayed mean. The average has the same unit as the values you entered.
For the weighted mean formula and examples, see The Open University: Weighted means. For the sum of weighted products, see NIST: Weighted sum.
Common questions
Do the weights need to add up to 100?
No. The calculator always divides by the entered total weight. Weights 20, 30, 50 have the same proportions as 2, 3, 5 or 0.2, 0.3, 0.5. Keep the same basis throughout: mixing 20 with 0.3 would give different proportions.
What if some weights are zero?
A zero-weight row contributes nothing to the weighted sum and has no effect on the average. Its value must still be a valid number, so typing errors are not silently ignored. You can remove an unused row instead, while keeping at least two rows. If every weight is zero, the average is undefined and the calculator shows an error.
Can I use negative values or negative weights?
Negative values and zero values are accepted. Weights must be nonnegative, with at least one positive weight. With these rules, the weighted mean stays between the smallest and largest values that have positive weights.
Can this calculate a course average?
It can combine scores that are already on the same scale with their relative weights. It does not convert scores with different maximum marks, apply letter-grade rules, or infer missing work. If you enter only completed items, it normalizes over those items' weights. It does not automatically treat missing items as zero.
How is this different from an ordinary average?
An ordinary arithmetic mean gives each entry equal weight. Here, a row with weight 3 counts three times as much as a row with weight 1. Setting every weight to the same positive number produces the ordinary mean.
Can I average rates or percentages this way?
Only when the weights match what those values represent. To combine group percentages, for example, use the underlying group sizes when appropriate. An average of speeds may need time weights or another formula, depending on the question. The calculator applies the weights you enter; it cannot choose the correct weighting basis for you.