How to Calculate Weighted Average
By Tools Star Hub Editorial Team · Published
Quick answer: weighted average = (value₁ × weight₁ + value₂ × weight₂ + …) ÷ (weight₁ + weight₂ + …). For a course where homework scores 80 and counts 20%, the midterm scores 90 and counts 30%, and the final scores 70 and counts 50%, the weighted average is (80×20 + 90×30 + 70×50) ÷ 100 = 78. The Average Calculator finds a simple mean, but you can check a weighted average with it by repeating each value by its whole-number weight: enter 80 twice, 90 three times and 70 five times, and the mean is 78.
Many real averages are weighted: course grades, GPA, a shop’s average selling price, portfolio returns and survey results. Using a simple average where weights apply gives the wrong answer, often by a lot. In the example, the simple average of 80, 90 and 70 is 80, two points higher than the true weighted grade.
What is the weighted average formula?
Multiply each value by its weight, add those products and divide by the sum of the weights. Weights can be percentages, credits, quantities or any measure of importance. If the weights are percentages that add up to 100, dividing by 100 is the same as multiplying each value by its decimal weight and adding: 0.2×80 + 0.3×90 + 0.5×70 = 16 + 27 + 35 = 78.
OpenStax Introductory Statistics uses the same idea when it finds the mean of a frequency table: each value is multiplied by how often it occurs, and the products are divided by the total frequency. Frequencies are simply weights.
How is it different from a simple average?
A simple average, or arithmetic mean, adds the values and divides by how many there are, so every value has a weight of 1. The Average Calculator does this: it accepts up to 1,000 numbers separated by commas, spaces or new lines and shows the mean, the median and the mode.
A simple average is right when every value counts equally, such as daily temperatures. A weighted average is right when some values represent more, such as a test worth half the grade or a product you sold more of.
| Item | Score | Weight | Score × weight |
|---|---|---|---|
| Homework | 80 | 20 | 1,600 |
| Midterm | 90 | 30 | 2,700 |
| Final | 70 | 50 | 3,500 |
| Total | 100 | 7,800 |
Weighted average = 7,800 ÷ 100 = 78. Simple average = (80 + 90 + 70) ÷ 3 = 80.
How can I use the average calculator for a weighted average?
When weights are whole numbers or can be scaled to them, repeat each value as many times as its weight. Weights of 20%, 30% and 50% scale to 2, 3 and 5. Enter 80, 80, 90, 90, 90, 70, 70, 70, 70, 70: the tool reports a mean of 78, a median of 75 and a mode of 70. Only the mean is the weighted average; the median and mode describe the repeated list.
This works because repeating a value is the same as multiplying it by a weight. It is practical for small weights. For weights such as 3.7 or 12.5%, multiply all weights by the same factor to make whole numbers, or use the formula directly.
Is GPA a weighted average?
Yes. GPA weights each course’s grade points by its credits. The GPA Calculator does exactly this: it multiplies each course’s points by its credits, adds them and divides by total credits. A 4-credit A- counts more than a 3-credit A.
So for credit-weighted grades on a 4.0 scale, the GPA Calculator is the easier tool, while the formula or the repeat method handles other weights.
What mistakes should I avoid?
Do not divide by the number of items instead of the total weight. With weights 2, 3 and 5, divide by 10, not 3. Make sure percentage weights add up to 100; if a syllabus lists 20%, 30% and 40%, the missing 10% may be a part you have not entered yet.
Do not average averages without weights. If one class of 10 students averages 70 and another of 30 averages 90, the combined average is (10×70 + 30×90) ÷ 40 = 85, not 80.
How do I find the score I need on a final?
Rearrange the formula. If you have 80 on homework (20%) and 90 on the midterm (30%) and want 85 overall, you need 0.2×80 + 0.3×90 + 0.5×F = 85, so 16 + 27 + 0.5F = 85 and F = 84. Check it by entering 80, 80, 90, 90, 90 and five 84s: the mean is 85.
If the required score is above 100, the target is not reachable with the remaining weight.
How is a weighted average used for money?
Investors use weighted averages for returns. If 6,000 is in a fund that returned 5% and 4,000 in one that returned 10%, the portfolio return is (6,000×5 + 4,000×10) ÷ 10,000 = 7%. The simple average of 5% and 10% is 7.5%, which overstates the result because less money was in the better fund.
