How the weighted average is calculated
Each value is multiplied by its own weight before averaging, so items with a larger weight count for more. Dividing by the sum of weights keeps the result on the same scale as the original values.
- vᵢ — value i (e.g. a test score)
- wᵢ — weight i — relative importance, must be ≥ 0
More detail
Weighted vs. simple average
A simple average treats every item equally: (80+90+70)/3 = 80. The weighted average above instead multiplies each score by its weight before dividing by the total weight — with weights 1, 2, 1 the same three scores give (80×1+90×2+70×1)/(1+2+1) = 82.5, because the middle score counts twice as much.
Practical tip. Weights only matter relative to each other — weights of 1/2/1 give the same result as 10/20/10. Use whatever scale matches how the weights were originally given (percent, credit hours, points).
Frequently asked questions
What's the difference between a weighted average and a simple average?
A simple average of 80, 90, 70 is (80+90+70)/3 = 80, treating all three equally. With weights 1, 2, 1 the weighted average above is (80×1+90×2+70×1)/(1+2+1) = 82.5 — the second item, weighted twice as heavily, pulls the result up.
What should I enter as the weight?
Enter each item's relative importance — like a course's credit hours, an exam's percent of the final grade, or how many units a rating represents. Only the ratio between weights matters, and weights must be zero or greater.
What happens if the weights add up to zero?
The calculator shows "—" instead of a number whenever the weights can't define an average: if all three weights are 0 (the total weight is zero, so the division is undefined), or if any weight is negative — even one negative weight makes the result undefined, no matter what the total comes to. An empty box gives the same "—", because reading a blank as 0 would turn an item you simply have not filled in into an item scored zero.
Can I use this for a GPA or grade calculation?
Yes — enter each grade's numeric value as vᵢ and its credit hours or grading weight as wᵢ. For example, grades 80, 90, 70 with credit weights 1, 2, 1 give a weighted average of 82.5, exactly like a credit-weighted GPA.