The formula
Multiply each value by its weight, add the results, and divide by the sum of the weights. Dividing by the sum is what lets the weights be any positive numbers.
Weighted average = Σ(value × weight) ÷ Σ weight
Σ means “add up over all rows”.
Example: any values
Values 4, 10, 7 with weights 2, 3, 5.
- Value × weight: 4 × 2 = 8; 10 × 3 = 30; 7 × 5 = 35
- Sum of products: 8 + 30 + 35 = 73
- Sum of weights: 2 + 3 + 5 = 10
- Weighted average: 73 ÷ 10 = 7.3
The plain average of 4, 10 and 7 is 7. Because the 10 counts more than the 4, the weighted average is a little higher, 7.3.
Example: grades with percent weights
Scores of 92%, 85%, 74% counting 15%, 25%, 60%.
- Value × weight: 92 × 15 = 1,380; 85 × 25 = 2,125; 74 × 60 = 4,440
- Sum of products: 7,945; sum of weights: 100
- Weighted average: 7,945 ÷ 100 = 79.45%, a C on the scale below.
Letter grades
Letters use the scale Florida law sets for public middle and high schools [1]. Each band starts at its published lower bound and nothing is rounded, so 89.99% shows as a B.
| Letter | Percent |
|---|---|
| A | 90–100 |
| B | 80–89 |
| C | 70–79 |
| D | 60–69 |
| F | 0–59 |
Schools set their own cut-offs, weights and rounding rules. Check your school’s scale before relying on a letter.
Questions
Do the weights have to add up to 100?
No. The formula divides by the sum of the weights, so any positive weights work: 2, 3 and 5, or 20, 30 and 50 give the same average. They only need to total 100 when they are percentages of a grade, and the grade calculator checks that for you.
What is the difference between a weighted and a simple average?
A simple average treats every value equally. A weighted average lets some values count more. With equal weights, the two are the same.
What can I use as weights?
Anything that says how much a value should count: percentages, credit hours, points possible, number of items, dollars, days. The units of the weights cancel out.
What does a weight of 0 do?
The row is allowed but has no effect on the result. At least one row needs a weight above 0.
How is this different from a GPA?
A GPA is a weighted average of grade points, with credit hours as the weights. The GPA calculator does that for letter grades.
What does the grades preset change?
It labels the rows as grades and weights in percent, and adds a letter grade for the result. The calculation is the same.