What is a weighted average?

A weighted average (or weighted mean) is a type of average in which each value is multiplied by a corresponding weight before summing, and the total is divided by the sum of the weights. Unlike a simple average, a weighted average gives more influence to values with higher weights. For example, a final exam worth 40% of your grade matters more than a quiz worth 10%, so the weighted average reflects this by multiplying each score by its respective weight.

How do you calculate a weighted average?

The formula is: Weighted Average = Σ(value × weight) / Σ(weight). Multiply each value by its corresponding weight, sum all those products, then divide by the total of all weights. For example: values 80, 90, 70 with weights 0.3, 0.5, 0.2 → (80×0.3 + 90×0.5 + 70×0.2) / (0.3+0.5+0.2) = (24 + 45 + 14) / 1.0 = 83.00.

What is the difference between a weighted and a simple average?

A simple (arithmetic) average treats every value equally — it is the sum of all values divided by the count. A weighted average assigns more importance to some values than others via weights. Using the same example (80, 90, 70): simple average = (80+90+70)/3 = 80.00, but with weights 0.3, 0.5, 0.2 the weighted average = 83.00. The difference arises because the 90 score carries more influence (50% weight) than in the unweighted case.

When should you use a weighted average instead of a simple average?

Use a weighted average whenever different items contribute unequally to a total or outcome. Common scenarios include: grade calculations (exams worth more than homework), financial portfolio returns (investments with different sizes), economic indices (like the Consumer Price Index), quality control (samples with different batch sizes), and survey results (respondents representing populations of different sizes). When all weights are equal, the weighted average reduces to the simple average.

How do you calculate a weighted grade average?

List each assignment category (exams, quizzes, homework, participation), note its weight (percentage of final grade), and enter your score in each category. The weighted average gives your overall course grade. For example: Homework 90 (weight 20%), Midterm 78 (weight 30%), Final 85 (weight 50%) → (90×0.2 + 78×0.3 + 85×0.5) / 1.0 = (18 + 23.4 + 42.5) = 83.90%.

Can weights be percentages?

Yes. Weights can be percentages (like 30, 50, 20 summing to 100), decimals (0.3, 0.5, 0.2), or any positive numbers — the formula works the same way because the result is always Σ(value × weight) / Σ(weight), and dividing by the total sum normalizes the weights automatically. Whether your weights are 1, 2, 3 or 10, 20, 30, you get the same weighted average. The only constraint is that all weights must be non-negative and their sum must be greater than zero.

How is the Consumer Price Index (CPI) a weighted average?

The CPI measures inflation by tracking the cost of a fixed "basket" of goods and services. Each category — housing, food, transportation, medical care, etc. — has a weight reflecting how much the average household spends on it. Housing has the largest weight (~33%), food ~14%, transportation ~17%. The CPI is a weighted average of price changes: if housing costs rise 5% and food rises 3%, and housing has a weight twice as large, the CPI rises more than a simple average of 4% would suggest. This same weighted-basket approach is used in the Producer Price Index (PPI) and most economic indices.

What is a weighted GPA and how is it calculated?

A weighted GPA assigns extra grade points to honors, AP (Advanced Placement), and IB (International Baccalaureate) courses to reflect their greater difficulty. Under common weighting schemes, an A in a standard course earns 4.0 points while an A in an AP course earns 5.0. The weighted GPA is then the weighted average of all grade points using the credit hours of each course as weights: Σ(grade points × credits) / Σ(credits). A student with a 4.0 in all AP classes could have a weighted GPA above 4.0, which is why weighted GPAs and unweighted GPAs must always be reported together.

Weighted Average Calculator — Values & Weights

Calculates the weighted mean from any list of values and weights, showing each value's contribution and the unweighted average for comparison.

