Weighted Average Calculator
Enter each value with its weight. The label is optional.
Working
| Label | Value | Weight | Value × weight |
|---|---|---|---|
| Homework | 92 | 20 | 1840 |
| Midterm | 78 | 30 | 2340 |
| Final exam | 85 | 50 | 4250 |
| Total | 100 | 8430 |
Working out what you need on an exam? Try the grade calculator. For a plain average, use the average calculator.
When an average needs weights
A plain average treats every number as equally important. That is wrong whenever the numbers stand for different amounts of something: a final exam worth half the course, a 4-credit class next to a 1-credit lab, or 100 shares bought at one price and 10 at another. Aweighted average fixes this by letting each value count in proportion to its weight.
The formula is Σ(value × weight) ÷ Σ(weight). Dividing by the total weight is what makes the units of the weights irrelevant: percentages, points, credit hours or share counts all work, as long as they are on the same scale as each other. That is also why weights do not need to add up to 100.
One check worth doing: the weighted average always lands between the smallest and largest value. If yours does not, a weight has been typed in the value column or the other way round.
Frequently asked questions
How do you calculate a weighted average?
Multiply each value by its weight, add up those products, and divide by the sum of the weights. For grades of 92, 78 and 85 weighted 20%, 30% and 50%: (92 × 20 + 78 × 30 + 85 × 50) ÷ (20 + 30 + 50) = 8,430 ÷ 100 = 84.3.
Do the weights have to add up to 100?
No. Dividing by the sum of the weights rescales them automatically, so weights of 2, 3 and 5 give exactly the same answer as 20%, 30% and 50%. If your weights are meant to be percentages of a whole course and they do not total 100, though, it usually means a category is missing, so the calculator warns you when the percentage option is ticked.
How is a weighted average different from a normal average?
A normal (arithmetic) average gives every value the same weight. A weighted average lets some values count more than others. When all the weights are equal, the two are the same.
How do I calculate a weighted grade or GPA?
Use each assignment or course grade as the value and its percentage or credit hours as the weight. For GPA, enter each course's grade points (A = 4, B = 3 and so on) as the value and its credit hours as the weight. A 4-credit A and a 3-credit B give (4 × 4 + 3 × 3) ÷ 7 ≈ 3.57.
Can a weight be zero or negative?
A weight of zero is allowed: that row simply does not count. A negative weight is rejected, because a weight says how much a value counts and cannot be less than nothing.
Where are weighted averages used?
Course grades, GPA, portfolio returns weighted by the amount invested, average purchase price across several buys, inventory cost, survey results weighted by group size, and index numbers such as the Consumer Price Index.