Weighted Average & GPA Calculator (Free)
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A weighted average calculator multiplies each value by its weight, adds the products and divides by the total weight: Σ(w × x) ÷ Σw. For tests of 82, 90 and 76 worth 20%, 30% and 50%, the products are 1,640, 2,700 and 3,800, so the weighted average is 8,140 ÷ 100 = 81.4, a little below the simple average of 82.67.
Paste a list of value and weight pairs
Show steps
- Multiply each value by its weight: 82 × 20 = 1,640; 90 × 30 = 2,700; 76 × 50 = 3,800.
- Add the products: Σ(w × x) = 1,640 + 2,700 + 3,800 = 8,140.
- Add the weights: Σw = 20 + 30 + 50 = 100%.
- Divide: 8,140 ÷ 100 = 81.4.
- Check: the answer must lie between the smallest value (76) and the largest (90). 81.4 does, so the arithmetic is consistent.
| Item | Value x | Weight w | Share | w × x | Adds |
|---|---|---|---|---|---|
| Test 1 | 82 | 20% | 20% | 1,640 | 16.4 |
| Test 2 | 90 | 30% | 30% | 2,700 | 27 |
| Final exam | 76 | 50% | 50% | 3,800 | 38 |
| Total | 100% | 100% | 8,140 | 81.4 |
How to use the weighted average calculator
- Values & weights is the general tool. Type each value and its weight on its own row (a label is optional), or open Paste a list and paste one pair per line. Choose Percentages when the weights are percents and Numbers for counts, credits, hours or dollars.
- Grade categories is for a class syllabus such as homework 20%, quizzes 30%, exams 50%. Type the scores in each category (92 or 45/50) and leave a category blank if it has not been graded yet.
- Score needed answers “what do I need on the rest?” from your current average, the weight already counted, the weight still to come and your target.
- GPA turns letter grades and credit hours into a grade point average, which is a weighted average with credits as the weights.
- Read the answer at the top, then the share-of-weight bar, the contribution bars and the table. Show steps writes out the full working with your numbers.
Weighted average formula
A weighted average gives some values more say than others. If x₁, x₂, … are the values and w₁, w₂, … their weights:
Weighted average = (w₁x₁ + w₂x₂ + … + wₙxₙ) ÷ (w₁ + w₂ + … + wₙ) = Σ(w × x) ÷ Σw
The weights can be any non-negative numbers. Only their relative sizes matter: weights of 1, 2 and 2 give the same answer as 20%, 40% and 40%. When percentage weights add up to exactly 100, dividing by Σw is dividing by 100, so you can also convert each weight to a decimal and add the products (0.2 × 82 + 0.3 × 90 + 0.5 × 76 = 81.4).
Each value adds w × x ÷ Σw to the result. In the opening example the final exam adds 38 points, Test 2 adds 27 and Test 1 adds 16.4, and those contributions add up to 81.4. The heaviest item pulls the average toward itself, which is why a weighted average always lies between the smallest and largest value.
Worked examples
Example 1: course grade with weights that add to 100%
Test 1 = 82 (20%), Test 2 = 90 (30%), final exam = 76 (50%). Products: 82 × 20 = 1,640, 90 × 30 = 2,700, 76 × 50 = 3,800. Sum = 8,140. Weights sum to 100, so the weighted average is 8,140 ÷ 100 = 81.4. The simple average (82 + 90 + 76) ÷ 3 = 82.67 is higher because the weakest score carries half the weight.
Example 2: percentage weights that do not add to 100
Homework 85 (30%), quizzes 92 (25%), midterm 70 (30%), and the final (15%) has not happened yet. The weights entered add to 85%. Products: 2,550 + 2,300 + 2,100 = 6,950, and 6,950 ÷ 85 = 81.76. Dividing by 85 rescales the weights so they add to 100% (homework’s 30% now counts as 35.29%). That is your grade on the work done so far. If you wrongly divide by 100 you get 69.5, which is what you would finish with only if you scored 0 on the final.
Example 3: average price paid (weights are quantities)
You bought 40 units at $12.50, 60 at $11.00 and 25 at $13.20. Spend: 500 + 660 + 330 = $1,490 for 125 units, so the weighted average price is 1,490 ÷ 125 = $11.92 per unit. The simple average of the three prices, $12.23, ignores that most units were bought at the cheapest price.
Example 4: what do I need on the final?
Your average is 86 on 70% of the course and the final is worth 30%. To finish at 90 you need 90 × 100 = 9,000 weighted points in total and you have 86 × 70 = 6,020. The final must supply 2,980 points over a weight of 30: 2,980 ÷ 30 = 99.33. A perfect 100 would give 90.2, so 90 is reachable, but only just.
How much a final exam moves your grade
Starting from an 85% average on everything else, this is the course grade for each final exam score and final weight.
| Final weight | Final = 60 | 70 | 80 | 90 | 100 |
|---|---|---|---|---|---|
| 20% | 80 | 82 | 84 | 86 | 88 |
| 25% | 78.75 | 81.25 | 83.75 | 86.25 | 88.75 |
| 30% | 77.5 | 80.5 | 83.5 | 86.5 | 89.5 |
| 40% | 75 | 79 | 83 | 87 | 91 |
Every 10 points on the final moves the course grade by the final’s weight as a fraction of 10: 2 points when it is worth 20%, 4 points when it is worth 40%.
