Weighted Average Calculator

Calculate the weighted average of up to 5 values, each assigned a weight. Used for GPA, exam grading, portfolio returns, and survey scoring.

Inputs

Results

\begin{aligned} \bar{x}_w &= \dfrac{\sum v_i w_i}{\sum w_i} \\ &= \dfrac{(85)(0.5) + (90)(0.3) + (70)(0.2) + (0)(0) + (0)(0)}{?} \\ &= ? \end{aligned}
\begin{aligned} \Sigma w &= w_1 + w_2 + w_3 + w_4 + w_5 \\ &= 0.5 + 0.3 + 0.2 + 0 + 0 \\ &= ? \end{aligned}
Contribution 1 0
Contribution 2 0
Contribution 3 0
Contribution 4 0
Contribution 5 0

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Definition

A weighted average is a mean where each value contributes proportionally to its assigned weight rather than equally. Enter up to five values alongside their weights and this calculator returns Σ(vᵢ · wᵢ) ÷ Σwᵢ — the standard weighted mean formula used in GPA calculations, exam grading, portfolio performance, and survey scoring.

The formula

xˉw=∑i=1nviwi∑i=1nwi\bar{x}_w = \frac{\sum_{i=1}^{n} v_i w_i}{\sum_{i=1}^{n} w_i}

Each value vᵢ is multiplied by its weight wᵢ, the products are summed, and the result is divided by the total weight. This ensures that a value with a larger weight pulls the average toward itself more strongly.

The plain arithmetic mean is a special case where all weights are equal — in that case the denominator equals n and the formula reduces to (v₁ + v₂ + … + vₙ) / n.

Why weights do not need to sum to 1

Weights do not have to be expressed as percentages summing to 100%, or as fractions summing to 1. Because the formula divides by the total weight, the scale is irrelevant — weights of 1, 2, 3 produce the exact same result as weights of 0.1, 0.2, 0.3 or 10, 20, 30. Only the ratios between weights matter.

Worked example — GPA calculation

A student completes four courses in a semester:

CourseGrade (v)Credit hours (w)v × w
Mathematics3.7414.8
History3.339.9
Physical Education4.014.0
Chemistry2.7410.8

Total weight: 4 + 3 + 1 + 4 = 12 credit hours

Weighted sum: 14.8 + 9.9 + 4.0 + 10.8 = 39.5

GPA (weighted average): 39.5 ÷ 12 = 3.29

The unweighted average of the four grades would be (3.7 + 3.3 + 4.0 + 2.7) ÷ 4 = 3.43 — noticeably higher, because it gives equal weight to the 1-credit gym course and the 4-credit chemistry course. The weighted GPA correctly penalizes the low Chemistry grade by its larger credit-hour contribution.

Worked example — exam grading

A course uses this weighting scheme:

ComponentScoreWeight
Homework780.10
Midterm840.35
Final exam910.55

Weighted grade: (78 × 0.10 + 84 × 0.35 + 91 × 0.55) ÷ (0.10 + 0.35 + 0.55) = (7.8 + 29.4 + 50.05) ÷ 1.00 = 87.25

Because weights already sum to 1, the denominator is 1 and the weighted average equals the weighted sum directly. A student scoring 91 on the heavily-weighted final exam ends up with an 87.25 course grade, well above the simple unweighted average of the three scores (84.3), because the final carries more than half the total weight.

Portfolio returns

Fund managers use weighted averages to compute the return on a portfolio of assets. If you hold three positions:

AssetReturnPortfolio allocation
Equities12%60%
Bonds4%30%
Cash1.5%10%

Portfolio return: (12 × 0.60 + 4 × 0.30 + 1.5 × 0.10) ÷ 1.00 = 7.2 + 1.2 + 0.15 = 8.55%

A simple average of the three returns would give (12 + 4 + 1.5) ÷ 3 = 5.83% — wrong because it ignores that 60% of the money is in equities.

Using unused slots

This calculator supports up to 5 value–weight pairs. To use fewer than 5, leave the extra weights at 0. Any pair with weight 0 contributes nothing to the numerator or denominator and is effectively excluded. The total weight must be greater than 0 — if all weights are 0 the average is undefined.

Frequently Asked Questions (FAQ)

How do I assign weights to values?

A weight expresses how much each value counts relative to the others. If a midterm exam is worth twice as much as a quiz, assign the midterm weight 2 and the quiz weight 1. The calculator divides the sum of weighted values (Σvᵢwᵢ) by the total weight (Σwᵢ), so the scale of the weights does not matter — only their ratios do. You can use credit hours, percentages, raw counts, or any other consistent measure.

Do the weights need to sum to 1 (or 100%)?

No. The formula divides by the total weight automatically, so the result is the same whether you use weights of 0.5, 0.3, 0.2 or 5, 3, 2. Expressing weights as percentages that sum to 100% is a common convention, but it is purely cosmetic — any proportional set of weights produces the same weighted average.

When does the weighted average differ from the plain arithmetic mean?

The weighted average equals the plain mean only when all weights are identical. As soon as weights differ, higher-weighted values pull the result toward themselves. Example: scores of 60 and 90 have a plain mean of 75. If 90 carries three times the weight of 60, the weighted average is (60×1 + 90×3) ÷ 4 = 330 ÷ 4 = 82.5 — pulled toward 90. In GPA calculations this happens whenever courses carry different credit-hour counts.

What happens when a weight is zero?

A value with weight 0 contributes nothing to the weighted average — it is effectively excluded from the calculation. This is useful for leaving unused slots at 0 in this calculator. Note that the total weight must still be greater than 0; if all weights are 0 the weighted average is undefined.

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