Weighted Average Calculator
Enter up to four values and their corresponding weight to calculate the weighted average.
- Weighted average
- 6.6
How the weighted average is calculated
Unlike the arithmetic mean, the weighted average gives more importance to values with a higher weight. Each value is multiplied by its weight, the results are summed, and the total is divided by the sum of the weights.
It's commonly used to calculate a final course grade when each exam or assignment carries a different percentage, to average credit-based university grades, or to calculate stock indices where each company is weighted by its market capitalization.
weighted average = Σ(value × weight) ÷ Σ(weight)
When all weights are equal, the weighted average exactly matches the simple arithmetic mean; the difference only shows up when the weights vary.
Worked example
A final exam counts for 60% and two midterms 20% each, with grades of 8, 7, and 6: average = (8×20 + 7×20 + 6×60) ÷ 100 = 6.6. If all three carried equal weight instead, the simple average would be (8+7+6)/3 = 7.
Frequently asked questions
- How is this different from the arithmetic mean?
- The arithmetic mean gives every value the same weight; the weighted average accounts for each value's relative importance through its weight.
- Do the weights need to add up to 100?
- No, that's not required. The formula divides by the total sum of the weights, so you can use any scale (percentages, credits, hours, etc.).
- Can I leave rows empty if I have fewer than four values?
- Yes, empty rows or rows with a weight of 0 are ignored in the calculation.
- Can a weight be negative?
- No, weights must be zero or positive; a negative weight doesn't make mathematical sense in a standard weighted average.
- Why doesn't my final grade match the simple average of my scores?
- Because each score likely carries a different weight (for example, the final exam counts more than an assignment); the weighted average reflects that difference in importance, while the simple average doesn't.
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