# Why are GPAs calculated the way they are?

At most schools an A is a 4.0, an A- is a 3.7, and so on. I feel like this system is not really representative of a person's true skill. For example, a person who got a 100% in a class will get the same GPA as a person who got a 94% in the class. However, a person who gets a 91% in a class will get a significantly higher GPA than someone who got an 89%. Why don't schools base GPA off the actual percentage that someone gets in a class instead of their letter grades?

• My sophomore year I took an advanced physics course. My raw score across homework and tests was something like 35%. That was an A in the class. Why? Because the professor liked setting really hard problems and seeing how far you could go with them. If you could actually solve it it was a really good feeling. Why would he do that? To really make you wrestle with the problems and come at them from many different directions, learning many problem solving skills. So, until you invent an absolutely uniform evaluation system that is proven 'correct', go with the flow. It isn't important, really. – Jon Custer Mar 23 '17 at 12:59
• This question's like "Why don't Americans use metric?" Sure the current system's stupid, but it's hard to overcome cultural inertia. – Nat Mar 23 '17 at 17:33
• @JonCuster In France this is solved by renormalizing. The grade is out of 20 and with the first decimal included. – Marko Karbevski Mar 24 '17 at 20:47

The big reason: exact numerical scores are not comparable across classes and professors.

Suppose I told you that two students took a class offered in different semesters. We look at their transcript and see that student A scored a 94% with Professor X and Student B scored a 99% with Professor Y. Student B beat out the first person by five percentage points, but do we actually know that Student B is a better student? Maybe Professor Y is a soft grader or Professor X had a really harsh curve that semester. We don't really know whether Student B is better. All we really know is that both students did pretty well.

Hence, grades tend to be assigned and interpreted with a large degree of subjectivity, which fits the ABCDF model better than a score-based model. The general interpretation is:

``````A - excellent
B - good
C - average
D - needs improvement
F - failing
``````

If the first and second student both get A's, then this means that an expert in their fields (the professors) have said that both students did excellent. This isn't a perfect system, but it is about as good a comparison as you can get.

• exact numerical scores are not comparable across classes and professors ABCDF grades are not comparable across classes and professors, neither. – scaaahu Mar 23 '17 at 4:17
• Actually, I think ABCDF system is bad for weak students. 10% and 20% are both F. If I were 10%, why should I work harder to get another 10%? . In a per cent system, I would see progress (from 10 to 20) if I work harder. – scaaahu Mar 23 '17 at 4:30
• @scaaahu As I said, ABCDF is not a perfect system, but the difference is that it explicitly acknowledges that it is a subjective system. As in the example above, comparing one student's 94% to another student's 99% is meaningless. Saying that both students were "excellent" is at least meaningful in that both students were judged to be excellent. In other words, the ABCDF system does not invite the fallacy of direct comparison. – David Mar 23 '17 at 5:12
• @schaaahu: "If I were 10%, why should I work harder to get another 10%?" Maybe you shouldn't. In many courses, a 10% grade means "Get out while you still can." Of course not all: there is of course no claim that any one grading scale could have a standard or even nontrivial common meaning across all possible situations and contexts. – Pete L. Clark Mar 23 '17 at 5:27
• @IPlant: Your example seems artificial: I know of no context in which students A and B are compared to each other using the GPA among their common classes. If students A and B have taken several classes in common, then one can ask the instructors who is better. Also, if A has a 3.95 GPA and B has a 4.0 GPA then the correct conclusion to draw is that both students have excellent GPAs. I don't know of any context in which such a small discrepancy results in differing treatment of the two students; do you? – Pete L. Clark Mar 23 '17 at 23:25

At most schools an A is a 4.0, an A- is a 3.7, and so on.

This is true at most American colleges and universities, yes. (It's not true in most of the rest of the world, and the discrepancy is an issue when one wants to compare students from different countries, e.g. in graduate admissions.)

I feel like this system is not really representative of a person's true skill.

I have given out hundreds of grades in university courses, and I make no claim that a student's course grade is "really representative of their true skill." For instance, it has happened that I wrote grad school letters for an A- student and an A student for whom my primary interaction was teaching them the same course and that I wrote an overall stronger letter for the A- student: based on my interactions with him, I felt that his true skill was higher, whereas the A student did noticeably better on the midterm and the final (though both did very well).

For example, a person who got a 100% in a class will get the same GPA as a person who got a 94% in the class.

There seems to be a premise of this question that universities use standard "letter grade cutoffs." This is really not always true (though it is sometimes true, and it would be interesting to understand this better). These cutoffs have not been applied at any of the universities I've been affiliated with as a student or instructor: University of Chicago, Harvard, McGill, University of Georgia. (See e.g. Question 12 here.) To be honest -- and in part because my own experience with American universities, though quite temporally extensive, is far from universal and probably even from generic -- such talk reminds me of high school, and I get surprised when university students think too seriously about it. (And this sometimes includes my own university students!) In the STEM fields in particular, it is common for exams to be written in such a way that a 50% grade would be a clear A and a 90% grade would be preposterous.

Let me say though that I have not seen it go the other way: in any class I have ever taken or taught: yes, 94% is worth the same letter grade as 100%. One could go on at great length about this, but for now let me say: I see nothing inherently problematic here from anyone's perspective.

Rather I would like to call attention to the fact that there is a mistake above: students who get a 100% and a 94% will probably get the same course grade. GPA means grade point average. This error becomes more clear as follows:

However, a person who gets a 91% in a class will get a significantly higher GPA than someone who got an 89%.

