Grade (education)

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(Redirected from Grade point average)
For meanings of GPA other than Grade point average, see GPA (disambiguation).

A grade in education can mean either a teacher's evaluation of a student's work or a student's level of educational progress, usually one grade per year (often denoted by an ordinal number, such as the "3rd Grade" or the "12th Grade"). This article is about evaluation of students' work and various systems used in different countries.



In Argentina , where the comma "," is used as a decimal separator (instead of the dot), grades from 1 (sometimes 0) up to 10 are used, with some schools allowing decimals (up to 2) and some others only allowing whole numbers where:

  • 10 (excellent) is the best possible grade
  • 8-9,99 (very good)
  • 6-7,99 (good)
  • 4-5,99 (sufficient)
  • up to 3,99 (insufficient)

Most universities evaluate classes with two mid exams and a final. The final exam encompasses the whole course syllabus wheres the mid exams usually take just half. In some schools, if the average grade of the two mid exams is equal to or higher than 7, the student passes the class without the need for a final exam (since there are only two exams, some teachers also pass students who average 6,5, others weigh in that decision the student's performance in class). An average of less than 4 is failing, the student doesn't even have the chance to take that final exam.

In High Schools, the year is divided into three trimesters and classes are usually year-long. The student needs an average of 6 or higher in the three trimestral exams to avoid having to take a final to pass the class. In the event ot a student scoring less than 6 in the 3rd trimester he will have to take a final exam regardless of his average.

This last point is considered controversial since the last trimestral exam is not more important than the first two but the rule stands to prevent students that already reached the minimum average (e.g.: two 10 in the first two give you a lowest possible average of 6,33) from not making an effort the last three months of the year.


In Chile, where the comma "," is used as a decimal separator (instead of the dot), grades from 1,0 up to 7,0 (with one decimal place) are used, where:

  • 7,0 (excellent) is the best possible grade
  • 6,0-6,9 (very good)
  • 5,0-5,9 (good)
  • 4,0-4,9 (sufficient); 4,0 is the lowest passing grade
  • 1,0-3,9 (insufficient) are failing grades; 1,0 is the worst possible grade.

Generally, it's a linear scale, with 1,0 meaning 0% achievement, 4,0 meaning 50% achievement, and 7,0 meaning 100% achievement. Rounding of averages is generally done to the second decimal; hence, a 3,95 is rounded up to a 4,0, whereas a 3,94 is rounded down to a 3,9.


Several systems are in use in different educational institutions in Finland.

The "school grade" system has historically been a scale of 0 to 10, but all grades lower than 4 were discarded. Thus, it is divided between 4, the failing grade, and 5–10, the succeeding grades.

  • 10 (excellent), represents about 5% of the top
  • 9 (excellent)
  • 8 (good)
  • 7 (satisfactory), the mode
  • 6 (satisfactory)
  • 5 (mediocre)
  • 4 (fail)

In the individual exams, but not in the final results, it is also possible to divide the scale further with '½', which represents a half grade, and '+' and '–', which represent one-fourth a grade better or inferior. For example, the order is "9 < 9+ < 9½ < 10– < 10". The grade '10+' can also be awarded to represent perfect performance added with extra effort by the student.

The matriculation examination grades are similar to the above, but in Latin.

Grade Abbrv. Gloss Translation Comments
laudatur L excellent with praise Top 5%
eximia cum laude approbatur E excellent accepted, with extraordinary commendations
magna cum laude approbatur M good accepted, with much commendations
cum laude approbatur C satisfactory accepted, with commendations
lubenter approbatur B satisfactory readily accepted
approbatur A mediocre accepted
improbatur I fail not accepted bottom 5%

Universities and vocational institutions use a scale of 0 (fail) and 1-5 (pass), or fail/pass. The professor selects which grading scheme is used; short, compulsory courses typically have pass/fail grades.

International Baccalaureate

The International Baccalaureate uses an integer scale ranging from 1 through 7, 7 being the highest grade and 4 being the lowest passing grade. Students in the IB Diploma Programme are graded in six subjects for a total of 42 points. An additional three points are awarded for the Theory of Knowledge subject and the Extended Essay. For the diploma to be awarded students must accumulate at least 24 points and a passing grade in each subject. In admission to university programmes, the IB grades are often converted to a local or national assessment system by some appropriate formula.


