Weighted Average Calculator
Enter each value with its weight. Rows with a blank or zero weight are skipped, so you can use as few as one row or as many as six.
Weighted average
85.5
Simple (unweighted) average
85.75
Sum of value × weight
1,026
Sum of weights
12
Rows counted
4
Working
(92 × 3 + 85 × 4 + 78 × 3 + 88 × 2) ÷ (3 + 4 + 3 + 2) = 1,026 ÷ 12 = 85.5
How it works
A weighted average counts some values more than others. Each value is multiplied by its weight, the products are added up, and the total is divided by the sum of the weights. A plain average is the special case where every weight is the same.
The weights can be anything that measures how much each value should count: credit hours for a GPA, the number of students in each class, the quantity bought at each price, or a percentage of a course grade. They do not need to add up to 1 or to 100, because dividing by their sum normalises them.
Rows with a blank or zero weight are left out of the calculation entirely, so the simple average shown for comparison is the average of the rows that were counted. The working line shows the exact arithmetic so you can check it against a syllabus or an invoice.
Formula
weighted average = Σ(value_i × weight_i) ÷ Σ weight_i simple average = Σ value_i ÷ n (rows with weight > 0)
Example
Four course grades of 92, 85, 78 and 88 worth 3, 4, 3 and 2 credit hours: (92 × 3 + 85 × 4 + 78 × 3 + 88 × 2) ÷ (3 + 4 + 3 + 2) = 1,026 ÷ 12 = 85.5. The simple average of the four grades is 85.75; the weighted average is lower because the 78 carries more hours than the 88.
Two classes sit the same test. A class of 20 averages 80 and a class of 30 averages 90. The average over all 50 students is (80 × 20 + 90 × 30) ÷ 50 = 4,300 ÷ 50 = 86, not the 85 you would get by averaging the two class averages.
Assumptions and limitations
- A row is counted only when its weight is a number greater than zero. A blank weight, a non-numeric weight or a weight of 0 skips the row and its value is not read.
- Weights cannot be negative. Negative weights have specialised uses in statistics that this calculator does not cover.
- Weights are used as entered. Percentages such as 40 and 60 work as they are; there is no need to convert them to 0.4 and 0.6.
- Results are rounded to four decimal places for display only.
Frequently asked questions
How do I calculate a GPA with this?
Enter each course's grade points (for example A = 4.0, B = 3.0, C = 2.0) as the value and its credit hours as the weight. Three credits of A, four of B and three of C give (4 × 3 + 3 × 4 + 2 × 3) ÷ 10 = 30 ÷ 10 = 3.0. Check your school's grade-point scale, because some use 4.3 for an A+ or 3.7 for an A−.
Do the weights have to add up to 100%?
No. The calculator divides by the sum of the weights, so 40 and 60 give the same answer as 0.4 and 0.6, or 2 and 3. If a syllabus lists weights that add to 100%, enter them as listed.
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