The calculation, without hidden assumptions
A weighted average is not “multiply by percentages and hope they total 100.” The general formula divides the weighted sum by the actual sum of weights, so credits, quantities, probabilities, frequencies or percentages all work when they use one consistent scale. MAXScanner accepts two-column spreadsheet-style value/weight rows or optional three-column label/value/weight rows, normalizes the weights automatically, compares the answer with the plain mean and shows exactly how much each row contributes to the final result.
How to use this calculator
Paste one value and one weight per line, separated by a comma, tab, semicolon or spaces. To keep labels in the audit table, use label,value,weight on each line.
Use any consistent nonnegative weight scale—percentages, credits, quantities or frequencies. The weights do not need to add to 100 because the calculator divides by their actual total.
Compare the weighted result with the plain average, then inspect the contribution table to see each row’s weight share, value×weight product and contribution to the final answer.
Where people use it
- •Course grades and credit-weighted GPA checks
- •Weighted prices, rates and operational KPIs
- •Portfolio or scenario averages when weights represent allocations
- •Combining repeated/grouped values using frequency weights
Example: homework 92×20, midterm 78×30, final 85×50
The products are 1,840, 2,340 and 4,250, giving a weighted sum of 8,430. Divide by the total weight 100 to get a weighted average of 84.3. The row audit makes every contribution visible.
What the result does not assume
- •All weights must use one meaningful scale. Mixing percentages with raw quantities or unrelated scoring systems can produce a mathematically valid number with no useful interpretation.
- •Zero-weight rows are allowed and contribute nothing; negative weights are rejected because most grade, frequency, allocation and quantity use cases expect nonnegative weighting. Specialized models that intentionally use negative weights should use domain-specific analysis.
- •This is the general weighted arithmetic mean. Course-category grading systems that average several assignments inside each category before applying category percentages can require an additional grouping step.
Frequently asked questions
Do weights have to add up to 100?+
No. Multiplying every weight by the same constant does not change the weighted mean because the weighted sum and total weight scale together.
Can weights be percentages or credit hours?+
Yes. Percentages, credits, frequencies, quantities or allocations all work if they are nonnegative and use one consistent meaning across the rows.
How do I paste data from a spreadsheet?+
Copy two columns containing value and weight and paste them into the box; tab-separated spreadsheet rows are accepted. You can also use label,value,weight lines.
Why show the plain average too?+
The difference between the plain and weighted averages reveals how the weighting scheme shifts the result relative to treating every row equally.
Semantic next steps
Continue the calculation
These links move to a different input, formula or project stage rather than a keyword variation of this page.
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MAXScanner keeps the formula and assumptions beside the result so you can verify the number before using it in a drawing, estimate, specification, worksheet or document. Where a supplier, manufacturer, drawing or applicable standard owns a requirement, that source remains authoritative.