Weighted average calculator: enter values with weights, one pair per line, for the weighted mean, sum of weights and each value's contribution.
By AdminDrafted with AI writing toolsUpdated Checked examples: 7
The weighted average is 82.9: the products add up to 8,290 and the weights to 100. The unweighted average is 85. Value 3, with the largest weight (50% of the total), pulls the result down toward 78.
| Item | Value | Weight | Share of weight | Value × weight | Contribution |
|---|---|---|---|---|---|
| Value 1 | 92 | 20 | 20 % | 1,840 | 18.4 |
| Value 2 | 85 | 30 | 30 % | 2,550 | 25.5 |
| Value 3 | 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.
Multiply each value by its weight, add the products, and divide by the sum of the weights: Σ(value × weight) / Σweight. Homework at 92, a midterm at 85 and a final exam at 78, weighted 20%, 30% and 50%, give (1,840 + 2,550 + 3,900) / 100 = 82.9. Their plain average is 85.
Weights only need to be in proportion, so 2, 3 and 5 give the same 82.9. In a spreadsheet the formula is =SUMPRODUCT(values, weights)/SUM(weights). The NIST Dataplot weighted-mean reference defines it the same way.
Each value contributes value × weight ÷ Σweight, and the contributions add up to the average. In the grade example they are 18.4 + 25.5 + 39 = 82.9, so the final exam supplies almost half of the result.
For shares bought at different prices, the price is the value and the number of shares is the weight. Ten shares at 100 and twenty at 110 cost 1,000 + 2,200 = 3,200 for 30 shares, an average of 106.666667 per share.
Averaging the two prices gives 105, which ignores that twice as many shares were bought at 110. Write each purchase as price, then quantity, on its own line:
100 10
110 20
| First purchase | Second purchase | Total quantity | Average price |
|---|---|---|---|
| 100 × 10 | 110 × 20 | 30 | 106.666667 |
| 100 × 10 | 90 × 20 | 30 | 93.333333 |
| 100 × 10 | 120 × 20 | 30 | 113.333333 |
| 100 × 10 | 110 × 10 | 20 | 105 |
| 100 × 0.5 | 110 × 1.5 | 2 | 107.5 |
| 100 × 10 | 110 × 0 | 10 | 100 |
| 101 × 10 | 111 × 20 | 30 | 107.666667 |
Multiplying every quantity by the same factor leaves the average unchanged, and the average always lies between the lowest and highest prices bought. Fractional quantities work, and a lot with quantity 0 has no effect.
If you record lots as shares then price, with fees as one total, the stock average cost calculator works that way and also gives unrealized profit or loss and a position size.
For a course grade, the scores are the values and each component's share of the grade is its weight. A % sign marks a relative weight, so 20% counts as 20 and a plain 0.2 counts as 0.2. Use one scale on every line.
| Example | Sum of weights | Sum of products | Weighted average |
|---|---|---|---|
| Default percentage grade | 100 | 8290 | 82.9 |
| Proportional integer grade | 10 | 829 | 82.9 |
| Percentage total of eighty | 80 | 6400 | 80 |
| Mixed percent notation | 80 | 6400 | 80 |
| Credit-weighted GPA | 14 | 48.7 | 3.478571 |
| Equal general weights | 3 | 60 | 20 |
| Zero-weighted general value | 1 | 80 | 80 |
| Negative mathematical values | 8 | 24 | 3 |
Percentage weights need not total 100. If they total 80% because an exam is still to come, dividing by 80 gives the average of the work done so far. Mixing % and plain weights treats them all as plain numbers.
For GPA, use grade points as values and credits as weights. Grades of 3.0, 4.0, 3.7 and 3.3 over 4, 3, 4 and 3 credits give 48.7 / 14 = 3.478571. The GPA calculator converts letter grades for you.
Values can be negative, as in (−3 × 2 + 5 × 6) / 8 = 3, but weights cannot.
To include purchase fees, spread each fee over its lot. A fee of 10 on ten shares at 100 makes the price 101; a fee of 20 on twenty shares at 110 makes it 111. The total outlay is then 3,230 for 30 shares, an average of 107.666667.
Average purchase price is not always the cost basis allowed for tax; the rules depend on the asset and the country.
The IRS stock-basis FAQ separates specific identified lots and first-in, first-out treatment from the limited cases where average basis is allowed.
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
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. Equal weights always give the same result; unequal weights can also balance to the same average.
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 is the mathematical average purchase price before fees. Tax cost basis depends on the asset and applicable rules; this arithmetic does not select a permitted basis method.
This calculator includes 7 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.