How do I calculate a weighted percentage?

Multiply each score by its weight, add those products together, and divide by the sum of the weights. With 78% at weight 20 and 85% at weight 30, that is (78 × 20 + 85 × 30) ÷ 50 = 82.2%. The division by the total weight is what makes it an average rather than a sum, and it is the step most often skipped when the weights happen to total 100 — because then dividing by 100 looks like converting to a percentage.

Why is it different from a normal average?

Because a normal average gives every value the same say, and a weighted one does not. Scores of 78 and 85 average to 81.5; weighted 20 and 30 they come to 82.2, because the higher score carries more weight. The two agree exactly when all the weights are equal — which means an unweighted average is not the neutral option, it is the specific choice that everything counts the same.

Do the weights have to add up to 100?

No. The formula divides by whatever the weights actually total, so weights of 2, 3 and 5 give exactly the same answer as 20, 30 and 50 — only their ratios matter. Credits, contact hours and raw marks all work as weights without conversion. It matters only if you intended them as percentages of a whole, in which case a total other than 100 means a component is missing or mistyped.

How do I work out my grade so far?

Divide by the weight completed rather than the total. If coursework at 20% and a midterm at 30% are done, the standing is computed over 50 — not over 100, which would treat the unsat final as a zero. This page does that automatically when a score is left blank: the component still counts towards the total weight, so the outstanding amount is visible, but only the completed weight goes into the standing.

What do I need on the final to reach my target?

Rearrange the formula: needed = (target × total weight − points already earned) ÷ remaining weight. With 4110 points banked out of a possible 10,000 and 50 of weight left, an 80% overall needs 77.8% on the final and a 90% needs 97.8%. A figure above 100 means the target is no longer reachable — earlier marks have closed it off, and nothing done later reopens it.

Can a weighted average be higher than every value in it?

No, and that is a useful check. A weighted average with non-negative weights always lies between the smallest and largest of the values being averaged, however the weights are distributed. If your result sits outside that range, something has gone wrong — most commonly a negative weight, or dividing by 100 when the weights total something else. It cannot happen through weighting alone.

What happens if a weight is negative?

The result stops meaning anything, and this page ignores negative weights rather than using them. A weight says how much a component counts; a negative one would let a strong score drag the total down and a weak one lift it. It also breaks the guarantee that the answer lies between the smallest and largest input. If you meant a penalty, take it off the score rather than the weight.

Can a weighted average reverse a comparison?

Yes, and it is common enough to have a name. In Charig’s 1986 kidney-stone study, treatment A had a better success rate than B on small stones (93.1% against 86.7%) and on large stones (73.0% against 68.8%), yet a worse rate overall (78.0% against 82.6%). Nothing was miscalculated: A had been used on large stones about 75% of the time and B only 23%, so the overall figures were weighted averages of the same subgroup rates with very different weights. This is Simpson’s paradox.

How do I spot that kind of reversal in my own data?

Look at whether the group sizes differ sharply between the things being compared. A reversal needs two conditions together: the subgroups must have genuinely different rates, and the mix of subgroups must differ between the groups. If both hold, the aggregate can point either way and neither figure is wrong — they answer different questions. The safe move is to report the subgroup rates alongside the total rather than instead of it.

Can I use marks out of different totals as weights?

Yes, provided you convert the scores to percentages first. A test out of 40 and one out of 60 can be weighted 40 and 60, which reproduces adding the raw marks — but the scores going in must be the percentage achieved, not the raw mark, or you will be multiplying marks by marks. Mixing the two is a common slip and produces a figure that looks plausible and is not.

Weighted Percentage Calculator

A weighted percentage multiplies each score by how much it counts, adds those up, and divides by the total weight. The arithmetic is short; the traps are not. The first is averaging the percentages instead. Scores of 78% and 85% average to 81.5, but weighted 20 and 30 they come to 82.2 — and the tw...

weighted = Σ(score × weight) ÷ Σ(weight)

Leave a score blank and that component is treated as outstanding — it counts towards the total weight but not towards what has been achieved, which is how a running standing part-way through is worked out.

THE COMPONENTS

COMPONENTSCORE (%)WEIGHT

weights total 100.0· 50.0 outstanding

STANDING SO FAR

82.20%

Across the 50.0 of weight completed, out of 100.0 in total. This is not a final figure — 50.0 of weight is still outstanding, and the eventual result depends entirely on it.

COMPLETED

50.0 of 100.0

STANDING

82.2%

OUTSTANDING

50.0

82.20% is a standing, not a result. It describes only the 50.0 of weight already scored. Because the outstanding 50.0 is 50% of the total, the final figure could land anywhere from 41.1% — if nothing more is scored at all — up to 91.1% with full marks on the rest. That range is the honest summary of where things stand.

Component	Score	Weight	Share of weight	Contributes
Coursework	78.0%	20.0	20.0%	31.20
Midterm	85.0%	30.0	30.0%	51.00
Final exam	—	50.0	50.0%	pending
Total		100.0	100.0%	82.20

A weighted average can reverse a comparison, which is worth knowing before trusting one. In a well-known 1986 study of kidney-stone treatments, treatment A beat treatment B on small stones — 93.1% against 86.7% — and beat it on large stones too, 73.0% against 68.8%. Overall, A lost: 78.0% against 82.6%. Nothing was miscalculated. A had been used on large stones 75% of the time and B only 23%, so the two overall figures were weighted averages of the same subgroup rates with very different weights. Whenever an aggregate contradicts every part it is built from, the weights are the first thing to look at.

THE BREAKDOWN

A high score on a light component moves the result very little. Each bar is a score multiplied by its share of the weight, so the length reflects both — and a component carrying a tenth of the weight can only ever shift the total by a tenth of its own score.

Live calculation · updates as you type

Created with❤️byeaglecalculator.com

HOW TO USE

1
Enter each component with its score and its weight. The weights can be percentages, marks, credits or hours — anything proportional works, since only their ratios matter.
2
Leave a score blank for anything not yet completed. That component still counts towards the total weight, which is what makes the standing figure honest about how much is outstanding.
3
Read the range rather than the single figure while components are pending. A standing tells you where you are; the range tells you where you could still end up.
4
Check the contribution column. A component carrying a tenth of the weight can only ever move the result by a tenth of its own score, which is often not what people expect.

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Last updated: August 2, 2026 · Σ(score × weight) ÷ Σ(weight) · An unweighted mean is a weighting choice, not the absence of one.