A weighted average with the weights on any scale you like.
Who this is for: Course grades, portfolio returns, anything where the items are not equally important.
Values and their weights
Any scale of weights works.
One weight per value, in the same order. They do not have to add to 100.
3 values, total weight 100
83
The plain average would be 80.
Weighted average
83
each value counted by its weight
Plain average
80
every value counted once
The gap
+3
what the weights are doing
Largest share
50.0%
the value 90
What each row contributes
Each value with its weight, its share of the total and what it contributes to the answer
Value
Weight
Share
Contributes
Away from mean
90
50
50.00%
45
+7
80
30
30.00%
24
−3
70
20
20.00%
14
−13
The contributions add up to the answer. That is the whole calculation — each value scaled by its share of the total weight.
The weights add to 100, so each is already a percentage of the total. Dividing by 100 at the end is exactly what the formula does anyway.
The plain average of these values is 80; the weighted one is 83. The 3 gap is what the weights are doing, and it is why "just average them" gives a different answer.
90 carries the largest share at 50%; drop it and the answer moves to 76.
The weights are used as given — no normalisation step for you to get wrong.
What this tool shows
Weights do not have to add to 100. The formula divides by their total, so 2, 3 and 5 gives exactly the same answer as 20%, 30% and 50% — and normalising them yourself first only adds a chance to slip.
A weighted average from values and weights
Weights on any scale, not just percentages
What each row contributes to the answer
The plain average, for comparison
Which value carries the largest share
What the answer would be without it
Any scale of weights Plain average shown beside it Per-row contributions Zero weights allowed
Updated 7 September 2026 · Works in any browser, no installation
Multiply each value by its weight, add those up, and divide by the total of the weights. Marks of 90, 80 and 70 weighted 50, 30 and 20 give (4500 + 2400 + 1400) ÷ 100 = 83 — not the 80 you get by averaging them plainly. The weights do not have to add to 100: 5, 3 and 2 gives the same 83, because the total is what the formula divides by.
At a glance
Formula shown
Weighted mean = Σ(value × weight) ÷ Σ(weight). Because the denominator is the total of the weights, any consistent scale gives the same answer.
Scenario support
A course mark from components worth different percentages; a GPA from credit-weighted grades; an average price paid across purchases of different sizes.
Not the average of the averages
This is the mistake worth naming. Given marks of 90, 80 and 70, the obvious move is to add them and divide by three, which gives 80. If the components are worth 50%, 30% and 20%, the answer is 83.
Three marks is a small enough example that the gap looks minor. It is not always: a 95 on something worth 5% and a 60 on something worth 95% averages plainly to 77.5 and weights to 61.75 — a difference between a good grade and a poor one.
The page shows both numbers every time for exactly that reason. If they differ, the weights are doing something, and the difference is the size of what they are doing.
Weights do not have to add to 100
A weighted average divides by the total of the weights. So the SCALE of the weights cancels entirely: 2, 3 and 5 gives the same answer as 20%, 30% and 50%, or as 200, 300 and 500.
Tools that demand percentages have added a constraint the mathematics does not have, and the usual consequence is people normalising by hand — dividing by the total, rounding each to two places, and introducing an error that was never necessary.
Use whatever the weights naturally are. Credits, quantities purchased, headcounts, hours worked — all of them work as they stand.
Where weighted averages come up
Course marks. Components worth different percentages. The commonest reason anyone visits a page like this.
GPA. Grade points weighted by credit hours, so a four-credit course moves the average twice as far as a two-credit one. TheGPA Calculator does that specific job end to end.
Average price paid. Buying 100 at 12.50 and 250 at 9.75 is not an average of 11.13 — it is 10.54, because more units came at the lower price.
Index numbers. A consumer price index is a weighted average whose weights are how much people actually spend on each thing. Choosing those weights is most of the work in building one.
A zero weight is not a missing value
Giving a row a weight of zero removes it from the answer completely while leaving it visible in the list. That is often exactly what you want.
A dropped assignment, an excluded outlier, a product that was not stocked this month — all of them are better recorded as present with no weight than quietly deleted, because the row still shows what was excluded.
A NEGATIVE weight is a different matter and is refused here. It would subtract a value from the average rather than counting it less, which is not what anyone means by weighting.
Weighting is a judgement, not a calculation
The arithmetic on this page is exact. The weights are not: they are a claim about how much each value should matter, and that claim comes from outside the mathematics.
It is also where weighted averages get abused. Any desired answer can be produced by choosing weights to suit it, and a weighted figure quoted without its weights is not checkable at all.
So publish the weights alongside the answer. This page shows every share as a percentage for that reason — the reader can see what was decided before they see what it produced.
Checking a weighted answer
It must lie between the smallest and largest value. Always, whatever the weights. An answer outside that range means a sign error or a mispaired weight.
It leans towards the heavily weighted values. If the largest weight sits on the smallest number, the answer should be below the plain average. The page shows each row's distance from the answer so that lean is visible.
Equal weights must reproduce the plain average. A quick sanity check on any implementation, and one the suite runs.
Sources and methodology
The weighted mean is elementary; these are where its uses are defined.
Method. Values and weights are paired in order and the mean is Σ(value × weight) ÷ Σ(weight). No normalisation is applied first, because none is needed and doing it would introduce a rounding step. The unweighted mean is computed separately and shown alongside, and the suite asserts scale invariance directly: multiplying every weight by a constant must not move the answer. That engine is verified on every change against 61 hand-written assertions, including that scaling every weight by any constant leaves the answer unchanged across fifteen hundred generated cases. The count and the per-case breakdown are published on the formula verification page.
Related calculators
Where this goes next:
Geometric MeanThe average for things that compound. Growth of +50% then -50% averages to zero arithmetically and to a real 13.4% loss geometrically, which is what actually happened.
Harmonic MeanSixty there and forty back averages 48, not 50. The page simulates the journey from its legs as well as computing the formula, so the answer arrives with its own proof.
GPACalculate your GPA from letter grades or percentages and credit hours, or combine a new term with your existing cumulative GPA.
GradeCalculate your weighted overall grade from categories or points, or find the score you need on your final exam.
Standard DeviationSample and population standard deviation, plus variance, mean, median, quartiles, z-scores, outliers, and confidence intervals.
PercentageSolve X% of Y, what percent X is of Y, reverse percentage, increase/decrease, discounts, and tax, tip, or commission.
A weighted arithmetic mean is the right average when the quantities add. When they multiply — growth rates, index ratios, anything chained period on period — the geometric mean is the correct one, and when they are rates over a fixed distance or quantity, such as speeds over equal legs, the harmonic mean is. Using the arithmetic mean on either overstates the answer, which is the commonest averaging error there is and the one that survives review most easily.
Educational use disclaimer
This is an educational tool. The arithmetic is exact for the numbers entered; choosing the right weights is a judgement about your data rather than a calculation.
Published the weighted average page showing each item's share of the total weight, because the useful question is usually which entry is dominating the answer rather than what the answer is.
Weights are normalised rather than required to sum to one, so raw credit hours or dollar amounts can be entered as they come.
The unweighted mean is computed alongside, so the difference the weighting made is visible instead of implied.
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