Shops use the same idea for average cost. Buying 100 units at 3 and 50 units at 4 gives an average cost of (300 + 200) ÷ 150 ≈ 3.33 per unit. In both cases the weights are amounts of money or quantities, and you divide by their total.
How can I sanity-check my answer?
A weighted average always falls between the smallest and largest values. If your scores are 70, 80 and 90 and you get 95, a step went wrong. It also leans toward the values with the most weight: with half the weight on 70, the answer should be nearer 70 than the simple average is.
If all the weights are equal, the weighted and simple averages must match. Testing your method on equal weights first is a quick way to catch a formula mistake.
Where else do weighted averages appear?
Survey researchers weight responses so a sample matches the population, inflation indexes weight prices by how much households spend on each item, and teachers weight categories in a gradebook. In every case the method is the same: values multiplied by weights, summed and divided by total weight.
How do I calculate a weighted average step by step?
- List values and weights. Write each score or price with its weight, such as 80 at 20%.
- Multiply. Multiply each value by its weight.
- Add the products. Add all the products together.
- Add the weights. Find the total weight, for example 100.
- Divide. Divide the product total by the weight total.
- Check. For whole-number weights, enter each value repeated by its weight in the Average Calculator and compare the mean.
Example
Average price paid
You bought 3 items at 2 and 1 item at 6. Weighted average = (3×2 + 1×6) ÷ 4 = 3. Entering 2, 2, 2, 6 in the calculator also gives a mean of 3, while the simple average of 2 and 6 is 4.
Two class averages
10 students averaged 70 and 30 averaged 90: (700 + 2,700) ÷ 40 = 85.
Course grade
Homework 80 at 20%, midterm 90 at 30%, final 70 at 50%: weighted average 78.
What should I keep in mind?
Weights must be non-negative
A negative weight has no meaning for an average of scores or prices.
Large weights
The repeat method is limited by the calculator’s 1,000-number limit; use the formula for large counts.
Rounding
Round only the final answer, not each product.
FAQ
- What is the weighted average formula?
- Sum of value × weight, divided by the sum of the weights.
- What is the difference between a mean and a weighted mean?
- A mean gives every value equal weight; a weighted mean lets some values count more.
- Do weights have to add up to 100?
- No. Divide by whatever they add up to. Percentages that add to 100 make the arithmetic simpler.
- Can the Average Calculator do weighted averages?
- Not directly, but repeating each value by a whole-number weight gives the weighted mean.
- Is GPA a weighted average?
- Yes. Grade points are weighted by credits, which the GPA Calculator handles.
- Why is my weighted average lower than the simple average?
- The lower values carry more weight, as when a low final counts 50%.
- How do I average two group averages?
- Weight each average by its group size, then divide by the total size.
- How do I find the score needed to reach a target average?
- Rearrange the formula and solve for the unknown score.
- Can I use decimal weights?
- Yes in the formula. For the repeat method, scale them to whole numbers first.
- What happens if the weights are all equal?
- The weighted average equals the simple average.
- How do I enter values and weights in a weighted average?
- List each value with its weight, multiply, sum those products, then divide by the sum of weights.
- What if my weights are percentages that total 100?
- Convert them to decimals or use 100 as the total weight; both approaches match if applied consistently.
- How do course credits act as weights in GPA?
- Each grade’s points are weighted by credit hours, which is a classic weighted average.
- Why can a weighted average sit outside the simple mean of two groups?
- Larger groups pull harder; combining group means needs the original sizes as weights.
- Can weights be greater than one?
- Yes—weights are relative. Only the ratios matter, not a 0–1 limit.
- How do I find the missing score to hit a target average?
- Algebraically solve for the unknown value given remaining weight, or trial values in the calculator.
- What happens with a zero weight?
- That item contributes nothing; ensure you did not mean a missing mandatory component.
- Should survey Likert scores use weighted averages?
- They can if response options carry numeric weights; document the coding.
- How do I weight returns in a simple portfolio example?
- Weight each asset’s return by its portfolio share, then sum the weighted returns.
- Can negative weights appear?
- Rare in schoolwork; in finance they can mean short positions—know the context before using them.
Check your numbers with the free Average Calculator.
Weight grades by credits with the GPA Calculator.
Convert weights to percentages with the Percentage Calculator.
Compare changes in How to Calculate Percentage Change.