Weighted Mean Calculator

Average values that carry different importance. Enter each value with its weight — percentage weights for course grades, credit hours for a GPA, or any other weighting — and get the weighted mean with every step of the working shown.

Before You Calculate

  • Weights only need to be non-negative — they do not have to sum to 100 or to 1, because the formula divides by their total.
  • For a grade, the value is the score (85) and the weight is the component's share of the final mark (20 for 20%).
  • For a GPA, the value is the grade points for a course (4.0, 3.3, ...) and the weight is its credit hours.
Value (x)Weight (w)

The Weighted Mean Formula

The calculator evaluates the weighted arithmetic mean:

x̄ₑ = Σ(wᵢ × xᵢ) / Σwᵢ

Where:

  • xᵢ = the i-th value
  • wᵢ = the weight attached to that value
  • Σwᵢ = the sum of all weights

Each value is multiplied by its weight, the products are summed, and the total is divided by the sum of the weights. Because of that final division, only the relative sizes of the weights matter: weights of 20, 30, 50 give exactly the same answer as 0.2, 0.3, 0.5 or 2, 3, 5.

The ordinary arithmetic mean is the special case where every weight is equal. The calculator reports it alongside the weighted mean so you can see how much the weighting moved the answer.

Common Uses

  • Course grades: each assessment counts toward the final mark according to its syllabus percentage.
  • GPA: grade points weighted by credit hours, so a 4-credit course moves the average more than a 1-credit seminar.
  • Portfolio returns: each asset's return weighted by the fraction of money invested in it.
  • Survey estimates: responses weighted so that over- and under-sampled groups match their population shares.
  • Grouped data: class midpoints weighted by class frequencies give the mean of a frequency table.

Worked Example: A Course Grade

A course counts homework for 20%, the midterm for 30%, and the final exam for 50%. A student scores 85 on homework, 78 on the midterm, and 92 on the final.

  1. Multiply each score by its weight: 85 × 20 = 1700, 78 × 30 = 2340, 92 × 50 = 4600.
  2. Sum the products: 1700 + 2340 + 4600 = 8640.
  3. Sum the weights: 20 + 30 + 50 = 100.
  4. Divide: 8640 / 100 = 86.4.

The weighted course grade is 86.4 — noticeably higher than the unweighted mean of (85 + 78 + 92) / 3 = 85, because the best score landed on the heaviest component. Entering the three value/weight pairs into the calculator reproduces every number in this table, including the Σwx = 8640 and Σw = 100 totals.

Frequently Asked Questions

Do the weights have to add up to 100 or to 1?

No. The formula divides by the sum of the weights, so only their relative sizes matter. Weights of 20, 30, and 50 give exactly the same result as 0.2, 0.3, and 0.5. This also means you can use raw counts, credit hours, or dollar amounts directly as weights without converting them to percentages first.

What is the difference between a weighted mean and a regular mean?

A regular (arithmetic) mean treats every value as equally important, which is the special case of the weighted mean where all weights are equal. A weighted mean lets some values count more than others. If a final exam is worth half the course, its score should pull the average five times harder than a homework worth 10% - that is exactly what the weights encode.

How do I calculate a weighted grade for my course?

Enter each assessment's score as the value and its syllabus percentage as the weight. For example, homework 85 with weight 20, midterm 78 with weight 30, and final 92 with weight 50 gives (85 x 20 + 78 x 30 + 92 x 50) / 100 = 86.4. If some components have not happened yet, include only the completed ones - the division by the weight total automatically rescales.

How is a GPA a weighted mean?

Each course grade is converted to grade points (for example A = 4.0, B+ = 3.3) and weighted by the course's credit hours. A 4.0 in a 4-credit course contributes 16 grade points, while a 4.0 in a 1-credit course contributes 4. The GPA is the total grade points divided by total credits - precisely the weighted mean formula with credits as weights.

Can a weight be zero or negative?

A weight of zero is fine: it simply removes that value from the average, which is useful for modeling a dropped assignment. Negative weights are rejected by this calculator because they break the interpretation of the result as an average lying between the smallest and largest value - with negative weights the 'mean' can land outside the data entirely.

When should I use a weighted mean instead of a median?

Use the weighted mean when the weights represent genuine importance or frequency and every value should influence the result proportionally. Consider a median instead when extreme values would distort the picture, since the mean - weighted or not - is sensitive to outliers. For skewed data like incomes, medians usually summarize the typical case better.