Mathematics · Averages
Calculate a weighted average from pairs
Each line is a value and its coefficient. The mean is the sum of (value × weight) divided by the sum of weights — not the average of the values then of the weights.
Calculate
How the calculator works
Nonempty lines split on a semicolon into value and weight. Products are summed, weights are summed, then divided. Negative weights are refused. A zero weight on a line is allowed (that line contributes nothing) as long as the total weight is not zero.
Formula and method
x̄_w = (v₁w₁ + v₂w₂ + … + vₖwₖ) / (w₁ + … + wₖ)
Values 10 and 20, weights 1 and 3: numerator 10×1 + 20×3 = 70, denominator 4, mean 17.5.
This is the discrete weighted arithmetic mean. It matches a course grade with credit hours, a blend by volume, or a pooled average by sample size. It is not a GPA scale converter (4.0 vs 20-point) and not CAGR, which uses two endpoints and a time span.
Worked example
10 with weight 1, 20 with weight 3
10 ; 1 and 20 ; 3
- 10×1 + 20×3 = 70.
- Weights 1 + 3 = 4.
- 70 / 4 = 17.5.
Weighted mean 17.5 (the equal-weight mean of 10 and 20 would have been 15).
Input notes
- Value and weight
- One pair per line: value semicolon weight. Extra spaces are fine. A missing weight on a line is an error.
Assumptions and limits
Assumptions
- Weights are nonnegative.
- Total weight is strictly positive.
- Value and weight are in whatever units make the product meaningful to you.
Limits
- No extra-credit curve beyond the weights you type.
- Does not compute a time-weighted return.
How to read the result
17.5 sits closer to 20 because that value had triple weight. If the weights were class sizes, 17.5 is the pooled mean. If they were arbitrary scores, check that the coefficients really should add that way.
Common mistakes
Averaging 10 and 20 to 15, then “adjusting” by weights afterwards.
Multiply first, then divide by the sum of weights. That is the whole formula.
Using percents that do not add to 100 as if they were already normalized.
The formula normalizes for you: weights 1 and 3 are the same as 25% and 75%.
Related calculations
- AveragePaste numbers; the tool sums, counts, and divides. Every observation has weight 1. Min, max, and count sit beside the mean.
- CAGRCAGR is the fictional constant annual rate that would take a starting value to an ending value in n years. It smooths the trip: a crash and a rebound disappear into one number.
Frequently asked questions
Can a weight be zero?
On one line, yes. The total of all weights cannot be zero.
A zero weight drops that value from the mean. If every weight is zero, there is nothing to divide by.
Are weights required to sum to 1 or 100?
No. Any positive total works; the formula divides by that total.
Credit hours 3 and 1 work the same as 75 and 25. Do not convert to percents unless you prefer to.
Is this the same as CAGR?
No. CAGR uses two values and a number of years.
A weighted average does not know about time. For a constant annual rate linking a start and an end, use the CAGR calculator.
Author and update
Written by Rédaction HexaCalc (editorial team). Content last updated: August 25, 2026. No third-party medical or financial review is claimed.
This calculation uses a standard mathematical identity. See also the methodology.
Equal weights are enough
If every observation should count once, the simple mean is the shorter form of the same idea.
Calculate an arithmetic meanCategory: Mathematics