Weighted Average Calculator
Weighted mean of up to 8 values with any weights — percentages, credit hours or dollars — showing what each item contributes to the answer.
Weighted Average Calculator: with the default inputs, weighted average is 85.7.
Only the first N value/weight pairs are used. Items 5–8 live under More options.
- Total weight
- 100
- Plain (unweighted) average
- 85.75What you would get if every item counted the same.
- Weighting moved the average by
- -0.05
- Σ (value × weight)
- 8,570
- Largest contribution
- Final — 30.8 of the 85.7 total (35% of the weight)
Assumptions
- Weights must be zero or positive and must not all be zero.
- Only the first N value/weight pairs are used, where N is the item count.
- This is the arithmetic weighted mean; averaging rates over a shared numerator needs a weighted harmonic mean instead.
- Weight20100%
| Item | Value | Weight | Share of weight | Contribution |
|---|---|---|---|---|
| Homework | 92 | 20 | 20% | 18.4 |
| Quizzes | 85 | 20 | 20% | 17 |
| Midterm | 78 | 25 | 25% | 19.5 |
| Final | 88 | 35 | 35% | 30.8 |
The contributions add up to the weighted average, 85.7.
How this is worked out
The formula
Weighted average = Σ(value × weight) ÷ Σ(weight) Each item's contribution = value × weight ÷ Σ(weight) The contributions sum to the weighted average. When every weight is equal this reduces to the plain mean, Σvalue ÷ n.
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- How many items?
- Only the first N value/weight pairs are used. Items 5–8 live under More options.from 1 to 8 · whole numbers only · defaults to 4
- Homework — value
- A number.defaults to 92
- Homework — weight
- A number.0 or more · defaults to 20
- Quizzes — value
- A number.defaults to 85
- Quizzes — weight
- A number.0 or more · defaults to 20
- Midterm — value
- A number.defaults to 78
- Midterm — weight
- A number.0 or more · defaults to 25
- Final — value
- A number.defaults to 88
- Final — weight
- A number.0 or more · defaults to 35
- Item 5 — value(under More options)
- A number.defaults to 0
- Item 5 — weight(under More options)
- A number.0 or more · defaults to 0
- Item 6 — value(under More options)
- A number.defaults to 0
- Item 6 — weight(under More options)
- A number.0 or more · defaults to 0
- Item 7 — value(under More options)
- A number.defaults to 0
- Item 7 — weight(under More options)
- A number.0 or more · defaults to 0
- Item 8 — value(under More options)
- A number.defaults to 0
- Item 8 — weight(under More options)
- A number.0 or more · defaults to 0
What you get back
- Weighted averagemain answer
- Total weight
- Plain (unweighted) average
- What you would get if every item counted the same.
- Weighting moved the average by
- Σ (value × weight)
- Largest contribution
What this assumes
- Weights must be zero or positive and must not all be zero.
- Only the first N value/weight pairs are used, where N is the item count.
- This is the arithmetic weighted mean; averaging rates over a shared numerator needs a weighted harmonic mean instead.
About this calculator
A plain average treats every number as equally important. A weighted average doesn't — and most real averages are weighted, whether or not anyone says so. Course grades, portfolio returns, blended interest rates, customer satisfaction across regions of different sizes, and grade point averages are all weighted means.
How to use it
Enter each value and the weight that goes with it. Weights can be percentages that sum to 100 (a syllabus: homework 20%, midterm 25%, final 35%), counts (credit hours, number of customers, units sold), or amounts (dollars invested in each fund). The scale of the weights does not matter — only their ratios do, because the formula divides by their total. Weights of 1, 2, 3 give exactly the same answer as 10, 20, 30.
How to read the results
The contribution column is the part people find most useful: it splits the final answer into the piece each item is responsible for, and those pieces add up to the weighted average exactly. It makes clear at a glance that a 92 carrying 20% of the weight moves the result less than a 78 carrying 25%.
The plain average and the difference are there as a sanity check. If weighting moved the answer by four points, that gap is the whole reason you are using a weighted average, and it is worth being able to explain.
Common mistakes
- Averaging the averages. If one region surveyed 1,000 customers at 4.1 stars and another surveyed 50 at 4.9, the overall rating is not 4.5. Weight by the number of customers and it is 4.14. This is the single most common error in business reporting.
- Forgetting a missing item. If you leave out an assignment that has not been graded yet, the weights no longer sum to 100 and the calculator divides by what you actually entered — which is usually what you want (your average so far), but be clear about which question you are asking.
- Weighting by the wrong thing. For percentage returns across a portfolio you weight by dollars invested, not by the number of holdings.
- Averaging rates directly. Speeds, prices per unit and interest rates often need a harmonic weighted mean, not this one. If the quantity is a ratio and you are averaging over the denominators, weight by the denominator.
Frequently asked questions
▸How do I calculate a weighted average?
Multiply each value by its weight, add those products up, and divide by the sum of the weights. The steps above show each of those three numbers for your data.
▸Do my weights have to add up to 100?
No. Only the ratios between weights matter, because the formula divides by their total. Weights of 1, 2 and 3 give the same answer as 10, 20 and 30.
▸What if one item has no weight yet?
Give it a weight of 0 or reduce the item count. The average is then computed over the weights you did enter, which is your standing average so far rather than your final one.
▸Why is my weighted average different from the plain average?
Because the items with bigger weights pull harder. The difference is reported directly — if it is large, the weighting is doing real work and quoting the plain average would be misleading.
▸Can weights be negative?
Not here. A negative weight subtracts an item instead of counting it, which produces averages outside the range of your data and is almost always a mistake. Short positions in a portfolio are the rare exception and need a different model.
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