Danish Grade Calculator

The 7-trin-skalaen from 12 down to −3, ECTS-weighted, with your gennemsnit computed live.

Course recordDenmark - 7-trin-skalaen (12 to −3)

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Denmark grades on exactly seven values - 12, 10, 7, 4, 02, 00, and −3 - with 02 the lowest pass. Your gennemsnit (average) weights each grade by the course's ECTS points: grade times ECTS, summed, divided by total ECTS. Enter your courses below and the average updates live, with the pass-level band shown.

The scale's famous quirk is the −3: awarded for an unacceptable performance, it does not merely fail to add to your average, it subtracts from it, so a single −3 in a 10-ECTS course drags harder than anywhere else in European grading. The scale maps cleanly to ECTS letters (12 = A, 10 = B, 7 = C, 4 = D, 02 = E), which is how Danish transcripts travel abroad.

The scale this page uses

Grade	Grade points
12 (excellent)	12.0
10 (very good)	10.0
7 (good)	7.0
4 (fair)	4.0
02 (adequate / pass)	2.0
00 (inadequate)	0.0
−3 (unacceptable)	-3.0

Award class	Minimum GPA
Passing average (02+)	2.00

Denmark's 7-point scale (7-trin-skalaen) has exactly seven grades: 12, 10, 7, 4, 02, 00, and −3, with 02 the lowest pass. Averages are ECTS-weighted, and yes, a −3 subtracts from the total - one bad exam moves the average more than anywhere else in Europe. The scale maps to ECTS letters (12 = A, 10 = B, 7 = C, 4 = D, 02 = E).

Source. This scale is set by Karakterskalabekendtgørelsen, BEK nr 1125 of 4 July 2022, the Danish order on the 7-point grading scale (in Danish), which is the body that writes the rule. Click for authoritative source. We last read that document on 4 October 2026, and the sources page says when we check it again.

Worked examples

A normal semester: 12, 7 and 4

Say you got 12 in a 7.5 ECTS course, 7 in a 15 ECTS course and 4 in another 7.5 ECTS course. Each grade is multiplied by its ECTS, the results are added up, and the total is divided by all your ECTS: (12 × 7.5 + 7 × 15 + 4 × 7.5) ÷ 30 = 225 ÷ 30 = 7.50. The big 15 ECTS course pulls the average toward its 7, which is why the 12 doesn't lift you as far as you might hope.

What a −3 really costs

Two 10s and one −3, each in a 10 ECTS course: (10 × 10 + 10 × 10 − 3 × 10) ÷ 30 = 170 ÷ 30 = 5.67. Had that third exam been a 00 instead, the average would be 200 ÷ 30 = 6.67. The −3 doesn't just add nothing, it takes a full point off the whole average here.

A course graded Passed

You have 10 in a 15 ECTS course, 7 in another 15 ECTS course, and a third 15 ECTS course graded "Passed". Passed has no number, so it stays out of the sum and out of the ECTS total: (10 × 15 + 7 × 15) ÷ 30 = 255 ÷ 30 = 8.50. Leave a pass/fail course out of the calculator too, rather than typing it in as a grade.

How this scale works

Denmark uses one scale for every state-regulated exam: 12, 10, 7, 4, 02, 00 and −3. There's nothing in between, so you can't get an 11 or an 8. 02 is the lowest pass. 00 and −3 are both fails, and −3 is kept for work that's unacceptable in every way.

Each grade lines up with a letter on the European ECTS scale, which is how a Danish transcript is read abroad: 12 is A, 10 is B, 7 is C, 4 is D, 02 is E, 00 is Fx and −3 is F.

Your average is weighted by ECTS, because ECTS measure how much work a course is. A 15 ECTS course counts three times as much as a 5 ECTS one. Courses graded only pass or fail have no number and are left out.

Gymnasium is a little different. Your certificate shows a weighted average, and the one used for university admission in Denmark is raised by a factor of 1.03 if you took one more subject at the highest level than your programme required, or 1.06 if you took two or more.

Where these rules come from

Read from a government instrument and the institution's own rules, quoted below in their own words.

The scale itself. The Danish Agency for Higher Education and Science says the 7-point scale is "the grading system used in all state-regulated education since August 2007", and that "02 is the minimum grade for passing an exam". It describes a 12 as "an excellent performance displaying a high level of command of all aspects of the relevant material", and gives the ECTS letter for every grade. Source: Danish Agency for Higher Education and Science, Grading system.

The fails. The Ministerial Order on the Grading Scale for higher education says "The grade -3 is given for a performance which is unacceptable in all respects" and "The minimum pass grade is 02." Source: Ministry of Higher Education and Science, Ministerial Order on the Grading Scale (English translation, PDF).

The weighted average. The University of Copenhagen tells graduates to "Multiply the grade for each course/subject element by the prescribed number of ECTS credits", add the results, and divide by the ECTS of all the courses included. It adds that a grade of "Passed" "should not be included in your calculation, as it does not have a numerical value." Source: University of Copenhagen, How do I calculate a weighted grade point average?

Gymnasium averages. The agency's factsheet on upper secondary grades says the admission average is calculated "by raising the temporary weighted average mark by a factor of 1.03" for one extra subject at the highest level, and "by a factor of 1.06" for two or more. Source: Grading system of Danish general upper secondary education (PDF).

Checked on 2026-10-01 against the sources linked above.

Questions this calculator gets asked

How is the Danish grade average calculated?

Each grade (12, 10, 7, 4, 02, 00, or −3) is multiplied by the course's ECTS points, summed, and divided by total ECTS. This calculator runs that weighted average live - including the subtraction when a −3 appears.

What is the Danish 7-point grading scale?

Seven fixed values: 12 (excellent), 10, 7, 4, 02 (the lowest pass), 00, and −3. There is nothing between them - no 11s, no 8s - which is deliberate: the scale was designed in 2007 to map onto ECTS letters A through F.

Why does Denmark have a −3 grade?

To mark a completely unacceptable performance and to make it mathematically costly: a −3 actively subtracts from your average rather than just adding zero. It is rare in practice, mostly seen for blank or off-topic exams.

What is a good average in Denmark?

A gennemsnit of 7+ is solid (the good middle grade), 10+ is strong, and anything approaching 12 is exceptional since 12 is the ceiling. Danish Master's programmes commonly ask for averages around 7-8 for competitive admission.

How do Danish grades convert to GPA or ECTS?

By design: 12 = A, 10 = B, 7 = C, 4 = D, 02 = E on the ECTS scale, which US evaluators then read roughly as A = 4.0 downward. The official mapping to ECTS letters is printed on Danish transcripts.

Is this Danish grade calculator free and private?

Yes. No sign-up, nothing uploaded - the average is computed in your browser, your courses stay on your device, and the page keeps working offline.

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