Weighted Average Calculator

How to use the calculator

1. Enter the values in the first box, separated by commas, spaces or line breaks: grade points, scores, returns, prices.
2. Enter the weights in the second box, in the same order: credit hours, percentages, dollar amounts or quantities. The first weight belongs to the first value, the second to the second, and so on.
3. Use a period for decimals and leave out thousands separators and symbols, so write 30000, not $30,000.
4. Read the results: the weighted mean first, then the sum of weights, the sum of products, the simple mean and the number of values.

Both lists must have the same length. Weights can't be negative, and at least one weight must be greater than zero.

The weighted average formula

Multiply each value by its weight, add up the products and divide by the sum of the weights:

weighted mean = Σ(xᵢ × wᵢ) ÷ Σwᵢ

The weights don't have to add up to 1 or 100. Because the calculator divides by their total, weights of 20, 30 and 50 give exactly the same result as 0.2, 0.3 and 0.5, and credit hours of 3, 4 and 3 work as they are. Only the proportions between weights matter.

If every weight is the same, the weighted mean equals the simple mean. The calculator shows both so you can see how much the weighting changes the answer. A weight of zero keeps a value in the list without letting it affect the result.

Examples

1. GPA weighted by credit hours

A semester with an A (4.0) in a 3-credit course, a B+ (3.3) in a 4-credit course, an A− (3.7) in a 3-credit course and a C (2.0) in a 1-credit lab. Enter 4.0, 3.3, 3.7, 2.0 as values and 3, 4, 3, 1 as weights. Quality points total 38.3 over 11 credits, so the GPA is 3.48. Averaging the four grades without credits would give 3.25.

2. Course grade with category weights

A syllabus counts homework 20%, quizzes 30% and the final exam 50%. With 92, 85 and 78 in those categories, the course grade is 82.9, while a plain average of the three would suggest 85. Entering the weights as 0.2, 0.3 and 0.5 gives the same 82.9.

3. Portfolio return

You hold $30,000 in a fund that returned 7.2%, $15,000 in one that returned 3.1% and $5,000 in cash earning 4.5%. Use the returns as values and the dollar amounts as weights: the portfolio return is 5.7%, compared with a simple average of 4.93%.

Interpreting a weighted average

The weighted mean always lies between the smallest and the largest value. It moves toward the values with the biggest weights: in the GPA example the C counts for only one credit, so the GPA of 3.48 ends up above the simple mean of 3.25. If the weighted mean is far from the simple mean, a few heavily weighted items are driving the result.

Choose weights that reflect real importance or size: credits, shares of a total, quantities bought. Policies differ on rounding, on how plus and minus grades convert to points and on whether honors or AP courses get extra points, so follow your school's rules for an official GPA.