Scores 70, 82, 88 with weights 20, 30, 50
Weighted average 82.6, against a simple average of 80.
Weighted average calculator
Each value counts in proportion to its weight. Weights can be percentages, credits or any units, as long as you use the same scale for every row. Leave unused rows blank.
Enter the value 4.
Enter the weight 4.
Enter the value 5.
Enter the weight 5.
Weighted average
82.60
The plain average of the same values is 80.00. The weights moved it by 2.60.
- Total weight
- 100
- Simple average
- 80.00
Row 1 (value 70, weight 20)14.00
Row 2 (value 82, weight 30)24.60
Row 3 (value 88, weight 50)44.00
Why a plain average is often wrong
Average of 70, 82 and 88 is 80. If those are the scores for an assignment worth 20%, a test worth 30% and a final exam worth 50%, then 80 is the wrong answer. The final counts more than the assignment, and the result needs to show that.
Multiply each score by its weight, add them, and divide by the total weight. Here: 70 × 20 + 82 × 30 + 88 × 50 = 1,400 + 2,460 + 4,400 = 8,260. Divide by 100 and you get 82.6. The weighting moved the answer up by 2.6 points because the strongest score had the most weight.
The same method shows up in money. If you bought 10 shares at ₹100 and 30 at ₹120, your average cost is not ₹110. It is (10 × 100 + 30 × 120) ÷ 40 = ₹115.
In college, grade point average is a weighted average by credit hours. See the GPA calculator for that use.
Sources
What this calculator does not account for
- Weights that are wrong or out of date.
- More than five rows of data.
- Grading rules such as drops or caps.
How this is calculated
Formula: Weighted average
weighted average =Σ(value × weight) ÷ Σ weightWhat the symbols mean
- valueEach number being averaged.
- weightHow much that number counts, in any consistent unit.
Good to know
- Weights can be percentages, credit hours or quantities bought.
- With equal weights it becomes the ordinary mean.
Read the full methodologyFound an error? Contact us
Worked examples
Each example is worked out by the same code as the calculator above.
10 shares at ₹100 and 30 at ₹120
Average cost ₹115, not ₹110.
Embed this calculator
The frame shows the tool only.
<iframe src="/embed/weighted-average-calculator" title="Weighted average" width="100%" height="720" style="border:0;max-width:42rem" loading="lazy"></iframe>Questions
Do the weights need to add to 100?
No. The formula divides by the total weight, so any scale works.
When should I use a weighted average?
Whenever items matter unequally: course grades by credit, shares bought at different prices, or exam sections of different length.
How is it different from the mean?
The mean treats every value the same. The weighted average gives bigger items more pull.
Can a weight be zero?
Yes, but the row then has no effect. The tool skips rows with zero weight.