Weighted average vs simple average
A simple (arithmetic) mean is the special case where every weight is equal. Use a weighted average whenever the items are not equally important or not equally large: graded categories, credit hours, numbers of items bought at each price, class sizes when you combine class averages, or money invested in each fund. If two classes of 20 and 30 students average 78 and 88, the combined average is (20 × 78 + 30 × 88) ÷ 50 = 84, not 83. For the plain mean, median and mode of a list, use the mean, median and mode calculator.
Common mistakes with weighted averages
| Mistake | How to catch it |
|---|---|
| Dividing by the number of items instead of the sum of the weights | The answer must lie between the smallest and largest value. 8,140 ÷ 3 = 2,713 clearly does not. |
| Dividing by 100 when the percentage weights do not add to 100 | Add the weights first. If they total 85, divide by 85 (or plan the missing 15% in Score needed). |
| Averaging category averages without their weights | A 95 homework average and a 70 exam average do not make 82.5 if exams count three times as much. |
| Swapping values and weights | Weights are the “how much it counts” numbers: percents, credits, quantities. Values are the scores or prices. |
| Rounding each product before adding | Keep full precision until the last step, then round once. |
Checking homework and working by hand
Before you enter a problem, estimate: the answer sits closer to the value with the biggest weight. After you get the result, compare it with the simple average; if the heavy items are low, the weighted average should be lower. Do one problem fully by hand (products, sum, divide) and then use the calculator to check the rest. On a test, writing the products in a small table, like the one under the result above, prevents most slips.
Weighted averages practice quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
(1 × 70 + 3 × 90) ÷ (1 + 3) = 340 ÷ 4 = 85. 80 is the simple average, which ignores the weights.
0.4 × 92 + 0.6 × 75 = 36.8 + 45 = 81.8. 83.5 averages the two scores without weights.
Σ(w × x) = 6,950 and Σw = 85, so 6,950 ÷ 85 ≈ 81.76. Dividing by 100 (69.5) treats the missing 15% as a zero.
(10 × 8 + 30 × 12) ÷ 40 = 440 ÷ 40 = $11. The simple average of the prices, $10, ignores that most shirts cost $12.
(4 × 4 + 2 × 2) ÷ 6 = 20 ÷ 6 ≈ 3.33. 3.00 is the unweighted mean of 4.0 and 2.0.
Multiplying every weight by the same number multiplies both Σ(w × x) and Σw by it, so the ratio does not change.
(20 × 78 + 30 × 88) ÷ 50 = (1,560 + 2,640) ÷ 50 = 4,200 ÷ 50 = 84. 83 is the average of the two class averages.
SUMPRODUCT adds each value times its weight and SUM(C2:C6) adds the weights. Dividing by COUNT gives the wrong denominator.
The final adds 0.20 × score to the grade, so 10 more points on the final adds 0.20 × 10 = 2 points.
Quiz complete
Frequently asked questions
How do you calculate a weighted average?
Multiply each value by its weight, add those products, and divide by the sum of the weights. For scores of 80 (weight 2) and 90 (weight 3): (160 + 270) ÷ 5 = 86.
What is a weighted average for grades?
It is a course grade where each category counts by its syllabus percentage. With homework 95 at 20%, quizzes 85 at 30% and exams 78 at 50%, the grade is 19 + 25.5 + 39 = 83.5. The grade calculator adds letter grades and a final exam planner.
Is a weighted average the same as an average?
Only when every weight is equal. Then Σ(w × x) ÷ Σw reduces to the sum of the values divided by how many there are. With unequal weights, the result moves toward the heavily weighted values.
Is a weighted average the same as GPA?
A GPA is a weighted average of grade points with credit hours as the weights: an A (4.0) in a 3-credit course and a B (3.0) in a 4-credit course give (12 + 12) ÷ 7 = 3.43. A high school “weighted GPA” means something different: extra points for honors or AP classes. The GPA calculator handles both.
How do you find a weighted average of percentages?
Treat each percentage as a value and its base as the weight. A 90% pass rate in a class of 30 and 70% in a class of 10 combine to (30 × 90 + 10 × 70) ÷ 40 = 85%, not the 80% you get by averaging 90 and 70. To work with the percentages themselves, see the percentage calculator.
How do you calculate a weighted average in Excel?
Put the values in B2:B4 and the weights in C2:C4, then use =SUMPRODUCT(B2:B4,C2:C4)/SUM(C2:C4). SUMPRODUCT adds the products w × x and SUM adds the weights, which is the same formula this calculator uses.
Related calculators
- Grade calculator: course grade with letters, points and a final exam planner
- GPA calculator: semester, cumulative and honors/AP weighted GPA
- Mean, median and mode calculator: the plain averages of a data set
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- Descriptive statistics calculator: mean, spread and shape in one place
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