Give each value the influence it should have

Weights can be credits, percentages, shares, units, importance scores, or portfolio allocations. Only the ratios between weights matter unless the total weight has real-world meaning.

Calculate a weighted average

Enter each value and its weight.
Multiply each pair.
Sum the weighted products.
Sum the weights.
Divide weighted total by total weight.
Inspect total weight before trusting interpretation.

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Weighted average formulas

The weighted average is a weighted total divided by total weight.

General

weighted average = \frac{\sum_{i}^{n} x_{i} w_{i}}{\sum_{i}^{n} w_{i}}

Grades and credits

course average = \frac{\sum_{i}^{n} g_{i} c_{i}}{\sum_{i}^{n} c_{i}}

Portfolio allocations

weighted return = \frac{\sum_{i}^{n} r_{i} a_{i}}{\sum_{i}^{n} a_{i}}

Signed weights

W = \sum_{i}^{n} w_{i}, W \neq 0

Edge cases

Zero weights exclude rows from the average.
Negative weights are signed contributions, not ordinary importance.
A total weight of 0 makes the result undefined.
Weights do not need to sum to 1 or 100.

FAQ

Do weights need to add to 100?

No. The calculator divides by the total weight, so weights like 1, 2, 3 and 10, 20, 30 describe the same influence pattern.

Can I use zero or negative weights?

A zero weight removes that row from the average. Negative weights can model signed exposure, corrections, or short positions, but they change the meaning of the result and are undefined if total weight is zero.

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