Weighted Average Calculator

1

Add a value/weight pair for each item

On the Weighted Average tab, type each item's value and the weight that says how much it should count. Give rows an optional label like "Exam 1" or "US stocks" so the result is easy to read. Use the ➕ Add row button for as many items as you need, and ✕ to drop one.

2

Choose raw or percentage weights

Leave the mode on raw weights when your weights are counts or importance scores — only the ratio between them matters. Switch to percentage mode when the weights should add up to 100; the calculator flags when they don't and offers a one-click Normalize to 100%.

3

Read the weighted average and its contrast

The result card shows the weighted average to two decimals, the sum of the weights, the plain (unweighted) average for contrast, and the weighted sum Σ(value×weight). The contribution chart shows how much each item pushed the total.

4

Switch to Grade Mode for a course grade

In Grade Mode, enter each assignment's score and its percentage of the final grade. You get a course grade, a letter grade, and — if your weights total under 100% — the score you'd need on the remaining work to hit a target grade.

Weighted average

WA = Σ(vᵢ × wᵢ) / Σ(wᵢ)

Multiply each value vᵢ by its weight wᵢ, sum those products, and divide by the sum of the weights. The weights can be any positive numbers; only their ratio affects the result. If Σweights = 0 the average is undefined.

Worked example (grades)

(90×20 + 85×30 + 95×50) / (20+30+50) = 9,100 / 100 = 91.00

Three exams weighted 20, 30, and 50. The weighted sum is 9,100 and the weights total 100, giving 91.00 — higher than the simple average of 90.00 because the best score (95) carries the most weight.

Percentage normalization

weight%ᵢ = wᵢ / Σw × 100

Percentage weights are just raw weights rescaled so they sum to 100. Weights of 1, 1.5, 2.5 normalize to 20, 30, 50 and produce the identical weighted average — proof that scale doesn't matter, only ratio.

Grade what-if

needed = (100 × target − Σ(score × weight%)) / remaining%

In Grade Mode, if your graded weights total under 100%, this gives the average score you need on the ungraded remainder to finish at your target final grade. A result above 100 means the target is out of reach.

Weighted mean (weighted average) An average where each value counts in proportion to its weight, rather than equally. Computed as Σ(value×weight) ÷ Σ(weight). It's the right average whenever items differ in importance, frequency, or size.

Weight A number that says how much a value counts toward the average. Weights can be percentages (worth 30% of the grade), counts (40 students, 3 shares), or arbitrary importance scores. Only the ratio between weights matters to the result.

Normalization Rescaling a set of weights so they sum to a fixed total, usually 100. Dividing each weight by the sum of the weights and multiplying by 100 converts raw weights into percentages without changing the weighted average.

Simple (unweighted) average The plain arithmetic mean: add the values and divide by how many there are, giving every value equal weight. The calculator shows it next to the weighted average so you can see how much the weighting moved the result.

Weighted sum The numerator of the weighted average: Σ(value×weight), the total of every value multiplied by its weight before dividing by the total weight. Each item's value×weight as a share of this sum is its contribution.

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Student checking a course grade

Three exams weighted 20%, 30%, 50%

Exam 1 90 (weight 20) Exam 2 85 (weight 30) Final 95 (weight 50)

Weighted sum = 90×20 + 85×30 + 95×50 = 1,800 + 2,550 + 4,750 = 9,100. Weights total 100, so the weighted average is 9,100 ÷ 100 = 91.00. That's above the simple average of 90.00 because the highest score (95) carries half the weight. The final exam alone is 4,750 ÷ 9,100 ≈ 52% of the weighted sum.

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Investor blending portfolio returns

60% stocks, 30% bonds, 10% cash

US stocks 11.2% (weight 60) Bonds 3.5% (weight 30) Cash 1.0% (weight 10)

Portfolio return = (11.2×60 + 3.5×30 + 1.0×10) ÷ 100 = (672 + 105 + 10) ÷ 100 = 7.87%. The simple average of the three returns is 5.23%, but that would be misleading — stocks dominate the portfolio at 60% weight, so the weighted figure of 7.87% is the real blended return.

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Product team averaging review stars

100 reviews across 1–5 stars

5★ / 4★ counts 42 and 31 3★ count 15 2★ / 1★ counts 7 and 5

Here the star rating is the value and the number of reviews is the weight. Weighted sum = 5×42 + 4×31 + 3×15 + 2×7 + 1×5 = 210 + 124 + 45 + 14 + 5 = 398. Total reviews = 100, so the average rating is 3.98 stars — the true average across all reviewers, not an average of the five rating buckets.

