Weighted Average CalculatorFree online math calculator — instant results, no sign-up
Calculate an average using nonnegative weights.
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About the Weighted Average Calculator
The Weighted Average Calculator combines a list of values using nonnegative weights that determine each value’s influence on the result. It pairs entries in Values with entries in Paired values or weights by position, then divides the sum of their products by the total weight. With the default inputs, the weighted average is 7.3333333333.
- Values
- Enter the observations to average, such as the default 2, 4, 6, 8, 10, all expressed in the same units or all unitless.
- Paired values or weights
- Enter a nonnegative weight for each corresponding value, such as the default 1, 2, 3, 4, 5, using unitless relative weights or consistently expressed quantities such as counts.
Formula and method
x̄_w = (Σᵢ₌₁ⁿ wᵢxᵢ) / (Σᵢ₌₁ⁿ wᵢ); with the defaults: (1×2 + 2×4 + 3×6 + 4×8 + 5×10) / (1+2+3+4+5) = 110/15 ≈ 7.3333333333.
- x̄_wThe weighted average, expressed in the same units as the input values.
- xᵢThe value at position i in the Values list.
- wᵢThe nonnegative weight paired with xᵢ.
- iThe position of a value–weight pair in the lists.
- nThe number of value–weight pairs.
- ΣSummation over all pairs from position 1 through n.
Pair each value with the weight at the same position, multiply each pair, and add the products. Separately add the weights, then divide the product total by the weight total. For the default inputs, the products are 2, 8, 18, 32, and 50, totaling 110; the weights total 15, so the result is 110/15, displayed as 7.3333333333.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Values2, 4, 6, 8, 10
- Paired values or weights1, 2, 3, 4, 5
Results
- Weighted average7.3333333333
How to use the Weighted Average Calculator
- 1Enter 2, 4, 6, 8, 10 in Values to reproduce the default example, or enter your own observations.
- 2Enter 1, 2, 3, 4, 5 in Paired values or weights for the default example, keeping each weight aligned with its intended value.
- 3Check that both lists contain the same number of entries, every weight is nonnegative, and at least one weight is positive.
- 4Run the calculation to divide the sum of value–weight products by the total weight.
- 5Read the Weighted average output; the default inputs produce 7.3333333333 in the same units as the values.
Reading your result
The Weighted average row reports the average after accounting for each value’s assigned influence. For the default inputs, 7.3333333333 is greater than the unweighted average of 6 because the larger values receive larger weights. The result is in the same units as Values; it is not the sum of the weighted products or the total weight.
Limitations
The lists must have equal lengths and contain finite numeric entries. Weights must be nonnegative, and their total must be positive; all-zero weights make the average undefined. A zero-weight value has no influence on the result. Values must represent comparable quantities in consistent units, and the weights must meaningfully express their intended influence. The calculator does not assess whether the chosen weights are appropriate or report uncertainty or spread. Displayed decimals may be rounded.
Common questions
Do the weights need to add up to 1 or 100?+
No. The calculator divides by the total weight automatically. The default weights 1, 2, 3, 4, 5 total 15 and are valid without normalization.
Why is the default result 7.3333333333 rather than 6?+
The ordinary average gives each value equal influence and is 6. Here, the weights increase with the values, so larger observations contribute more: the weighted products total 110, and dividing by the total weight of 15 gives approximately 7.3333333333.
Can I use zero or negative weights?+
Zero weights are allowed and exclude their paired values from influencing the average, provided at least one other weight is positive. Negative weights are not allowed for this calculator.
Does the order of the two lists matter?+
Yes: entries are paired by position, so the defaults pair 2 with 1, 4 with 2, 6 with 3, 8 with 4, and 10 with 5. Reordering complete pairs leaves the result unchanged, but reordering just one list can change it.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
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Results are estimates for informational purposes and are not financial, medical or legal advice.