Direct answer: A weighted average gives some values more importance than others: multiply each value by its weight, add the results, and divide by the total weight. For scores of 90 (worth 40%), 80 (worth 30%), and 70 (worth 30%): 90 × 0.40 + 80 × 0.30 + 70 × 0.30 = 36 + 24 + 21 = 81. The plain average would be 80 — but 81 is the real grade, because the 90 counted most.
A plain average treats every number equally. Real life rarely does: a final exam counts more than homework, a 4-credit course counts more than a 3-credit one, and a big survey counts more than a small one. Whenever the values in your list have different importance, a simple average gives the wrong answer — sometimes by a little, sometimes by a lot. This guide shows you the weighted average formula, three worked examples with exact numbers, and the traps to avoid. If you need the basics first, start with our guide on how to find the average.
What Is a Weighted Average?
A weighted average is an average in which each value is multiplied by a weight — a number that says how much that value counts — before the values are combined. The weights can be percentages (40%, 30%, 30%), decimals (0.40, 0.30, 0.30), or whole numbers (3 credits, 2 credits, 1 credit). What matters is the ratio between them.
The plain average is just a special case: a weighted average where every weight is equal. That is why the weighted average is the more general tool — and why every grade average in school is really a weighted average, whether the syllabus says so or not.
The Weighted Average Formula
Weighted Average = Σ(Value × Weight) ÷ Σ(Weights)
In plain words:
- Multiply each value by its weight.
- Add all those products together.
- Divide by the sum of the weights.
If the weights are percentages that add to 100%, step 3 is just dividing by 1 (or by 100, if you kept the percentages as whole numbers) — the division still matters, so never skip it.
Worked Example: Weighted Average of Grades (90, 80, 70 = 81)
A student’s scores are: an exam worth 40% (score 90), homework worth 30% (score 80), and quizzes worth 30% (score 70).
| Assessment | Score | Weight | Contribution |
|---|---|---|---|
| Exam | 90 | 40% (0.40) | 90 × 0.40 = 36 |
| Homework | 80 | 30% (0.30) | 80 × 0.30 = 24 |
| Quizzes | 70 | 30% (0.30) | 70 × 0.30 = 21 |
Add the contributions: 36 + 24 + 21 = 81.
Divide by the total weight: 0.40 + 0.30 + 0.30 = 1.00, so 81 ÷ 1 = 81.
The weighted average is 81 — not 80. The plain average (90 + 80 + 70) ÷ 3 = 80 ignores the fact that the 90 was worth the most. One point may not sound like much, but on a grade boundary it is the difference between a B and an A-. You can check this example instantly with Calcrio’s free weighted average tool.
Worked Example: Credit Hours (GPA-Style Average)
Course credits act as weights. A student takes three courses:
| Course | Grade points | Credits | Weighted points |
|---|---|---|---|
| Mathematics | 3.7 | 4 | 3.7 × 4 = 14.8 |
| English | 3.3 | 3 | 3.3 × 3 = 9.9 |
| Science | 4.0 | 4 | 4.0 × 4 = 16.0 |
Add the weighted points: 14.8 + 9.9 + 16.0 = 40.7.
Divide by the total credits: 4 + 3 + 4 = 11, so 40.7 ÷ 11 = 3.70.
The credit-weighted average is 3.70. Notice it is not the plain average of the grade points (3.7 + 3.3 + 4.0) ÷ 3 = 3.67 — the 4-credit courses pull the result slightly toward their grades. The exact GPA scale and grading rules vary by institution, so always use your school’s policy.
Worked Example: Weights That Do Not Add to 100%
Weights do not have to be percentages. A teacher weights three assignments 3, 2, and 1:
| Assignment | Score | Weight | Contribution |
|---|---|---|---|
| Project | 90 | 3 | 90 × 3 = 270 |
| Test | 80 | 2 | 80 × 2 = 160 |
| Quiz | 70 | 1 | 70 × 1 = 70 |
Add the contributions: 270 + 160 + 70 = 500.
Divide by the total weight: 3 + 2 + 1 = 6, so 500 ÷ 6 = 83.33.
The weighted average is about 83.33. This is the step people skip most often: when the weights do not add to 1 or 100, you must divide by their total. Skipping the division gives 500 — a meaningless number.
