# How is cumulative GPA calculated?

This might be a dumb question, but since I couldn't find what I am looking for, I decided to ask here. I think that cumulative GPA is the average of all each semesters' GPA, however the part that I don't understand is if I have the below points for three semesters,

``````1st semester = 3.1
2nd semester = 3.4
3rd semester = 2.9
``````

would the cumulative GPA for the three semesters be calculated as:

• ((1st + 2nd)/2 +3rd)/2, or
• (1st + 2nd + 3rd)/3 ?

## 1 Answer

The cumulative GPA can't in general be known from just the GPAs of the individual semesters. The cumulative GPA is your total grade points divided by your total possible grade points, over all semesters completed so far. If you took the same number of classes each semester, and all had equal numbers of units, and all were included in GPA (i.e., no pass/fail or the like), then it would be `(1st+2nd+3rd)/3`.

The reason it can't be known just from the GPA of the individual semesters is that it depends on how many units you took each semester. If you took more classes/units in one semester than in another, then that semester will have greater weight in the cumulative GPA.

This applies to averages in general. If I tell you I have one bag of stones with an average weight of 1kg, and another bag of stones with an average weight of 2kg, you don't know what the average weight would be if you combined all the stones into one group. To know that, you have to know how many stones are in each bag.

• Thanks. However even if you multiply the each grade by the corresponding units and added each separately then divided by the total number of units taken the answer would be the same. I did that and got same thing unless my calculations are wrong. – Magna Jan 24 '15 at 6:28
• @Magna: Your question didn't mention any individual grades or units, so I don't know what calculation you did. Averaging the actual grade points in the way you describe will always work. What I said in my answer is that if you have the same number of units in each semester, then averaging the individual GPAs will also work. – BrenBarn Jan 24 '15 at 6:31