Weighted Average Calculator
Weighted mean of values and weights for grades, GPA, prices or ratings, with each item's share and points added, and the score needed to hit a target.
The interactive tool loads here when JavaScript runs.
About this toolWhat is the Weighted Average Calculator?
A weighted average counts some values more than others. Enter each item with its value and its weight, and the calculator returns Σ(w × x) / Σw along with each item's share of the total weight and how many points it adds to the average. The contributions add up to the answer, so you can see exactly which item is pulling the result up or down.
Weights can be percentages, credit hours, quantities, vote counts or any other positive numbers; only their proportions matter. A course where homework is 20%, quizzes 15%, the midterm 25% and the final 40% works the same way as a GPA weighted by credits or an average purchase price weighted by number of shares.
A "What do I need?" box answers the follow-up question: given a target average and the weight still to come, what value do you need on the remaining item? Rows can be typed or pasted straight from a spreadsheet, and arithmetic is exact, so averages of thirds and sevenths are not rounded until they are shown.
- Any number of items with optional names
- Exact arithmetic with fraction and repeating-decimal output
- Each item's weight share and points contributed
- Plain mean shown for comparison
- Value needed on remaining weight to reach a target
- Paste rows from a spreadsheet
How to use the Weighted Average Calculator
- Enter one row per item: an optional name, the value and the weight. A blank weight counts as 1.
- Add rows as needed, or paste rows from a spreadsheet as name, value, weight.
- Read the weighted average, the plain average for comparison, and the sums of weights and products.
- Check each item's share of the weight and its contribution in points.
- To plan ahead, enter a target average and the weight still to come to see the value you need on the rest.
Worked examples
Course grade by category
Input
92 (20%), 85 (15%), 78 (25%), 88 (40%)
Output
85.85
The products 1840 + 1275 + 1950 + 3520 = 8585, divided by 100. The final exam alone contributes 35.2 points.
GPA by credit hours
Input
4.0 × 4, 3.3 × 4, 3.7 × 3, 4.0 × 1
Output
3.691(6) = 443/120
The one-credit A adds less than the four-credit B+, so the GPA is below the plain average of 3.75.
Average share price
Input
100 at 42.10, 250 at 38.75, 50 at 45.00
Output
40.36875
Weighted by shares bought. The plain average of the three prices, 41.95, ignores that most shares were bought at the lowest price.
What do I need on the final?
Input
90 (20), 78 (30), 85 (50 so far), target 90 with 25 to come
Output
114.4
A result above the maximum score means the target is out of reach; a negative one means it is already secured.
Background and insight
The weighted arithmetic mean is x̄ = Σ(wᵢxᵢ) / Σwᵢ. When all weights are equal it reduces to the ordinary mean. Dividing by the sum of the weights is what makes the scale of the weights irrelevant: weights of 20, 30 and 50 give the same answer as 0.2, 0.3 and 0.5, or 2, 3 and 5.
Weights should reflect how much each value represents. In a grade, that is the syllabus percentage; in a GPA, the credit hours; in a portfolio, the money invested; in a survey, the number of respondents who gave each answer. Using the wrong weights is the most common error, for example averaging the average price of two purchases without weighting by the quantity bought, which overstates the influence of the smaller purchase.
A related trap is Simpson's paradox: when groups have very different sizes, a weighted overall average can move in the opposite direction from every group's own average. Showing each item's share of the weight next to its value makes these effects visible instead of hiding them inside a single number.
Common use cases
Grades
Work out a course grade from category weights and see what you need on the final exam to reach a letter grade.
GPA
Weight grade points by credit hours to get a term or cumulative GPA.
Investing
Find the average cost of shares bought at different prices, weighted by quantity.
Ratings and surveys
Turn star-rating counts into an average score, with each star level weighted by the number of votes.
Inventory and costing
Calculate a weighted average unit cost across purchase batches.
Tips and limitations
- If category percentages do not add to 100 because some work is not graded yet, the result is your average on the graded part so far.
- Weights must not be negative. A weight of zero simply removes that item.
- Compare the weighted and plain averages: a big gap means a few heavily weighted items dominate.
- For a GPA, convert letters to grade points first using your school's scale.
- The needed value can exceed the maximum score; that is the calculator telling you the target is not reachable.
Frequently asked questions
How do you calculate a weighted average?
Multiply each value by its weight, add the products, and divide by the sum of the weights. For 90 with weight 20, 78 with weight 30 and 85 with weight 50: (1800 + 2340 + 4250) / 100 = 83.9.
Do the weights have to add up to 100?
No. Dividing by the total weight takes care of the scale, so weights of 2, 3 and 5 give the same answer as 20%, 30% and 50%. If percentages add to less than 100 because some work is not done yet, you get the average of the completed part.
What is the difference between a weighted average and a normal average?
A normal (arithmetic) mean counts every value once. A weighted mean lets some values count more. When all weights are equal, the two are the same.
How do I work out what I need on my final exam?
Enter your current categories, then put your target average and the final's weight in the What do I need box. The calculator solves (target × total weight − current points) / final weight.
How is GPA a weighted average?
Each course's grade points are weighted by its credit hours. A 4-credit B (3.0) counts four times as much as a 1-credit A (4.0).
What does an item's contribution mean?
It is value × weight ÷ total weight: the number of points that item adds to the average. All the contributions add up to the weighted average, so they show where the result comes from.
Can a weight be zero or negative?
Zero is allowed and simply removes the item. Negative weights are rejected because they have no meaning for an average and can push the result outside the range of the values.
Is there an in-depth guide to the Weighted Average Calculator?
Yes. “How to Calculate a Weighted Average: Grades, GPA, Prices and Pitfalls” covers the background, how it works, common pitfalls and worked examples. Read the full guide.
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