These grades are used in Grundskola and Gymnasium:

  • MVG - Mycket väl godkänd (Passed with special distinction)
  • VG - Väl godkänd (Passed with distinction)
  • G - Godkänd (Passed)
  • IG - Icke godkänd (Fail)

When grading tests, the following limits are sometimes used:

  • >90% - MVG
  • >75% - VG
  • >50% - G
  • <50% - IG

but the grades relate to stated goals and not to a certain percentile of students. Until the nineties relative grades on the scale 1, 2, 3, 4, 5 were used. The scale was intended to have a national average of 3 and a standard deviation of 1. 5 was the highest grade.

Up until the sixties yet another scale was used:

  • A - Berömlig (Passed with great distinction)
  • a - Med utmärkt beröm godkänd (Passed with distinction)
  • AB - Med beröm godkänd (Passed with great credit)
  • Ba - Icke utan beröm godkänd (Passed with credit)
  • B - Godkänd (Passed)
  • Bc - Icke fullt godkänd (Not entirely passable)
  • C - Underkänd (Fail)

A was the highest grade, but rarely given.

Universities, with some exceptions, use:

  • VG - Väl godkänd (Passed with distinction)
  • G - Godkänd (Passed)
  • U - Underkänd (Fail)

Engineering colleges and universities use (5 is the highest grade):

  • 5
  • 4
  • 3
  • U - Underkänd (Fail)

Central and Eastern Europe

In Russia, Ukraine, Hungary and likely the rest of the former Soviet Union and countries formerly associated with the Eastern Bloc, a five-point grading scale is used, where:

  • 5 (very good or excellent) is the best possible grade,
  • 4 (good),
  • 3 (satisfactory) indicates "average" performance,
  • 2 (unsatisfactory),
  • 1 (poor) is the lowest possible grade.

Qualifiers `+' and `–' are often used to add some degree of differentiation between the grades, eg. 4+ is better than 4 but a little worse than 5–. Grading varies greatly from teacher to teacher and tends to be entirely subjective even for courses that lend themselves to objective marking such as mathematics and applied sciences. Even though the grades technically range from 1 to 5, 1 is uncommon and is rarely given for academic reasons—in many cases a failure to show up for an exam or to answer any questions only results in a 2.

Students in these countries may be labelled by their teachers according to their average grade, the labels stemming from the respective digits. For example, someone with a 5-point average is a пятёрышник (m) (pronounced: pyatyorishnik, from Russian "5", пять (pyat'))/ пятёрышница (f) (pyatyorishnitsa), while someone with a 1-point average is a еденишник (m) (yedyenishnik, hard to see if you don't know Russian, but from Russian "1", один (adin))/еденишница (f) (yedyenishnitsa).

Since mid-90s, Polish primary and secondary schools expanded this system to include 6 as a grade. In this system 5 became equivalent to `very good', and the highest mark 6—`excellent'—is awarded primarily when it is clear that the student knows the material considerably beyond the level taught in the course. In universities, a traditional four-point system is used, the grades are: 2.0 (failed), 3.0 (pass), 3.5, 4.0, 4.5, 5.0 (very good, the higest grade). There are some universities that use non-standard, additional 5.5 and 6.0 grades.


In France, Belgium and Peru, a 20-point grading scale is used, in which 20 is the best possible grade and 0, the lowest. A score of 20 is considered perfect; accordingly, it is rarely if ever given in courses that are graded subjectively. The "passing" grade is usually 11, and in contrast to the U.S. system, grades of 12 or 13 out of 20 are usually not considered so bad.


For system used in Croatia please see the entry in the Yugoslavia (former) section.


The Danish gradation scale consists of 10 grades ranging from 00 to 13, with 00 being the worst.