How to Use the Weighted Average Calculator

This weighted average calculator computes the weighted mean from any list of values and weights — enter a value and a weight for each row and add as many rows as you need using the + Add Row button — there is no maximum. Weights can be any positive numbers: percentages (20, 30, 50), decimals (0.2, 0.3, 0.5), or raw counts. The calculator normalizes them automatically. You will see the weighted average, the sum of weights, and the simple (unweighted) average side by side, plus a breakdown table showing each row's contribution. Use the Share button to save a link with your data pre-filled.

For finding the middle value in a dataset rather than the mean, use our mean, median, and mode calculator instead.

The Weighted Average Formula

The weighted mean gives each value a different level of influence based on its weight:

Weighted Average = Σ(Value × Weight) / Σ(Weight)

Multiply each value by its weight, sum all those products, then divide by the sum of the weights. When all weights are equal, this reduces to the familiar arithmetic mean.

Worked Example: Grade Calculation

A course has three components: Homework (weight 20%), Midterm (weight 30%), Final Exam (weight 50%). Scores: Homework 90, Midterm 78, Final 85.

Products: 90 × 20 = 1,800 · 78 × 30 = 2,340 · 85 × 50 = 4,250
Sum of products: 1,800 + 2,340 + 4,250 = 8,390
Sum of weights: 20 + 30 + 50 = 100
Weighted average: 8,390 / 100 = 83.90
Simple average (for comparison): (90 + 78 + 85) / 3 = 84.33

The difference (83.90 vs 84.33) reflects the fact that the lowest score (78) carries the most weight after the final exam.

When Weights Are Counts

Weights do not need to be percentages. If you are averaging test scores across three classes of different sizes — 25 students scored 80, 30 students scored 75, 45 students scored 88 — use class sizes as weights. Weighted average = (80×25 + 75×30 + 88×45) / (25+30+45) = (2,000 + 2,250 + 3,960) / 100 = 82.10, versus a simple average of (80+75+88)/3 = 81.00.

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Weighted Average vs. Simple Average

The simple arithmetic mean treats every value as equally important. The weighted mean accounts for the fact that some data points represent more — more students, more dollars, more time, or more importance to a final score. Here are common scenarios where weighted averages are essential:

Academic grades — final exams typically count more than daily homework. A weighted grade average reflects this correctly; a simple average would overstate the value of low-stakes work.
Portfolio returns — if you have $10,000 in one fund returning 8% and $1,000 in another returning 12%, your blended return is not (8%+12%)/2 = 10%, it is (8%×10,000 + 12%×1,000) / 11,000 = 8.36%.
Supplier quality — if Supplier A ships 500 units at 98% quality and Supplier B ships 100 units at 94%, the weighted quality is (98×500 + 94×100)/600 = 97.33%, not (98+94)/2 = 96%.
Survey data — when responses represent groups of different sizes, weight by population to get a representative result.

Common Use Cases

The weighted average appears across almost every quantitative field:

Education — GPA calculations, course grade breakdowns, standardized test composite scores
Finance — weighted average cost of capital (WACC), blended interest rates, weighted portfolio returns
Economics — Consumer Price Index (CPI), Producer Price Index (PPI), GDP deflators
Manufacturing — weighted defect rates, average unit cost across production runs
Data science — ensemble models, class-imbalanced datasets, importance-weighted features

For more advanced statistical measures, our standard deviation calculator shows how values spread around the mean.

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Understanding the Contribution Table

The breakdown table below the result cards shows four columns for each row: the value, the weight, the product (value × weight), and the percentage of total weight that row contributes. The "% of Total Weight" column is especially useful — it reveals at a glance which inputs drive the final result most strongly. Any row contributing more than 50% of total weight dominates the average; errors in that row's value will have an outsized effect on the result.

If your weights are percentages that should sum to 100, check that the "Sum of Weights" result card shows exactly 100.00. If it does not, you have a data entry error — the individual row percentages in the contribution table will help you find it quickly.

Sources & References

Weighted Average — Statistics Reference — Khan Academy
Mean, Median, and Weighted Average — National Council of Teachers of Mathematics

Weighted Average Calculator