Weighted Average Calculator
Averages values that do not count equally — grades by credit, prices by quantity, scores by weight.
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Your details
Weights need not add to 100 — they are scaled by their own total.
Result
- Weighted average
- 82.300000
- Plain (unweighted) average
- 78.750000
- Total weight
- 10.000000
- Sum of value × weight
- 823.000000
Across 4 values
The weighting moves the answer by 3.550000
Each value counts in proportion to its weight…
x̄ = Σ(wᵢ × xᵢ) ÷ Σwᵢ
Σ(w × x) = 823.000000
Σw = 10.000000
823.000000 ÷ 10.000000
Weighted average = 82.300000
Formula — written step by step
Grades of 90, 75, 88 and 62 with weights 4, 3, 2, 1…
x̄ = Σ(wᵢ × xᵢ) ÷ Σwᵢ
90×4 + 75×3 + 88×2 + 62×1
= 360 + 225 + 176 + 62 = 823
Σw = 4 + 3 + 2 + 1 = 10
823 ÷ 10
Weighted average = 82.3
xᵢ is each value and wᵢ its weight. The plain average of these four grades is 78.75 — the weighting pulls the result up because the highest marks carry the heaviest credit.
A worked example
A course graded by component
- Coursework 85
- weight 20%
- Midterm 72
- weight 30%
- Final 91
- weight 50%
- 85 × 20 = 1700
- 72 × 30 = 2160
- 91 × 50 = 4550
- Total = 8410, Σw = 100
Final grade = 84.1
The plain average of 85, 72 and 91 is 82.67. The weighting lifts it because the strongest performance carries half the credit — and it is why a weak midterm matters far less here than a weak final.
How to use this calculator
- Enter your values, separated by commas, spaces or new lines.
- Enter one weight for each value, in the same order. The count must match, and the calculator says so if it does not.
- Weights can be any scale — percentages, credit hours, quantities, or plain importance scores. They are divided by their own total, so they need not add to 100.
- Read the contribution table to see which values are actually driving the result.
When a plain average misleads
A plain average treats every value as equally important. That is right when the values genuinely are equal in standing, and wrong whenever they are not — which covers most real data. A final exam worth half the grade should not count the same as a quiz worth five percent.
The weighted average fixes this by multiplying each value by its weight, summing, and dividing by the total weight. When all the weights are equal it reduces exactly to the plain average, so it is a generalisation rather than a different method.
Weights do not need to sum to one
A common misconception is that weights must be percentages adding to 100. They do not. The formula divides by the total of the weights, so any consistent scale works: credit hours, unit counts, or a simple 1-to-5 importance rating.
This matters in practice because it removes a conversion step where mistakes happen. Enter three courses of 4, 3 and 2 credit hours directly — there is no need to turn them into 44.4%, 33.3% and 22.2% first, and doing so only introduces rounding error.
The classic trap: averaging averages
Averaging a set of averages without weighting them is one of the most persistent errors in data work. If one class of 10 students averages 90 and another of 40 averages 60, the overall average is not 75. It is (10×90 + 40×60) ÷ 50 = 66.
The same trap appears in unit prices, fuel economy and survey results. Whenever you are combining figures that each already summarise a different number of items, the counts are the weights, and ignoring them produces an answer that can be badly wrong in either direction.
When to weight, and by what
| Situation | Values | Weights |
|---|---|---|
| Course grade | Component scores | Percentage of final grade |
| GPA | Grade points | Credit hours |
| Average purchase price | Price per unit | Units bought |
| Portfolio return | Return of each holding | Value of each holding |
| Survey result | Response per group | Size of each group |
The weight is always "how much of this there is". Getting the weight wrong — averaging prices by transaction rather than by quantity, for example — is a more common error than getting the arithmetic wrong.
Frequently asked questions
Do the weights have to add up to 100?
No. The calculator divides by whatever the weights total, so you can enter credit hours, quantities or importance ratings directly without converting them to percentages.
Can I use negative weights?
Arithmetically yes, but the result is rarely meaningful. A negative weight subtracts a value from the average rather than including it, which almost never matches what "weighting" is meant to express.
What happens if all the weights are the same?
You get the plain arithmetic mean. The weighted average is a generalisation of the ordinary average, not a competing one.
Why is my weighted average outside the range of my values?
It should never be, if the weights are all positive — the result always lies between the smallest and largest value. If it falls outside, a weight is negative or a value has been mistyped.
Contribution of each value
| Value | Weight | Share of total | Contribution |
|---|---|---|---|
| 90.000000 | 4.000000 | 40.00% | 36.000000 |
| 75.000000 | 3.000000 | 30.00% | 22.500000 |
| 88.000000 | 2.000000 | 20.00% | 17.600000 |
| 62.000000 | 1.000000 | 10.00% | 6.200000 |