Weighted Average Calculator
Enter each value with its weight and how many pairs to use. Choose the check mode when your weights are percentages that must total 100.
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Formula
weighted average = (v1 × w1 + v2 × w2 + ... + vn × wn) ÷ (w1 + w2 + ... + wn)
In percentage mode the weights must satisfy w1 + w2 + ... + wn = 100. The weight left is 100 - total weight.
Worked example
Values 80, 90 and 70 with weights 30, 20 and 50:
- 80 × 30 = 2400, 90 × 20 = 1800, 70 × 50 = 3500, so the sum is 7700
- Total weight = 30 + 20 + 50 = 100
- Weighted average = 7700 ÷ 100 = 77
With the last weight changed to 40 the total is 90, the sum is 7000 and the average is 7000 ÷ 90 = 77.78. In check mode the calculator reports that 10 weight points are missing.
Frequently asked questions
How do you calculate a weighted average?
Multiply each value by its weight, add the products, then divide by the total weight. For grades 80, 90 and 70 with weights 30, 20 and 50: (2400 + 1800 + 3500) ÷ 100 = 77.
What if my weights do not add up to 100?
The weighted average still works, because dividing by the total weight rescales it. With weights 30, 20 and 40 (total 90) the result is 7000 ÷ 90 = 77.78. Use the check mode to see how far short of 100 you are.
What is the difference between a weighted average and a simple average?
A simple average treats every value equally. A weighted average lets some values count more. The simple average of 80, 90 and 70 is 80, but with weights 30, 20 and 50 it is 77.
Can a weight be zero?
Yes. A zero weight removes that value from the result. At least one weight must be above zero, otherwise the total weight is zero and the average is undefined.
Can I use percentages as weights?
Yes. Pick the percentage mode and enter weights such as 30, 20 and 50. The calculator confirms they total 100 and tells you the shortfall or excess if not.