GradeGiven for...
00the completely unacceptable performance.
03the very hesitant, imperfect and unsatisfactory performance.
5the hesitant and non-satisfactory performance.
6the somewhat hesitant but more or less satisfactory performance. Minimum passing grade
7the performance slightly below average.
8the average performance.
9the performance slightly above average.
10the excellent but somewhat routinized performance.
11the independent and excellent performance.
13the exceptionally independent and excellent performance.

The gaps between 00 & 03, 03 & 5 and 11 & 13 are there to signify a larger difference between those grades. The leading 0 in 00 and 03 are used to prevent fraud with grades.

Please note that 00 is nearly impossible to achieve, presuming one actually is present, while 13 is a fairly rare grade, almost never given outside of exams.


The French grading system is similar to that of Belgium in secondary schools and universities; the passing grade is 10. Primary schools generally use a 10-point grading scale.


In Germany, a 6-point grading scale is used, where:

  • 1 (excellent) is the best possible grade.
  • 2 (good) is the next-highest.
  • 3 (satisfactory) indicates "average" performance.
  • 4 (sufficient) is the lowest passing grade.
  • 5 (unsatisfactory) is the higher of two failing grades.
  • 6 (poor) is the lowest possible grade.

Five and six are both considered to be failing grades, though in earlier years students are not required to repeat classes with '5' grades if they perform well in other classes. Grades '1' to '5' can be suffixed with '+' and '-'. To calculate averages of suffixed grades, they are assigned fractioned values, where '1' is 1.0, '1-' is 1.3, '2+' is 1.7, '2' is 2.0, '2-' is 2.3 and so on. As a 1.0 average is considered perfect, there is no such thing as an '1+'.

In school reports, only unmodified integer grades may be used; they are written in text form:

  • 1 sehr gut
  • 2 gut
  • 3 befriedigend
  • 4 ausreichend
  • 5 mangelhaft
  • 6 ungenügend

"In-between" grades such as '1-2', '2-3', '3-4' etc., which used to count as 1.5, 2.5 and so on, have largely been discontinued due to ambiguities when converting the averages back to integer values.

In the final classes of Gymnasiums the grades are converted to numbers ("points") in order to calculate the average for Abitur. In this case an '1+' exists (and counts as 15), '1' is 14, '1-' is 13, '2+' is 12, etc. up to '5-' is 1 and finally '6' is 0. Because 1+ exists in this system, "ultra-perfect" Abitur averages below 1.0 are possible. When the point system is used, 4 (5 points) is the lowest passing grade, and 4- (4 points) the highest failing grade.

In converting German grades to the A-F scale, a 1 = A, ... 4 = D scale is often used (with 5 and 6 both converted to Fs) but this conversion is nearly never accurate, since, for example, a grade of '2' is usually more difficult to obtain in Germany than a 'B' in the United States. (The average grade in Germany is normally supposed to be around or a bit above 3, whereas in the US average grades are often supposed to be between B- and B.)


In primary school in Italy is used a 5-grades scale, as following: Ottimo(excellent) Distinto(good) Buono(average) Sufficiente(pass) Non Sufficiente(non pass)

In high school is used a 10-point scale , being 6 the minimum grade for passing Often are used specifications like + and -, haòf grades, and grades like 6/7. Note that the grades used in primary school are derived from this scale, with Non Sufficiente meaning "5 and under", and the other grades standing respectively for 7, 8, 9, 10.

Universities in Italy use a 30-point scale simply divided in two, non passing (0 to 17 points), and passing grades (18 to 30 points), for ordinary exams, and a 110-point scale, divided in two as well, being 66 the minimum grade for passing.For outstanding results the Lode "praise", is added at the maximum grade.

The Netherlands

In The Netherlands, grades from 1.0 up to 10.0 are used, with 1 being worst and 10 being best. Generally one decimal place is used, and 5.5 and up constitute a pass whereas 5.4 and below constitute a fail. If no decimal places are used, 6 and up is a pass and 5 and below a fail.


Peru's grading system is very similar to Belgian, please see that entry.


For the Polish system, please see section on Central and Eastern Europe.


For the Russian system, please see section on Central and Eastern Europe.


Singapore's grading system in schools, by far is one of the more complex because of the existence of many types of institutions with different education focus and systems. Here are the more fundamental grading systems that is used at Primary, Secondary, and Junior College levels.

