A weighted average multiplies each value by its weight, sums the products and divides by the total weight. It is the right tool whenever the components are not equally important — a final exam worth half the grade should not count the same as a homework worth five percent.
Dividing by the total weight rather than by the number of components is the step people miss, and it is what allows weights in any units at all. Percentages, credit hours, share counts and dollar amounts all work identically, because only the ratios between the weights matter. The unweighted mean is shown alongside so you can see exactly how much the weighting moved the answer.
Below the calculator sits the same four scores under different weightings table: 5 rows — 25 / 25 / 25 / 25 at one end, 40 / 40 / 10 / 10 at the other — which is usually faster than entering a value you have seen before. The page opens with value 1 already set to 85, so there is a finished result on screen before anything is typed. The result is also read against 4 bands, from low at the low end to very strong at the high end, each with a note on what that range means in practice. Most visitors arrive here from, or leave for, Geometric Mean Calculator and Percentile Rank Calculator.
The formula
x<sub>i</sub>- Each component value
w<sub>i</sub>- The weight attached to it
Σw- Total weight, which becomes the divisor
How it works, step by step
- Enter each component score.
- Enter the weight for each, in any consistent unit.
- The gauge shows the weighted average.
- Compare it with the plain mean below to see the effect of the weighting.
Worked examples
Four components with weights 20, 30, 40 and 10
The weighted sum is 8,100 over a total weight of 100, giving 81.0000. The plain mean would be 77.00, so the weighting adds +4.0000 points.
Why the divisor is the total weight
Weights of 2, 3, 4 and 1 give exactly the same answer as 20, 30, 40 and 10, because only the ratios matter. Dividing by four instead of by the weight total would give a meaningless number in both cases.
Checking the 50 / 20 / 20 / 10 row
The reference table lists 50 / 20 / 20 / 10, giving Weighted average: 81.1000, Plain mean: 77.0000, Difference: +4.1000. Entering that above should reproduce the same figures — if it does not, the input is being read differently to the way the table assumes.
How to read your score
Frequently asked questions
Do the weights have to add to 100?
No. Only the ratios between them matter, since the total weight is the divisor. Weights of 1, 2 and 1 behave identically to 25, 50 and 25.
How do I calculate a GPA with this?
Use the grade points as values and the credit hours as weights. That is exactly the weighted mean universities compute.
What if one weight is zero?
That component is excluded entirely, which is a convenient way to drop an item without deleting it.
Why does the weighted average differ from the plain mean?
Because the plain mean implicitly weights everything equally. Any difference between the two is purely the effect of the weights you applied.
What do the bands under the weighted average mean?
They label the figure so it can be read without a reference point of your own: Low from 0 to 50; Middling from 50 to 70; Strong from 70 to 85; Very strong from 85 upwards. The band is a reading aid only — the number itself is exact, and a value sitting just over a boundary is not meaningfully different from one just under it.
What formula does the Weighted Average Calculator use?
It computes Weighted mean = Σ(w_ix_i) ÷ Σw_i, where x<sub>i</sub> is each component value; w<sub>i</sub> is the weight attached to it; Σw is total weight, which becomes the divisor. The same expression is printed on the page above the inputs, so the result can be reproduced by hand or in a spreadsheet.
How weighting shifts the result
| Weights | Weighted average | Plain mean | Difference |
|---|---|---|---|
| 25 / 25 / 25 / 25 | 77.0000 | 77.0000 | +0.0000 |
| 20 / 30 / 40 / 10 | 81.0000 | 77.0000 | +4.0000 |
| 50 / 20 / 20 / 10 | 81.1000 | 77.0000 | +4.1000 |
| 10 / 10 / 70 / 10 | 85.4000 | 77.0000 | +8.4000 |
| 40 / 40 / 10 / 10 | 77.9000 | 77.0000 | +0.9000 |
Scores of 85, 72, 91 and 60 throughout; only the weights change.