A Grade Point Average (GPA) is a summary statistic that represents a student’s average performance in their studies over a stated period of time, such as one semester. Being numerical, GPAs are often calculated to two decimals. They are used as indicators of whether levels of student performance meet some fixed criterion, and for sorting groups of students into rank order.

However, grading scales differ considerably across institutions and countries. Conversion tables are usually available for comparing grades and GPAs within countries and internationally.

When an entire study program is organised as a collection of “units”, each period of time gives rise to its own GPA. The most common study period for a course is one semester, usually 12-15 weeks of class. If a full-time student enrols in four courses in a particular semester, the GPA is calculated as the average performance over those four courses.

## How is a GPA calculated?

A student’s level of attainment in a course is typically represented by a grade chosen from a set of approved ordered symbols. Depending on the institution’s preferences, the grade labels may take the form of letters (A, B, C, D…), descriptive terms (Distinction, Honour, Credit, Pass, Fail), or numerals on an arbitrary scale (7, 6,…, 1).

For a GPA to be calculated, all letter and word labels must be given numerical equivalents, such as A = 4.0, B = 3.0, C = 2.0; D = 1.0 and F = 0.0. The numerals are deemed to represent genuine measurements and, under this assumption, facilitate the calculation of GPAs.

The GPA is the “weighted average” of course grades calculated over the defined period of study. The weights reflect the relative contributions of courses to the program measured in arbitrary units, called “credit value”, based on contact hours or presumed total student workload. Each course has a credit value or “weight” approved by the institution.

As an example of how a GPA is calculated, suppose a student enrols in four courses in a particular semester. Three of these are designated as “five credit” courses but the fourth is designated a “ten credit” course because the academic demands involved are about double those of the other courses. The student receives grades of A, B and B in the three five-credit courses and an A in the ten-credit course.

The first step in calculating the GPA is to multiply the credit value of each course by the respective grade’s numerical equivalent.

Symbolically, using the equivalence scale above, this is as follows:

```
(5 x A) + (5 x B) + (5 x B) + (10 x A)
= (5 x 4.0) + (5 x 3.0) + (5 x 3.0) + (10 x 4.0)
= 90.0
```

The second step is to divide that aggregate (90.0) by the total number of credits for all the courses studied in that semester (25) to give a GPA of (90.0/25) = 3.6.

Only the relativities of the weights assigned to the various courses matter in a GPA calculation. Suppose the student had studied exactly the same courses at another institution and received the same grades – the same grade scale with the same numerical equivalents. The GPA would come out exactly the same (3.6) even if the second institution used 20, 20, 20, and 40 to represent its course weights instead of 5, 5, 5 and 10.

A related statistic, the “cumulative GPA”, uses the same calculation formula but takes into account all studies completed from the time of enrolment in an academic program up to the time of calculation. Many academic transcripts show details of the grade scale used, a GPA for each semester and a running (cumulative) GPA for all studies up to that point. Institutions differ in how they treat pass/fail courses, fail grades and transfer credits.

## What use are GPAs?

GPAs often serve as input data for decisions on: progression through degree programs; admission to advanced studies; rankings for prizes, medals, honours and scholarships; determinations of degree classification; and accreditation and quality assurance. Too low a GPA, or too many marginal or failing grades, may prevent a student from continuing. Consistently poor performance may lead to a period of exclusion from the degree program or the institution.

It is hard to find clear evidence that potential employers place significant emphasis on GPAs in hiring decisions, although in general they like to know the GPA. Probably more important would be the graduate’s pattern of grades attained in courses that make up the major.

Basing decisions on grades gives the appearance of being both objective and meritocratic. A notable weakness of GPAs is that their basic input data are derived from course grades. The relationship between the grade awarded and a student’s actual level of achievement is not assured.

This means there is no guarantee that course grades are comparable. Pooling grades (for a GPA) does nothing to improve that. However, using GPAs almost always delivers administrative solutions when required, so there usually is in practice little incentive to place the grades themselves under close scrutiny.