No, this is really not the case. The typical American university student takes about 40 courses overall. So a student who gets A's in all but one course and fails the other course will have a GPA of (39*4 + 1*0)/40 = 39*4/40 = 3.9. If that student got at least a C+ instead of an F, their GPA rounded to one decimal place would be 4.0. In fact, my undergraduate GPA rounded to one decimal place was 4.0, though I remember well the course in which I received a B (the first graduate course I took) and more vaguely that I got less than A grades in at least two other courses. (Because culturally speaking a "4.0 GPA" generally implies all A's, I reported my GPA to two decimal places.)

This is, I think, a really key point: the inference of skill and achievement from course grades is a statistical process, and like most statistical processes, investing too much meaning in any one data point is dubious. I am currently directing graduate admission in the math department at UGA. There are occasions when individual course grades are meaningful to us: a student who has generally good grades but quite poor ones in two or three key courses that are the most foundational to graduate success is viewed negatively beyond the influence of the GPA (and this of course is why we do not just look at GPAs but get much more information, including full transcripts and lists of textbooks from the courses taken in the major). But for one of these key courses -- say real analysis -- what if one student gets a B+ and another gets an A-? Then we really don't care, and if we don't care, I'm not sure who would.

Let me finally make a few more remarks about the system of letter grades at universities.

• It would be great if the kids would believe you, Pete. :) – paul garrett Mar 24 '17 at 0:06
• Part of students' anxiety over grades results from the discretization, as a small variance in performance can result in a larger bump in the overall grade. This is, no matter what, they're still going to stress over their final evaluation - just in one case, it's a smooth, well-behaved function, whereas in the other, it's a series of cliffs that they might fall off of. This gets worse as the cliffs get higher; for example, when +/-'s aren't used, the distinction been an A, B, and C really stresses some students out, as a single false answer on the final can majorly affect their grade. – Nat Mar 24 '17 at 4:53
• I completed my stint in academia, and now I largely share the perception that students worry far too much about their grades. In fact, I started my own company out of grad school, so no one's ever even seen or cares about my GPA - can't tell you what a sap I feel like for having stressed over it so much. But, I still find it just about impossible to convince current students that they should worry less about the grades and more about personal growth. Those cliffs seem small looking back, but I still remember how much I worried about losing that 4.0 due to one little slip; it wasn't small then. – Nat Mar 24 '17 at 4:57
• @Nat: "Part of students' anxiety over grades results from the discretization, as a small variance in performance can result in a larger bump in the overall grade." Yes, I agree with that and take steps to minimize it, as recorded in my comments on your answer. But I disagree that the discretization of letter grades is anything close to the source of this anxiety. As I recorded in my answer, my high school environment was the highest level of grade-anxiety I have ever seen. The level of grade grubbing I see at UGA is less than I saw at Harvard which was much less than at my high school... – Pete L. Clark Mar 24 '17 at 5:21
• Almost all of the grade grubbing I see comes from students who got good grades but want better ones. Especially, the absence of a clear distinction between an A- and an A invites this more than anything else. With a numerical system, every student has a clear incentive to ask for a few more points on everything, and whereas in the current system everyone who gets an A leaves with a smile, in a numerical system students really will fight for a 98% rather than a 95%. That is not going to reduce anxiety! – Pete L. Clark Mar 24 '17 at 5:27

### Historically, simplicity

For most of history, it would've been tedious to average all of a student's course grades weighted by credit hours. It was a lot easier to call an "A" a 4, a "B" a 3, etc., then just average.

It made curving a lot easier, too. Teachers could just sort the grades, then the top 10% got an A. Who wants to calculate an actual normal curve by hand? Heck, how many teachers even knew how to?

### Today, cultural inertia

Today, it'd be a lot easier to do the calculation without all of the arbitrary rounding. We can do away with the arbitrary break point that's between 92.9% and 93.0%, and we can do away with how a 93% is the same thing as a 100%.

We don't need a simple method for curving because we've got computers and spreadsheets that'll calculate an actual bell curve, rather than the weird sorta-bell-curve that comes from splitting students up into discrete grade categories like A/B/C/D/F.

Today, we can do away with that common situation where students reason that getting a 75% on the final exam is the same thing as getting a 100%, leading them to not study or review the material.

But, suppose that an instructor or dean reads this question and agrees that the current system is messed up. What could they actually do about it? They're caught up in cultural inertia; same reason those of us in America still use inches/feet/yards/miles rather than meters with a metric prefix.

• "Today, we can do away with that common situation where students reason that getting a 50% on the final exam is the same thing as getting a 100%" Is that situation so common? Using your assumed letter grade cutoffs (which are not uniformly used at any American university I've ever been affiliated with, BTW) and assuming that a final exam is worth 30% of the course grade, the difference between 100% and 50% on a final is 15% of the final grade: using the assumptions above, this would change their letter grade unless they were already failing. – Pete L. Clark Mar 23 '17 at 17:46
• @PeteL.Clark 50%-vs-100% is on the high end, for classes where there're more tests and the final's weighted similarly. But, yes, it's a completely common calculation that students are doing; there's rarely a reason to work hard to do better on the final when your prior test average would give you the same final grade as a perfect score. – Nat Mar 23 '17 at 17:49
• @PeteL.Clark Also, apparently my grad school had 93% as the cut-off between an A- and an A, rather than the 92% I'd used above without checking. Hah arbitrary tables. I disliked how we had A-'s, but not A+'s; it's like we had no reason to aim for better than a, well, 93% I guess - dunno why I seem to recall 92%. – Nat Mar 23 '17 at 17:53
• @PeteL.Clark Fixed up the numbers. Also, does the "top 10% gets an A" thing look reasonable? I forget how many people usually get A's in a stereotypical curve. Given grade inflation, it's probably a lot higher than 10% these days, I'd guess? – Nat Mar 23 '17 at 18:04
• @Nat off topic, but my former department had to introduce an A++ equal to 100% since an A+ was a 97%. – StrongBad Mar 23 '17 at 18:40