Weighted Mean Calculator

StatisticsLast updated: August 17, 2026

A weighted mean is an average in which each value contributes not equally, but in proportion to its own weight (its importance). Midterm-and-final course grades (midterm 40%, final 60%), credit-weighted course averages, and index calculations are all cases where a plain arithmetic mean gives the wrong answer; the correct method is to multiply every value by its weight and divide by the sum of the weights.

All you need to do is enter the values and their matching weights into the two boxes in the same order: the weighted mean, the sum of weights, and — for comparison — the simple mean are computed instantly, together with a table showing each value's contribution and a chart of the weight distribution. It is built for students working out a passing course grade and for anyone producing a credit-weighted average.

Grades, prices, or scores — separate them with commas, spaces, or line breaks.
The weight of each value, in the same order as the values. Weights can be percentages (40, 60) or credits (3, 4); they do not have to add up to 100.

Formula

Weighted Mean = (w₁·x₁ + w₂·x₂ + … + wₙ·xₙ) / (w₁ + w₂ + … + wₙ)
Example (midterm 40%, final 60%): Grade = (Midterm × 0.40) + (Final × 0.60)

The common mistake is to multiply by the weights and add them up, but forget to divide by the sum of the weights. If the weights are percentages that add up to 100, skipping the division changes nothing; but with weights that do not add up to 100 — course credits, for instance — omitting it makes the result completely wrong.

How to Calculate

  1. Enter your values (grades, prices, scores) into the first box, in order.
  2. Enter the weight of each value into the second box, in the same order — the two lists must contain the same number of items.
  3. Weights can be percentages (40, 60) or credits (3, 4, 2); they do not have to add up to 100.
  4. Read the weighted mean, the contribution table, and the weight distribution chart in the results section.

Worked Examples

Midterm and final course grade (40% - 60%)

For a student who scores 70 on the midterm and 85 on the final, the course grade is (70×40 + 85×60) / 100 = (2,800 + 5,100) / 100 = 79. The simple mean would be 77.5; because the final carries more weight, the result comes out higher.

Weighted mean: 79.00 · Sum of weights (Σw): 100 · Weighted total (Σw·x): 7,900

Credit-weighted course average

A student who scores 80 in a 4-credit course, 65 in a 3-credit course, and 90 in a 2-credit course has a weighted mean of (320 + 195 + 180) / 9 = 695 / 9 ≈ 77.22. The simple mean would be 78.33.

Weighted mean: 77.22 · Sum of weights (Σw): 9.00 · Weighted total (Σw·x): 695

Weights that do not add up to 100

With the value 100 carrying a weight of 1 and the value 50 carrying a weight of 3, the result is (100×1 + 50×3) / 4 = 250 / 4 = 62.5. The heavier value, 50, pulls the mean toward itself.

Weighted mean: 62.50 · Sum of weights (Σw): 4.00 · Weighted total (Σw·x): 250

Frequently Asked Questions

How is a course grade calculated when the midterm is 40% and the final is 60%?
Multiply the midterm score by 0.40, the final score by 0.60, and add the two. For a midterm of 70 and a final of 85, the grade is 70×0.40 + 85×0.60 = 28 + 51 = 79. In this calculator you simply enter 70, 85 as the values and 40, 60 as the weights.
Do the weights have to add up to 100?
No. Because the formula divides the weighted total by the sum of the weights, the weights can be course credits (3, 4, 2) or any other scale. What matters is their ratio to one another; 40-60 gives exactly the same result as 2-3.
What is the difference between a weighted mean and a simple mean?
In a simple mean every value counts the same; in a weighted mean each value contributes in proportion to its importance. Heavily weighted values pull the result toward themselves: with a midterm of 70 and a final of 85, the simple mean is 77.5, while the 40%-60% weighting raises the result to 79.
Why must the number of values equal the number of weights?
Each value has to be multiplied by its own weight in the formula; an unmatched value or weight leaves the calculation undefined. If the two boxes contain different numbers of items, the calculator does not compute a result and shows a warning instead — enter both lists in the same order and with nothing missing.
Can a weight be zero?
Yes, individual weights can be 0; a value with a weight of 0 contributes nothing to the result. All the weights cannot be 0, however, because the denominator of the formula (the sum of the weights) would be zero and the mean would be undefined. Negative weights are not meaningful and are not accepted.
Where is the weighted mean used?
Passing course grades (midterm and final), term and cumulative grade point averages (credit-weighted), price indices such as the CPI, portfolio returns, and survey scoring are the most common applications. Whenever the values are not equally important, this is the correct average to use.