Weighted Average Calculator

What is a weighted average?

A weighted average (or weighted mean) is an average where some values count more than others. Each value is multiplied by a weight that reflects its importance, frequency, or share of the total.

Weighted average formula

For values $x_1, x_2, \dots, x_n$ with corresponding weights $w_1, w_2, \dots, w_n$:

\[ \bar{x}_w = \frac{\sum_{i=1}^{n} w_i x_i}{\sum_{i=1}^{n} w_i} \]

If the weights are percentages that already sum to 100%, the denominator is 100 instead of $\sum w_i$.

How to calculate weighted average (step-by-step)

List your values $x_1, x_2, \dots, x_n$ (e.g., grades, prices, returns).
Assign a weight $w_i$ to each value (credits, shares, frequency, or %).
Multiply each value by its weight: $w_i x_i$.
Add up all the weighted values: $\sum w_i x_i$.
Add up all the weights: $\sum w_i$.
Divide the weighted sum by the sum of weights: $\bar{x}_w = \dfrac{\sum w_i x_i}{\sum w_i}$.

Example 1 – Weighted average grade

Suppose your course grade is based on:

Homework: 80% with weight 20%
Midterm: 75% with weight 30%
Final exam: 90% with weight 50%

Convert weights to decimals: 0.20, 0.30, 0.50.

\[ \bar{x}_w = 0.20 \cdot 80 + 0.30 \cdot 75 + 0.50 \cdot 90 \] \[ = 16 + 22.5 + 45 = 83.5 \]

Your weighted average grade is 83.5%.

Example 2 – Portfolio weighted return

You invest:

$4,000 in Fund A (return 5%)
$3,000 in Fund B (return 8%)
$3,000 in Fund C (return 2%)

Weights are based on invested amounts:

Total invested: $4{,}000 + 3{,}000 + 3{,}000 = 10{,}000$

Weights: $w_A = 4000/10000 = 0.4$, $w_B = 0.3$, $w_C = 0.3$

\[ \bar{r}_w = 0.4 \cdot 5\% + 0.3 \cdot 8\% + 0.3 \cdot 2\% \] \[ = 2\% + 2.4\% + 0.6\% = 5\% \]

The portfolio’s weighted average return is 5%.

When should you use a weighted average?

Grades & GPAs – courses with more credits or higher weight affect your GPA more.
Finance & investing – portfolio returns, average cost basis, bond yields.
Business – average price per unit, customer lifetime value, KPI dashboards.
Statistics – combining estimates from different sample sizes.

Weighted vs. simple average

Simple average (arithmetic mean): $\displaystyle \bar{x} = \frac{x_1 + \dots + x_n}{n}$ – all values count equally.
Weighted average: $\displaystyle \bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}$ – some values count more.

If all weights are equal (e.g., all $w_i = 1$), the weighted average equals the simple average.

FAQ

Can weights be percentages or raw numbers?

Yes. This calculator accepts both. If you choose “percent weights”, it treats inputs as percentages. If you choose “raw weights”, it uses the formula with $\sum w_i$ in the denominator and normalizes automatically.

What if my weights don’t add up to 1 or 100%?

That’s fine. The formula always divides by $\sum w_i$, so the weights are effectively normalized. For example, weights 2, 4, 4 behave the same as 20%, 40%, 40%.

Can weights be zero or negative?

Zero weights are allowed – that value simply doesn’t contribute.
Negative weights are mathematically allowed but unusual in basic applications. This tool blocks negative weights to avoid confusion for most users.

Is weighted average the same as weighted arithmetic mean?

Yes. “Weighted average” and “weighted arithmetic mean” are two names for the same concept.

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