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Short answer: The weighted average formula multiplies each value by its weight, adds those products, then divides by the total of the weights.
Weighted average = Σ(value × weight) ÷ Σ(weights)
A regular average treats every value equally. A weighted average gives more influence to values with larger credits, quantities, percentages, or importance.
Weighted average example with grades
Suppose a course grade contains homework worth 20%, a midterm worth 30%, and a final exam worth 50%.
| Component | Score | Weight | Score × weight |
|---|---|---|---|
| Homework | 90 | 0.20 | 18.0 |
| Midterm | 80 | 0.30 | 24.0 |
| Final | 70 | 0.50 | 35.0 |
| Total | — | 1.00 | 77.0 |
The weighted grade is 77%. The simple average of 90, 80, and 70 is 80%, but that is wrong here because the lower final-exam score carries half the grade.
What if weights do not add to 100%?
Divide by the total weight. Imagine three product ratings with 10, 30, and 60 verified purchases:
(4.8 × 10 + 4.2 × 30 + 3.9 × 60) ÷ (10 + 30 + 60)
= (48 + 126 + 234) ÷ 100 = 4.08.
Do not average the three ratings to get 4.3. The product with 60 ratings should influence the combined result six times as much as the product with 10.
Weighted average price example
A shop buys 20 units at $5 and 80 units at $7:
(20 × $5 + 80 × $7) ÷ 100 = $660 ÷ 100 = $6.60 per unit.
This is useful for inventory cost because the larger purchase at $7 deserves more influence. Use the average calculator and guide when checking arithmetic.
Weighted portfolio return example
Assume a hypothetical portfolio begins with 60% in Asset A returning 8% and 40% in Asset B returning −2% over the same period:
(0.60 × 8%) + (0.40 × −2%) = 4.8% − 0.8% = 4.0%.
This simplified calculation uses beginning weights. Contributions, withdrawals, rebalancing, fees, taxes, and changing values require more detailed methods. It is an arithmetic example, not an investment recommendation.
Percent weights versus whole-number weights
If weights add to 100%, convert them to decimals and add the products. If they are counts, credits, or quantities, add the weights and divide by that total.
| Weight format | Correct method |
|---|---|
| 20%, 30%, 50% | Use 0.20, 0.30, 0.50; products already produce the result |
| 2 credits, 3 credits, 5 credits | Add products and divide by 10 total credits |
| 20, 30, 50 units | Add products and divide by 100 total units |
Common mistakes
- Using a simple average: equal treatment is wrong when weights differ.
- Forgetting the denominator: divide by total weight when weights are not normalized to 1.
- Mixing units: do not combine percentages, credit hours, and raw counts without conversion.
- Double-weighting: do not convert a percent to a decimal and then divide by 100 again.
- Ignoring missing categories: a syllabus may renormalize completed work or count missing work as zero.
- Rounding too early: keep several decimals until the final step.
Weighted average in a spreadsheet
If values are in cells A2:A4 and weights are in B2:B4, a common spreadsheet formula is:
=SUMPRODUCT(A2:A4,B2:B4)/SUM(B2:B4)Check for blank cells, text values, and a zero total weight before trusting the result.
Frequently asked questions
What is the difference between weighted average and mean?
A simple arithmetic mean gives each value equal influence. A weighted average multiplies each value by a measure of its relative influence.
Can weights be negative?
Some advanced models allow negative weights, but the result may fall outside the original values. For ordinary grades, prices, and quantities, weights are typically nonnegative.
Do weights have to add to 100?
No. They can be counts or credits. Divide the total of value-times-weight by the sum of weights.
How do I calculate a weighted GPA?
Multiply each course’s grade points by its credit hours, total the quality points, and divide by total GPA credits. Use the GPA calculator for that specific case.
Why is my weighted average outside the expected range?
With nonnegative weights it should lie between the smallest and largest values. A result outside that range usually signals a formula, unit, or data-entry error.