Key takeaways
- Weighted average = (v₁w₁ + v₂w₂) ÷ (w₁ + w₂).
- Divide by the total weight, not by the number of values.
- Weights do not need to add up to 100. Only their ratio matters.
- The answer is pulled toward the value with the bigger weight.
In this guide
What is a weighted average?
In a normal average, every number counts the same. But suppose your homework is worth 40% of your grade and your exam is worth 60%. The exam should matter more.
A weighted average gives each value a weight that shows how important it is. Bigger weight, bigger influence.
Why does a weighted average matter?
A plain average can be unfair or simply wrong when things are not equally important. If you buy 10 kg of rice at $2 and 1 kg at $5, the average price you paid per kg is not $3.50. The 10 kg matters far more.
With homework 85 (40%) and exam 72 (60%), the plain average is 78.5 but the weighted average is 77.2. The lower exam mark counts more, so it pulls the grade down.
The formula
This calculator combines two values:
| Symbol | What it means | Example |
|---|---|---|
| v₁ | The first value | 85 (homework) |
| w₁ | Weight of the first value | 40 |
| v₂ | The second value | 72 (exam) |
| w₂ | Weight of the second value | 60 |
| w₁ + w₂ | The total weight | 100 |
Dividing by the total weight means the weights do not have to add up to 100. Weights of 40 and 60, 0.4 and 0.6, or 2 and 3 all give the same answer.
How to calculate a weighted average step by step
- 1Multiply each value by its weight.
85 × 40 = 3,400and72 × 60 = 4,320. - 2Add those products.
3,400 + 4,320 = 7,720. - 3Add the weights.
40 + 60 = 100. - 4Divide.
7,720 ÷ 100 = 77.2.
Now enter your own values and weights in the calculator below.
Try it yourself
Pre-filled with the example — change any value.
Common mistakes to avoid
- Mixing up values and weights. The weight is how much something counts, not the score itself.
- Using the plain mean. It treats unequal things as equal and gives the wrong answer.
- Weights that add to 0. The total weight must be more than 0, or you would divide by zero.
Tips and tricks
- Simplify the weights. 40 and 60 can become 2 and 3. The answer does not change:
(85 × 2 + 72 × 3) ÷ 5 = 77.2. - More than two values? Multiply every value by its weight, add them all, and divide by the sum of all the weights.
- Grades with credits? The GPA calculator does the credit-weighted version for you.
Where you'll use it in real life
- School: final grades from homework, tests and exams with different weights.
- Shopping: the average price per kg when you buy at different prices.
- Investing: the average price of shares bought at different times.
- Surveys: combining results from groups of different sizes. For a share of a total, the percentage calculator helps too.
Quick summary
To find a weighted average, multiply each value by its weight, add the results, and divide by the total weight. The answer leans toward the values that count most. Use the calculator above to combine two weighted values with every step shown.
Worked example
In your science course, homework is worth 40% of the final grade and the final exam is worth 60%. You scored 85 on homework and 72 on the exam.
- 01Weighted Average = (v₁w₁ + v₂w₂) / (w₁ + w₂)
- 02= (85×40 + 72×60) / (40 + 60)
- 03= (3400 + 4320) / 100
- 04= 7720 / 100
- 05= 77.2
These numbers are pre-filled in the calculator above.
Frequently asked questions
What is the difference between an average and a weighted average?
A plain average treats every value equally. A weighted average multiplies each value by its importance first, so values with bigger weights pull the answer toward them.
Do the weights have to add up to 100?
No. The formula divides by the total weight, so weights of 2 and 3 give the same result as 40 and 60.
How do I use more than two values?
Multiply every value by its weight, add all the products, and divide by the sum of all the weights. The idea is the same for any number of values.
What exam mark do I need for a target grade?
Work backwards. With homework 85 at 40% and a target of 80, you need 85 × 0.4 + x × 0.6 = 80, so x = (80 − 34) ÷ 0.6 ≈ 76.7 on the exam.
