Weighted Average Calculator
When some values matter more than others, a plain average is wrong. A weighted average multiplies each value by its importance before averaging, so a 4-credit course or a $50,000 holding counts for what it is actually worth.
Formula
- xᵢ
- = each value
- wᵢ
- = the weight attached to that value
- Σ
- = the sum across all items
The weights do not need to sum to 1 or to 100. Dividing by their total normalises them automatically, so raw credit hours, dollar amounts or counts can be entered directly.
How to use this calculator
- Enter your values in the first box — scores, prices, rates, whatever is being averaged.
- Enter the matching weights in the second box, in the same order. The counts must match, and the calculator says so if they do not.
- Press Calculate. The weighted average appears alongside the plain mean so you can see how much the weighting changed the answer.
- Open the contribution table to see how much of the total weight each item carried — that is usually where a surprising result is explained.
Worked example
A semester GPA across four courses
Scores of 88, 92, 75 and 96 in courses worth 3, 4, 2 and 1 credits. The plain average of the four scores is 87.75, but the 92 carries four credits and the 96 only one.
- 88×3 + 92×4 + 75×2 + 96×1 = 264 + 368 + 150 + 96 = 878
- Total weight: 3 + 4 + 2 + 1 = 10
- 878 ÷ 10 = 87.8
Answer: 87.8 weighted, against 87.75 unweighted — close here, but the gap widens as weights become more uneven.
What weighting actually does
A plain mean is a weighted average where every weight is 1. That is a real assumption, not a neutral default: it asserts that a 1-credit seminar counts as much as a 5-credit core course, or that a $500 holding counts as much as a $50,000 one. Weighting replaces that assumption with the one you actually intend.
Because the formula divides by the sum of weights, the scale of the weights is irrelevant. Weights of 3, 4, 2, 1 give exactly the same answer as 30, 40, 20, 10 or 0.3, 0.4, 0.2, 0.1. Only the ratios matter, which is why you can enter raw credit hours or dollar amounts without normalising them first.
Where weighted averages are the correct tool
Academic grades. Course credits weight a GPA; assignment categories weight a course grade. A final worth 40% and homework worth 10% are not equal inputs.
Investment returns. A portfolio's return is the weighted average of its holdings' returns, weighted by their value. Averaging the percentage returns of each holding equally would describe a portfolio you do not own.
Pricing and cost. Average selling price across products sold in different volumes, or weighted average cost of capital across debt and equity in different amounts.
Survey and poll aggregation. Larger samples carry more information, so poll averages weight by sample size — and often by recency and pollster quality as well.
The bounds a weighted average must respect
A weighted average with non-negative weights always falls between the smallest and largest values. If your result sits outside that range, something is wrong — almost always a negative weight or a mismatched pairing of values and weights.
It also cannot be "pulled" past a value by weighting alone. Giving one item 99% of the weight moves the answer very close to that item's value, but never beyond it. This makes the bounds a useful sanity check on any weighted calculation.
| Values | Weights | Weighted | Unweighted |
|---|---|---|---|
| 88, 92, 75, 96 | 3, 4, 2, 1 | 87.80 | 87.75 |
| 88, 92, 75, 96 | 1, 1, 8, 1 | 79.55 | 87.75 |
| 10, 90 | 9, 1 | 18.00 | 50.00 |
| 10, 90 | 1, 9 | 82.00 | 50.00 |
Common weighting schemes
Weights are usually a count (credits, units, respondents), a value (dollars, shares), or a declared importance (a syllabus saying the final is 40%). All three work identically in the formula. What differs is how defensible they are — a count is objective, a declared importance is a judgement that should be stated openly.
If your weights are percentages that should total 100 but do not, the calculator still produces a mathematically correct answer by normalising them. That can hide a data-entry error, so the total weight is shown in the breakdown for you to check.
Important considerations
- Values and weights must be listed in the same order and in equal numbers.
- Weights of any scale work — only their relative sizes matter.
- Negative weights are rejected, because they can push the result outside the data range.
- A total weight of zero makes the average undefined.
- Check the total weight against what you expected; a mismatch often reveals a missing item.
Common mistakes to avoid
- Mismatching the two lists. A missing weight silently shifts every pairing after it.
- Using a plain average when weights differ. This treats a 1-credit course as equal to a 5-credit one.
- Normalising weights unnecessarily. The formula does it for you; converting to percentages first only adds rounding error.
- Averaging weighted averages. Combine the underlying sums instead, or weight the sub-averages by their total weights.
- Ignoring a total weight that is not what you expected. That is usually an omitted or duplicated item.
Frequently asked questions
How do I calculate a weighted average?
Multiply each value by its weight, add all those products, then divide by the sum of the weights. For scores 88, 92, 75, 96 with credits 3, 4, 2, 1: 878 ÷ 10 = 87.8.
Do the weights have to add up to 100?
No. The formula divides by the total weight, so any scale works. Credits of 3, 4, 2, 1 give exactly the same result as percentages of 30, 40, 20, 10.
What is the difference between a weighted average and a normal average?
A normal average treats every value as equally important — it is a weighted average where all weights are 1. A weighted average lets some values count more, which is correct whenever the items genuinely differ in size or importance.
Can a weighted average be outside the range of my values?
Not with non-negative weights. The result always lies between the smallest and largest value. If it does not, check for a negative weight or a mismatch between the two lists.
How do I use this for course grades?
Enter your score in each category as a value and the category's percentage of the final grade as its weight. For a dedicated tool with categories, use the weighted grade calculator.
What if two items have the same weight?
That is fine and common — equal weights among some items simply mean those items count equally against each other while still differing from the rest.
Related calculators
Tools people usually open alongside this one.
Average Calculator
Mean, median, mode and range from one list of numbers, with the sorted data shown.
Open calculator
Median Calculator
The middle value of a data set, with quartiles and the interquartile range.
Open calculator
Geometric Mean Calculator
The right average for growth rates and ratios — the nth root of the product.
Open calculator
Percentage of Total Calculator
Convert a list of numbers into percentage shares of their total.
Open calculator