I'm applying for a Master's program and I would like to indicate that my GPA in the last two years of college has improved greatly and that my major GPA is high. However, my official transcript does not report major GPA or the GPA in my last two years. I want to manually calculate these two GPAs using the scale and key provided by my university and I will make a note saying that these numbers are not on my official transcript. Is that acceptable? I don't want the admissions committees to think that I'm trying to mislead intentionally, neither do I want to be viewed negatively for providing information that is not verifiable. Of course, I will include the GPA on my official transcript.
Yes, you can manually calculate your GPA. Additionally, mention the method or the formula you used to calculate your GPA so that the application reviewers can evaluate your application better. However, there are various third-party grade conversion/calculation tools available for free of cost, which you can use to get a better idea.
I think the most important thing is to list the specific courses that are most relevant to the master's program you are applying for. You could show a table listing the name of the course, a brief description if the course title isn't self-explanatory, and the grade received. If the grades in this table are all (or almost all) very strong, that will make more of an impact than some hand-calculated average.