Weighted average calculator: enter values with weights, one pair per line, for the weighted mean, sum of weights and each value's contribution.
The weighted average is 82.9: the products add up to 8,290 and the weights to 100. The unweighted average is 85; Final exam, with the largest weight (50% of the total), pulls the result down toward 78.
| Item | Value | Weight | Share of weight | Value × weight | Contribution |
|---|---|---|---|---|---|
| Homework | 92 | 20 | 20 % | 1,840 | 18.4 |
| Midterm | 85 | 30 | 30 % | 2,550 | 25.5 |
| Final exam | 78 | 50 | 50 % | 3,900 | 39 |
Weighting moves the average down by 2.1.
A weighted average multiplies each value by its weight, adds the products and divides by the sum of the weights: Σwx ÷ Σw. Values with larger weights pull the result toward themselves, and with equal weights it is the ordinary mean.
Course grades are the usual case. With homework at 92 counting 20%, the midterm at 85 counting 30% and the final at 78 counting 50%, the products add up to 8,290 and the weights to 100, so the weighted average is 82.9, while the plain average of the three scores is 85. Weights can be credits for a GPA, share counts for an average purchase price, or any relative importance.
Weights only need to be in proportion: 20%, 30% and 50% give the same answer as 2, 3 and 5. They must not be negative, and at least one must be above zero. A label before the numbers on a line, such as “Final exam”, is carried into the table.
Checked against: Hand calculation: (92 × 20 + 85 × 30 + 78 × 50) / 100 = 8290 / 100 = 82.9
Checked against: Inch Calculator weighted average page: (3.0×4 + 4.0×3 + 3.7×4 + 3.3×3) / 14 = 48.7 / 14, GPA 3.48
Checked against: Omni Calculator weighted average page: (4·4 + 3·4 + 4·3 + 2.3·2) / 13 = 3.43; Python Fraction(446, 130) = 3.4307692…
Checked against: Hand calculation: (100 × 10 + 110 × 20) / 30 = 3200 / 30 = 106.67
Multiply each value by its weight, add the products, and divide by the total weight. For scores of 92, 85 and 78 weighted 20%, 30% and 50%: 92 × 20 + 85 × 30 + 78 × 50 = 8,290, and 8,290 ÷ 100 = 82.9. In a spreadsheet the same formula is =SUMPRODUCT(values, weights)/SUM(weights).
No. Dividing by the sum of the weights rescales them automatically, so weights of 2, 3 and 5 give the same result as 20%, 30% and 50%. If percentage weights add up to 90% because a grade item is still missing, the result is the average of the work done so far, with each item's weight divided by 0.9.
Use the grade points as values and the credit hours as weights. For a B (3.0) in a 4-credit class, an A (4.0) in 3 credits, an A− (3.7) in 4 credits and a B+ (3.3) in 3 credits, the quality points are 12 + 12 + 14.8 + 9.9 = 48.7 over 14 credits, a GPA of 3.48. The GPA calculator converts letter grades for you.
A simple average gives every value the same weight, 1/n. A weighted average lets some values count more. For the default grades the simple average is (92 + 85 + 78) ÷ 3 = 85, but the final exam, worth half the grade, pulls the weighted average down to 82.9. The two agree only when all weights are equal.
Weight each price by the number of shares bought at it. Buying 10 shares at $100 and 20 at $110 costs $1,000 + $2,200 = $3,200 for 30 shares, an average of $106.67 per share, not the $105 you get by averaging the two prices. This weighted average is the cost basis per share used to work out a gain or loss.
Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 7 worked examples whose answers come from independent sources; for example, “Course grade (default)” is checked against Hand calculation: (92 × 20 + 85 × 30 + 78 × 50) / 100 = 8290 / 100 = 82.9.
Wolfram MathWorld: Weighted mean; NIST Dataplot reference manual: WEIGHTED SUM (Σ wᵢxᵢ).
7 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.
Average calculator for a list of numbers: mean, median, mode, range, count and sum, with the sorted data and the middle values highlighted.
GPA calculator: credit-weighted grade point average on the 4.0 scale from letter grades, plus percentage-to-GPA and CBSE CGPA-to-percentage conversions.
Grade calculator for weighted categories: your current course grade, and the score you need on the final exam or remaining work to reach a target.
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