Weighted Average Calculator
Calculate a weighted average from values and their weights — course grades, GPA, portfolio returns or scored criteria — with the weight-by-weight breakdown, the impact versus a simple average, and every step of the working.
Written by Suhaib Hassan. The formula and both worked examples on this page are re-derived by hand before publishing. Our methodology.
It multiplies each value by its weight, adds the products, and divides by the total of the weights. Weights can be percentages, credits, dollars or any other size measure.
Weights rarely sum to exactly 100. This tool works either way, shows each item's share of the result, and compares it with the plain average.
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How the weighted average is derived
A simple mean treats every observation as equally important. The weighted mean lets each observation count in proportion to its weight, so a heavy item moves the result more than a light one.
The formula
Multiply each value xᵢ by its weight wᵢ, add those products, then divide by the sum of the weights. Dividing by Σw is what makes the result a true average whatever units the weights use.
When weights are percentages
If the weights already total 100%, the denominator is 1 and the weighted mean is simply Σ(wᵢ · xᵢ) with each weight written as a fraction. If they do not total 100%, dividing by Σw rescales them automatically.
Variable glossary
What each symbol means and what values it can take.
| Symbol | Name | Allowed values | Meaning |
|---|---|---|---|
| x̄w | Weighted mean | Between the smallest and largest x (for non-negative weights) | The weighted average result. |
| xᵢ | Observed value | Any real number | A score, return, rating or measurement. |
| wᵢ | Weight | Usually ≥ 0 | How much xᵢ counts: a percentage, credit hours, dollars invested, and so on. |
| Σwᵢ | Sum of weights | Must not be 0 | The denominator. If it is zero the mean is undefined. |
Two worked examples
Both are checked by hand, and both can be reproduced above (the second uses a different weight scale).
Course grade percent weights
A student scores 78 on homework (20%), 85 on the midterm (30%) and 92 on the final (50%).
= 15.6 + 25.5 + 46.0 = 87.1
Σw = 0.20 + 0.30 + 0.50 = 1.00
Weighted average = 87.10 ÷ 1.00 = 87.10
Contrast: the simple average is (78 + 85 + 92) ÷ 3 = 85.00. The heavy final exam lifts the result by 2.10 points.
Portfolio return dollar weights
$50,000 earns 12%, $30,000 earns 8% and $20,000 earns 4%.
= 600,000 + 240,000 + 80,000 = 920,000
Σw = 100,000
Weighted return = 920,000 ÷ 100,000 = 9.20%
Contrast: the simple average is (12 + 8 + 4) ÷ 3 = 8.00%. The largest holding earns the most, so the portfolio return is 1.20 points higher.
Where weighted averages are used
Wherever items are not equally important, a simple average misleads.
Grades & GPA
Exams usually count for more than homework, and a 4-credit course counts for more than a 1-credit seminar in a grade point average.
Weight: percent or credit hoursPortfolio returns
A portfolio's return is the average of its holdings' returns weighted by how much money is in each.
Weight: amount investedScoring matrices
Vendor or product scoring gives more weight to the criteria that matter most, such as security over appearance.
Weight: priorityWhat is a weighted average?
A weighted average (weighted arithmetic mean) is an average in which each value counts according to an assigned weight. It is the right tool when some observations represent more of the total than others.
How to calculate a weighted average
- Multiply each value by its weight.
- Add the products together.
- Add the weights together.
- Divide the sum of products by the sum of weights.
By Suhaib Hassan · Reviewed 28 September 2026 · How CalculatePilot verifies formulas →
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods — 1.3.5.1 Measures of location (background on the arithmetic mean).
- ISO 3534-1:2006, Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in probability.
What grade do I need on the final exam?
To find the score you need on a remaining assignment, rearrange the weighted average formula:
needed score = (target grade − current grade × (1 − final weight)) ÷ final weight
Example: you have 82% going into a final worth 30% of the course and want an 85% overall. Needed = (85 − 82 × 0.70) ÷ 0.30 = (85 − 57.4) ÷ 0.30 = 92%. For an overall 80% the same formula gives about 75.3%. If the result is above 100%, the target cannot be reached without extra credit.
Frequently asked questions
What is the difference between a simple mean and a weighted average?
A simple mean gives every value the same importance: add and divide by the count. A weighted average lets each value count in proportion to its weight, so items with larger weights influence the result more.
What happens if the weights do not add up to 100?
Nothing goes wrong: the calculation divides by the total of the weights, so it rescales them automatically. For example weights of 2, 3 and 5 give the same result as 20%, 30% and 50%. This page flags a total other than 100 only so you can check for a typing slip.
Can weights be negative?
Mathematically the formula still works, but negative weights are unusual and can push the result outside the range of the values. In grading and finance weights are normally zero or positive, and this page warns you if any weight is negative.
How does a zero weight affect the result?
A zero-weight item contributes nothing to the numerator or the denominator, so it does not change the weighted average. It still counts in the simple average shown for comparison.
How do I calculate a GPA with this?
Enter each course's grade points (for example A = 4.0) as the value and its credit hours as the weight. The weighted average is your GPA on that scale. Check your institution's own grade-point conversion.
What if the sum of weights is zero?
The average is undefined because the formula would divide by zero. Give at least one item a non-zero weight.
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