Weighted Average Calculator
Each weight is paired with the value in the same position. Extra entries are ignored.
Weighted Average84.3000
Weighted Sum Σ(value×weight)8,430.0000
Total Weight Σweight100.0000
Pairs Used3
A weighted average gives some data points more influence than others by multiplying each value by a weight before averaging. This calculator multiplies every value by its matching weight, sums those products, and divides by the total of all weights. It is the right tool whenever your numbers do not count equally — grade categories, portfolio allocations, or survey responses with different sample sizes.
Formula
weighted average = Σ(vᵢ × wᵢ) / Σwᵢ
- vᵢ
- The i-th value in the dataset
- wᵢ
- The weight applied to the i-th value
- Σ
- Sum taken over every value/weight pair
How it works
- Enter your values as a comma-separated list, then enter the matching weights in the same order so each value lines up with its weight.
- The calculator computes Σ(value × weight), sums all the weights, and divides the first by the second to produce the weighted average.
- It also reports the weighted sum and total weight so you can sanity-check the inputs; weights need not add to 100 or 1.
Worked example
A course grade where exams count 30%, projects 30%, and the final 40%, with scores 85, 92, and 78.
- Weighted sum = 85×30 + 92×30 + 78×40 = 2550 + 2760 + 3120 = 8430.
- Total weight = 30 + 30 + 40 = 100.
- Weighted average = 8430 ÷ 100 = 84.3.
The weighted course grade is 84.3.
Frequently asked questions
- How is a weighted average different from a simple average?
- A simple average treats every value equally, while a weighted average lets each value contribute in proportion to its weight. When all weights are equal the two results are identical.
- Do the weights have to add up to 100% or 1?
- No. The formula divides by the total of the weights, so any consistent scale works — percentages, fractions, credit hours, or raw counts all produce the same weighted average.
- What happens if a weight is zero?
- A value with a weight of zero contributes nothing and is effectively excluded. If every weight is zero the total weight is zero and the average is undefined, so the calculator reports no result.
- Can weights be larger than the values?
- Yes. Weights and values are independent quantities. A weight simply scales how much a value counts, so it is common for weights such as credit hours or share counts to exceed the values being averaged.