Weighted Average vs Simple Average: Side by Side
| Simple average | Weighted average | |
|---|---|---|
| Every value counts | Equally | According to its weight |
| Formula | Sum ÷ count | Σ(value × weight) ÷ Σ(weights) |
| 90, 80, 70 (weights 40/30/30) | 80 | 81 |
| 3.7, 3.3, 4.0 (credits 4/3/4) | 3.67 | 3.70 |
| Use when | All values matter equally | Some values matter more |
The difference is usually small — one point, or three hundredths of a GPA point. But small differences decide grade boundaries, scholarships, and admissions cutoffs, which is why teachers weight grades in the first place.
A Real-World Cross-Check
An independent check from a weighted-average tool confirms the method: scores of 75, 90, and 88 (25% each), a quiz of 70 (15%), and homework of 86 (10%).
75 × 0.25 = 18.75; 90 × 0.25 = 22.5; 88 × 0.25 = 22; 70 × 0.15 = 10.5; 86 × 0.10 = 8.6. Total: 18.75 + 22.5 + 22 + 10.5 + 8.6 = 82.35. The plain average is (75 + 90 + 88 + 70 + 86) ÷ 5 = 409 ÷ 5 = 81.8. Again, weighting pulls the result toward the heavy weights — the three 25% scores dominate, and the 10% homework barely moves the needle.
The same math runs investments. Put $30,000 in an account earning 5%, $6,000 at 6%, and $4,500 at 7%: the returns are $1,500 + $360 + $315 = $2,175 on $40,500 invested, so the weighted return is 2,175 ÷ 40,500 = 5.37% — not the plain average of the three rates (6%). The biggest pot dominates, exactly as the biggest exam dominates a grade.
3 Common Mistakes with Weighted Averages
Mistake 1: Forgetting to divide by the total weight. If your weights are 3, 2, and 1, you must divide by 6. The sum of the products alone is not an average.
Mistake 2: Using a plain average for weighted grades. A final exam worth 40% should not count the same as an assignment worth 5%. If the syllabus gives weights, use them.
Mistake 3: Mixing up percentages and decimals. 40% is 0.40 in the multiplication. Using 40 instead of 0.40 gives an answer 100 times too big — a mistake that is easy to spot, because the answer will be far outside the range of the scores.
When to Use a Weighted Average
- Grades: exams, homework, and quizzes with different weights — the most common case in school.
- Credit hours: GPA-style averages where courses carry different credits.
- Surveys and polls: combining results from groups of different sizes (see the percentage trap in our guide to how to find the average of grades).
- Prices: the average price paid when you buy different quantities at different prices.
- Speeds: trips with different speeds over different times need total distance over total time — see the average speed formula.
And when the data has outliers, remember that a weighted average is still an average — it can be pulled by extremes. Check the average vs median vs mode guide when one huge value might be distorting the picture.
Check Your Work with Calcrio’s Free Tool
The free tool at Calcrio handles weighted averages: enter each value with its weight and it returns the weighted average, the plain average for comparison, and the full breakdown. It is free, with no sign-up — and the best way to check a grade calculation before it goes on a report card.
Frequently Asked Questions
What is a weighted average?
A weighted average is an average that gives different values different weights: multiply each value by its weight, add the results, and divide by the total weight. The formula is Σ(value × weight) ÷ Σ(weights).
How do you calculate a weighted average of grades?
Multiply each score by its weight as a decimal, add the results, and divide by the total weight. For 90 (40%), 80 (30%), 70 (30%): 90 × 0.40 + 80 × 0.30 + 70 × 0.30 = 36 + 24 + 21 = 81.
What is the difference between a weighted average and a simple average?
A simple average treats every value equally. A weighted average gives some values more importance. For 90, 80, 70 with weights 40%, 30%, 30%, the simple average is 80 and the weighted average is 81.
Do weights have to add up to 100%?
No. Weights can be any numbers — percentages, decimals, or whole numbers like credit hours (4, 3, 4). You just have to divide by the sum of the weights at the end.
How do you calculate a GPA with credit hours?
Multiply each grade point by its course credits, add the results, and divide by the total credits. For 3.7 (4 credits), 3.3 (3 credits), 4.0 (4 credits): (14.8 + 9.9 + 16.0) ÷ 11 = 3.70.
When should I use a weighted average instead of a simple average?
Whenever the values do not count equally — weighted grades, credit hours, surveys of different sizes, or prices for different quantities. If every value counts the same, the simple average is correct.