Lower Primary (Primary 1 to 3)

  • Band 1: 85% and above
  • Band 2: 70% to 84%
  • Band 3: 51% to 69%
  • Band 4: Below 50%

Upper Primary (Primary 4 to 6)

  • A*: 91% and above
  • A: 75% to 90%
  • B: 60% to 74%
  • C: 50% to 59%
  • D: Below 50%

In rare instances, a U (ungraded) grade may be awarded for exceptionally poor quality work.

Secondary Level (for GCE "O" levels)

  • A1: 75% and above
  • A2: 70% to 74%
  • B3: 65% to 69%
  • B4: 60% to 64%
  • C5: 55% to 59%
  • C6: 50% to 54%
  • D7: 45% to 49%
  • E8: 40% to 44%
  • F9: Below 40%

Note: Grades D7 and below are below the passing grades.

Students taking Higher Mother Tongue (eg: Chinese, Malay, Tamil) may be awarded a Distinction, Merit, Pass, or a Fail grade.

Junior College Level (GCE "A" and "AO" levels)

  • A: 75% and above
  • B: 60% to 74%
  • C: 55% to 59%
  • D: 50% to 54%
  • E: 45% to 49% (passing grade)
  • O: 40% to 44% (denotes standard is at "AO" level only),grade N in the British "A" Levels.
  • F: Below 40%

In addition, students who are taking Special Paper(s) ("S" paper in short) will be awarded either a Distinction, Merit, Pass, or a Fail grade.

Different JCs have different expectations and thus, the school reserves the discretion to moderate the marks when deem necessary. For example, some JCs may regard 50% as the passing mark instead of 45% by others.

Note: "AO" level grades at Junior College level follows the "O" level system above.

All percentages with their corresponding grades shown here are just approximate guidelines because ultimately at the end of all major examinations (Primary School Leaving Examinations or PSLE in short, GCE "N", "O" and "A" Levels) the Ministry of Education, Singapore, will moderate the results. Hence, an "A" grade for instance may no longer be at 75%. It could possibly be 73% or even 77% depending on the performance of the cohort. This is usually done to prevent grade inflation.

In addition, some schools are also offering the International Baccalaureate diploma programme.


For the Ukrainian system, please see section on Central and Eastern Europe.

United States, Canada, England and Wales

The A-F system

In many countries including the United States, grades are given on an A-F system where "A" is best and "F" is worst, but the letter "E" is typically omitted, since it traditionally stood for "Excellent" (see the section on the "E-S-N-U system" below), but would be very poor on an A-F system. An "F" grade is failing and results in denial of course credit, while a "D" is poor, but passing. Most U.S. colleges require grades of "C" or better in one's major, as well as a 2.0 (C) grade-point average.

  • A = excellent
  • B = good
  • C = average
  • D = poor
  • F = failure

By contrast, many institutions in Canada do include an "E" grade, which is a "near-fail" or "conditional pass", and may require mandated tutoring or partial repetition of the course.

In some cases, plus and minus modifiers are applied to grades to provide intermediate recognition of performance. An A−, for example, would be lower than an A but higher than a B+. Some educational institutions do not include A+s, while others do. Furthermore, pluses and minuses are not always applied to the "F" grade. Usually an "F+" is similar to Canada's "E" (and is often expressed as a "marginal fail"). An "F−" - or sometimes "FF", or particularly in England and Wales, "G" - is usually a grade given for exceptionally poor performance, academic dishonesty (frequently denoted by "FF"), or failure to produce any work ("Nothing of Merit" or "No Work Submitted").

