What Is a Weighted Average?
A weighted average (or weighted mean) is an average in which each value contributes according to its assigned weight, rather than every value counting equally. It is widely used to compute course grades, portfolio returns, average prices, survey scores, and any situation where some data points matter more than others.
How to Use This Calculator
Enter your data values in the first box, separated by commas (for example 80, 90, 70). Then enter the matching weights in the second box in the same order (for example 2, 3, 1). The calculator pairs each value with its weight, multiplies them, sums the products, and divides by the total of the weights. If you supply unequal counts, only the overlapping pairs are used.
The Formula Explained
The weighted average is defined as $$\bar{x}_w = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i} = \frac{\sum \text{Weights} \times \text{Values}}{\sum \text{Weights}}$$ Each value \(x_i\) is multiplied by its weight \(w_i\); these products are added together to form the numerator. The denominator is simply the sum of all weights. Dividing one by the other yields a single representative number that respects the relative importance of each value. If every weight is identical, the result collapses to the ordinary arithmetic mean.
Worked Example
Suppose a student scores 80, 90, and 70 on three assessments worth 2, 3, and 1 credit respectively. The numerator is $$(2\times80) + (3\times90) + (1\times70) = 160 + 270 + 70 = 500$$ The sum of weights is \(2 + 3 + 1 = 6\). The weighted average is \(500 / 6 \approx 83.33\), which is higher than the plain average of 80 because the highest score carried the most weight.
FAQ
What if my weights do not add up to 1 or 100? That is fine — the formula divides by the total of the weights, so weights can be any positive numbers and need not be normalized.
Can I use this for GPA? Yes. Use grade points as values and credit hours as weights to get your grade point average.
What happens if all weights are zero? The denominator would be zero, so no meaningful average exists; the calculator returns 0 to avoid dividing by zero.
