Math
Weighted Average Calculator
Calculate an average from values or percentage grades and their weights. See each entry's contribution and how the weights are normalized.
Your details
Enter your details below
Your result
Based on the values you enter
Useful next checks
- Use the result to check your working or homework.
- Change one input at a time to see how the answer moves.
- Read the method below if you want the steps.
Intro
Use this weighted average calculator to combine values that have different importance. Choose ordinary numbers or percentage grades, enter each value and its weight, and see the weighted mean and every row's contribution.
What this calculator does
Select between two and ten entries. In Numbers mode, values can be positive, zero or negative. In Percentage grades mode, enter numeric grades from 0 to 100. Weights are nonnegative relative amounts; at least one must be positive.
You can use weights such as 20 and 80, 2 and 8, or 0.2 and 0.8. Each pair has the same 1-to-4 relationship and produces the same weighted mean. Every active row must be filled, even if its weight is zero.
For equally important numbers, use equal weights or the Average Calculator.
How it works
Weighted average = sum(value × weight) ÷ sum(weights).
For each row, multiply its value by its weight. Add those products and divide by the total weight. Equivalently, divide each weight by the total first, then multiply each value by its normalized share.
The official R stats documentation for weighted arithmetic mean describes normalizing weights to sum to one and excluding zero-weight values from the sum. This calculator still requires a valid finite value in every active row, including zero-weight rows.
The result table shows each row's normalized contribution, not its unnormalized value-times-weight product. In grade mode these contributions are percentage points of the displayed average.
Example calculation
Suppose one assignment grade is 80% with weight 20, and another is 90% with weight 80.
- Assignment 1: 80 × (20 ÷ 100) = 16 percentage points.
- Assignment 2: 90 × (80 ÷ 100) = 72 percentage points.
- Add the contributions: 16 + 72 = 88%.
The calculation is (80 × 20 + 90 × 80) ÷ (20 + 80) = 88%. The ordinary average of 80 and 90 is 85%; the weighted average is higher because 90 has more weight.
Mercer University's weighted grade calculator illustrates this assignment-grade and course-weight workflow. Your own course's weights and grading policies must come from your instructor.
How to use the result
Check that every weight describes the same basis. If your weights are course percentages, do not mix them with assignment point totals in the same calculation.
The tool normalizes across the entries you supplied, even when the weights do not add to 100. For grades of 80 and 90 with weights 20 and 30, the average for those listed assignments is 86%. This does not predict the unlisted half of a course or treat missing assignments as zero.
For ordinary Numbers mode, a value of -10 at weight 1 and a value of 20 at weight 3 give 12.5: (-10 + 60) ÷ 4. All values must use the same meaningful units.
Averaging percentages
An equal-weight average of 50% and 100% is 75%. That is not always the overall percentage of two groups.
If the first score is 1 out of 2 and the second is 100 out of 100, the combined score is 101 out of 102, about 99.02%. Giving the two percentages equal weight would answer a different question. This page accepts percentages and explicit weights; it does not pool raw earned/possible scores automatically.
Assumptions and limitations
- Grades mode accepts numeric percentage scores from 0 to 100 only. Extra-credit scores above 100, letter grades, GPA, final-exam targets and school-specific grading rules are outside this tool.
- A zero individual weight is allowed and contributes zero. A zero total weight is undefined.
- All active rows require finite values and weights. Hidden rows are excluded from the calculation; selecting them again restores their fields.
- The final average uses up to four decimal places. Supporting contributions use up to six. Small nonzero or very large values use scientific notation rather than displaying a false zero or an unreadably long number.
- Browser Number arithmetic has finite precision. The tool rejects non-finite total weights and cases where scaling or a positive-weight contribution collapses. Rescale weights by a common factor, or use values closer in magnitude.
- Rounded table contributions may not add exactly to the rounded answer.
- Results describe only the entered data and chosen weights. No missing-data estimate or statistical significance test is performed.
Frequently asked questions
Do the weights need to add up to 100?
No. Each weight is divided by the total entered weight. For example, weights 20 and 80 give the same result as 2 and 8. At least one weight must be positive.
Can I use this for percentage grades?
Yes. Choose Percentage grades and enter numeric scores from 0 to 100 with their weights. The result describes the assignments listed; it does not predict missing assignments or assign a letter grade or GPA.
Can an individual weight be zero?
Yes. That entry contributes zero, but its value must still be valid. All weights cannot be zero because division by a zero total is undefined.
Is the average of percentages the same as a combined score?
Only when the weights represent the intended comparison. An equal-weight average of percentages can differ from a combined earned-points percentage when the original totals differ. This tool does not pool raw scores automatically.