Weighted average calculator
An average that respects how much each value counts: grades, shares, volumes.
Fill in the fields and the result will appear here automatically.
Averages values that do not count equally: a course grade weighted by credits, an average price weighted by the volume bought, a score weighted by hours. Pairs are entered one per line — the value first, then its weight. A line with only one number is rejected outright, because filling in a weight of 1 on your behalf would average a set you never entered.
How it works
Formula and logic
Each value is multiplied by its weight, the products are added up and divided by the total weight: x̄ = Σ(xᵢ·wᵢ) / Σwᵢ. When every weight is the same the result matches the plain arithmetic mean. Finite values of either sign and nonnegative weights are supported; at least one weight must be positive. A zero weight removes that value’s contribution. Values need one common unit, and weights one consistent meaning, such as the same volume unit or number of credits. The mean keeps the value unit while the weight unit cancels. The limit is 10000 pairs and 1000000 characters. An unrepresentable product sum is marked separately, although its ratio to total weight can still produce a valid finite mean.
Example
Grades of 90, 75 and 60 with weights 3, 4 and 2 give (270 + 300 + 120) / 9 = 76.6667 — closest to 75, which carries the largest weight.
Fields and units
- Value and weight pairs — one per line — value in a common data unit; weight on a consistent basis
How to use
- — Enter the pairs one per line: the value, a space, then the weight.
- — Each line contains exactly two finite numbers: “value weight”. A decimal point or a comma without whitespace is allowed; whitespace, a semicolon or a comma followed by whitespace separates the pair. Do not insert thousands separators inside list numbers.
- — Read the weighted average and the total weight.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- NIST Dataplot: mean Σ(wᵢxᵢ)/Σwᵢ — formula, not app accuracy
- Limitation
- Finite values of either sign and nonnegative weights are supported; at least one weight must be positive. Values need one common unit, and weights one consistent meaning, such as the same volume unit or number of credits.
FAQ
How is this different from a plain average?
A plain average treats every value as equally important. A weighted one accounts for some values mattering more — a four-credit exam moves the result further than a one-credit test.
What happens when all the weights are equal?
The result equals the plain arithmetic mean: the common factor cancels out of both the numerator and the denominator.
Can a weight be zero?
For an individual value, yes — it simply drops out of the result. If every weight is zero there is nothing to divide by, and the calculator says so.
Why is a line with one number an error?
Because there is no way to tell whether it is a value with no weight or a weight with no value. Supplying the missing number would be inventing data.