A weighted average lets some numbers count more than others. It's the right tool whenever your items differ in importance, frequency, or size — course assignments, portfolio holdings, survey responses, or prices across different quantities. This guide covers how it differs from a simple average, when weights are percentages versus counts, and the two most common uses: grades and portfolios.

Weighted vs. simple average

A simple average adds the values and divides by how many there are, treating every value equally. A weighted average multiplies each value by a weight first, then divides by the sum of the weights. When the weights are all equal, the two are identical — the weighted average is just a generalization of the simple average.

The gap between them tells you how lopsided your weighting is. If three exams are worth 20%, 30%, and 50%, scoring highest on the heaviest exam pulls the weighted average above the simple one. The calculator shows both side by side so the effect of weighting is never hidden.

When weights are percentages vs. counts

Weights come in two flavors. Percentages describe a share of a whole — a syllabus that says homework is 20% of the grade, or a portfolio that's 60% stocks. These should sum to 100, and percentage mode flags when they don't. Counts describe how many — 40 students in a class, 3 shares of a stock, 100 reviews at a given star level. Counts rarely sum to 100, and that's fine.

Crucially, only the ratio between weights matters. Weights of 20, 30, 50 give the exact same answer as 2, 3, 5 or 0.2, 0.3, 0.5. That's why you can mix raw counts freely without converting them to percentages first — though the Percent vs Raw tab will show you the normalized equivalents if you want them.

Grade weighting and the what-if

For grades, use each assignment's percentage of the final grade as the weight and your earned score as the value. The course grade is the weighted average, and the calculator maps it to a letter using a standard plus/minus scale (90–92 is an A−, 93–96 an A, and so on).

If your graded weights total under 100% — say you've finished 60% of the course — Grade Mode also solves the reverse problem: what average do you need on the remaining 40% to finish at a target grade? If the answer comes back above 100, the target is mathematically out of reach given what's already locked in.

Portfolio and survey weighting

The same formula powers a blended portfolio return: weight each holding's return by its share of the portfolio. A 60/30/10 split of 11.2%, 3.5%, and 1.0% returns blends to 7.87% — far from the naive 5.23% simple average, because stocks dominate. For surveys and ratings, weight each rating by the number of respondents who chose it to get the true mean rather than an average-of-buckets. Avoiding that "average of averages" trap is the single most common reason to reach for a weighted mean.

How do I calculate a weighted average?+

Multiply each value by its weight, add up those products to get the weighted sum, then divide by the sum of the weights. For grades of 90 (weight 20), 85 (weight 30), and 95 (weight 50): (90×20 + 85×30 + 95×50) ÷ (20+30+50) = 9,100 ÷ 100 = 91.0. The calculator does this live as you type each value/weight pair, and shows the weighted sum and weight total so you can check the steps.

Do the weights have to add up to 100?+

No. Weights can be any positive numbers — counts, percentages, or arbitrary importance scores. Because the formula divides by the sum of the weights, only the ratio between weights matters. Weights of 1, 1.5, 2.5 produce the same average as 20, 30, 50. Use percentage mode if you specifically want the weights to read as a share of 100, and the calculator will flag any total that isn't 100 and offer to normalize it.

What's the difference between a weighted average and a simple average?+

A simple (unweighted) average treats every value equally: add them up and divide by the count. A weighted average lets some values count more than others. If a final exam is worth more than a quiz, or stocks make up more of a portfolio than cash, weighting reflects that. The calculator shows both numbers so you can see exactly how much the weighting moved the result — when all weights are equal, the two are identical.

How do I weight my grades?+

Use each assignment's percentage of the final grade as its weight and the score you earned as the value. Homework worth 20% at a score of 92, a midterm worth 30% at 85, and a final worth 50% at 95 gives a course grade of 91.0 (an A−). Grade Mode also works backward: if your weights total under 100%, it tells you the average score you'd need on the remaining work to reach a target grade.

Can the weights be unequal counts instead of percentages?+

Yes — counts are one of the most common weightings. To average test scores across classes of different sizes, weight each class average by its number of students. To average a price across several purchases, weight each price by the quantity bought. To average review stars, weight each star value by the number of reviews. Using counts as weights gives the true overall average instead of a misleading average-of-averages.

What happens if the total weight is zero or a weight is negative?+

If the weights sum to zero, the weighted average is undefined (you'd be dividing by zero) and the calculator shows a prompt instead of a number. Negative weights are unusual but allowed — they're occasionally used to subtract an item's influence — and the calculator flags them so you can confirm the input was intentional rather than a typo.

Values & Weights