In the Canadian province of Ontario, another system is placed that replaces the A-F system. This system was instituted by the provincial government in around 2001. It is very much the same as the A-F system but uses numbers instead of letters. It goes like this:

  • 4 = A or excellent
  • 3 = B or good
  • 2 = C or average
  • 1 = D or poor
  • R = F or Remedial (20-49%)
  • I = Incomplete (0%)

The system also adopts the +s and -s of the A-F system. So a 4- is about equal to a A-. Some teachers may also attribute the +s and -s to the R, meaning that an R+ is an almost fail, and an R- meaning no work or work of inferior quality. Some teachers have been known to become overzealous and give students 5s for spectacular achievement and -1s for below what is possible. These are usually converted to 4+s and R-s on the report card. The students' marks in Canada are also weighed differently, the marks are divided in four categories, Knowledge, Thinking and Inquiry, Communication and Application. The categories are worth different amounts depending on the course. For example, a knowledge-heavy course such as math would have Knowledge worth more than Communication while an English class would be the opposite. Lastly, in secondary school, the categories are equal to around 70% with the exam and culminating performance task worth the other 30% of the mark. Also a student may not get lower than a 20% in a class as long as the student hands in work.

The English system is very similar to the A-F system, but with the inclusion of the grades G, U and at GCSE level A*. A* (at GCSE) or A (at A level) is the highest, C is average, E is the minimum pass mark and U being unacceptable. Modifiers such as B- or B+ are not used as extensively as in the US and final qualification grades are never expressed as such. FF is never used.

Percentage-based grading

In objective subjects such as mathematics, grades are normally computed according to percentages such as class attendance, homework completion, and test averages. A weighted average of these variables is used to compute one percentage, which is the index from which grades are determined.

In subjective disciplines where essay exams and papers are more common, grades are sometimes represented numerically, other times with letter grades.

The specific conversion of percentages to letter grades varies according to the class. In classes with very difficult problem sets, it's not unheard of for the cutoff for passing to be 20%, and that for an "A" grade to be given at 50%.

Usually, though, primary and secondary schools use fixed systems. The traditional system is the "Tens System", written as (90/80/70/60). In other words, the lowest A (or A/B line) is at 90%, while the lowest D (or D/F line) is at 60%. In order either to set a higher standard or correct for grade inflation, however, some schools use the "Nines System" (92/83/74/65) or "Eights System" (either 93/85/77/70 or 94/86/78/70). Usually, the system employed does not make grading easier, since difficulty of exam questions will be calibrated to the grading system; indeed, exams in a school using the Tens System will often be more difficult than those in schools using the other systems.

The Tens System is used in Canada but the A-F system (or in the case of Ontario, the 0-4 system) values are different than those of the United States. It goes as follows:

  • A = 80 or higher
  • B = 70-79
  • C = 60-69
  • D = 50-59
  • F = 49 or lower

The pluses and minuses are taken into account also, so a plus is closer to the higher end of the score or the minus is at the lower end of the score. The percentage system is not used in primary schools, as all marks shown on tests, assignments and on the report card are shown with the A-F or 0-4 system depending on province. Percentage may also be provided along with tests. In senior elementary or secondary schools, tests and assignments are provided with both the mark on the present system in the province and also with the percentage. On the report card, only the percentage is shown on the final mark.

Various rubrics exist for assigning pluses and minuses, usually assigning them to roughly the top and bottom third of a grade level, with the "base" grade (that is to say, the one that does not carry either a plus or minus sign) being widest if the number of points in the entire letter grade are not evenly divisible by three. For example, under the Tens System, the plus grades will most commonly end in 7, 8 or 9 while the minus grades will end in 0, 1 or 2, with the base grades ending in 3, 4, 5 or 6. In the Nines System the plus, base and minus bands are typically equal (spanning three points each) while plus and minus formats under the Eights System vary widely; often the base grade will consist of four points and the plus and minus grades will consist of two points each, but this is far from universal. If "A+" is omitted (and it often will be if the institution does operate under the grade-point system), the "A" and "A−" grades may cover the same number of points (or the "A" will contain one more point if their sum is an odd number), or the "A−" range may not be larger than those of the plus and minus grades found elsewhere along the grading scale, and the "A" range will be twice a large as that of the other base grades.

Rank-based grading

Informally, grading "on the curve" refers to any system wherein the group performance is used to moderate evaluation — grading need not be strictly or purely rank-based. In the most severe form, students are ranked and grades are assigned according to a student's rank, placing students in direct competition with one another.

The following is an example of a grade distribution commonly used when this sort of grading is employed.


These percentages derive from a normal distribution model of educational performance. An "A" is given here for performance that exceeds the mean by +1.5 standard deviations, a "B" for performance between +0.5 and +1.5 standard deviations above the mean, and so on.

"Grade-rationing": the case for rank-based grading

Rank-based grading is popular among some American educators, usually under the euphemism of "grade-rationing". The arguments for grade-rationing are that

  • grade inflation represents a serious problem in education, that can only be counteracted by the enforcement of rank-based standards, and
  • since many corporations used rank-based evaluation measures, sometimes even related to termination (see: rank and yank) such grading prepares students for the "real world".

Case against rank-based grading

Despite near-universal concerns about grade inflation, rank-based grading systems are mostly out-of-favor in the contemporary United States. When rank-based systems are used, in education or employment situations, cutthroat behavior and cheating become rampant. In some situations, high-scoring students are disliked by their classmates for "raising the curve".

Cited as a case against rank-based evaluation specific to employment, Enron used a rank-based evaluation scale; the cutthroat environment created there resulted in the disgrace and downfall of the corporation. Some predict that analogous problems, on a more minor scale (cheating, theft of reserved materials) will occur in schools that use rank-based grading.

Grade point average

Grade point average (GPA) is a number that represents the average of a student's grades during his or her time at an institution. Usually it is weighted by number of credits given for the course.

Most high schools and nearly all colleges in the United States use a "four-point" system, where numerical values are applied to grades as follows:

  • A = 4
  • B = 3
  • C = 2
  • D = 1
  • F = 0
  • FF/G (if given) = -1

This allows grades to be easily averaged. Additionally, many schools add .3 for a "+" grade and subtract .3 for a "−" grade. Thus, a B+ yields a 3.3 whereas an A− yields a 3.7. A+'s, if given, are usually assigned a value of 4.0 (equivalent to an A) due to the common assumption that a 4.00 is the best possible grade-point average, although 4.3 is awarded at some institutions. In some places, .33 instead of .3 is added for a "+" grade and subtracted for a "−" grade.

Some high schools, to bolster their students' chances in college admissions, will give higher numerical grades for difficult courses, often referred to as a weighted GPA. For example, a common conversion system used in honors and advanced placement courses is:

  • A = 5
  • B = 4
  • C = 3
  • D = 1
  • F = 0

The E-S-N-U system

At one time (until roughly the mid-20th Century), the most popular grading system in the United States used four letters, which ranked, in descending order:

  • E (excellent)
  • S (satisfactory)
  • N (needs improvement)
  • U (unsatisfactory)

This system has largely been replaced by the A-F system dealt with previously, but is still encountered quite often at the elementary school level, particularly in kindergarten and Grades 1 through 3 (this educational level being frequently referred to as primary school). It is also occasionally used at schools for older children, including high schools, in the issuance of "conduct" or "citizenship" grades.

Some variants exist in this system, including the use of an "O" (for "outstanding") grade, which is even higher than the "E"; and sometimes a "G" (for "good") is placed between the "E" and the "S".

Plus and minus grades are seldom used in this system, and on most of the occasions where they do exist, only the "S" grade may be so modified (with an "S+" and "S−" being available in addition to the base grade of "S").

De-emphasis of grades

A number of reputable liberal-arts colleges in the U.S. either do not issue grades at all (such as Bennington College) or de-emphasize them (St. John's College). In all cases, the rationale is that grades often do not provide a clear picture of academic aptitude or of potential for success, and that learning, not achieving the highest score, should be the goal of a liberal education.

Yugoslavia (former)

In Croatia and likely the rest of the former Yugoslavia, a similar five-point grading scale is used, where:

  • 5 (excellent) is the best possible grade
  • 4 (very good)
  • 3 (good)
  • 2 (sufficient) is the lowest passing grade
  • 1 (insufficient) is the lowest possible grade, and the failing one

Teachers in grade schools and high schools are also allowed to record individual exam results with grades such as "3+" or "5-" or "3/4" which indicate varying ambiguities, but final grades at the end of the year need to be one of the basic five. An arithmetic mean is usually calculated, with X.45 being the threshold.

Related topics

Degree grades:


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