The Danish grading scale

Denmark grades on seven values and nothing in between: 12, 10, 7, 4, 02, 00 and −3. There is no 11, no 8 and no 5. The scale has applied across all state-regulated Danish education since August 2007, when it replaced the old 00 to 13 scale, and it was designed so that every grade carries an official ECTS letter. 02 is the minimum grade for passing an exam.

Below is the table as the Danish Agency for Higher Education and Science publishes it, including the column most conversion sites leave out: the grade on the old 13-scale that each current grade corresponds to.

Denmark issues no GPA. The only equivalence the ministry publishes is the ECTS letter in that table, so a Danish transcript converts officially into A to F and into nothing else. Any Danish GPA you have been handed on a 4.0 scale is a conversion someone applied afterwards, and two evaluators using two tables will read the same transcript differently. Carry your gennemsnit, say it is on the 7-point scale where 12 is the ceiling, and let the receiving institution apply its own table.

The scale's real quirk is the −3. Being negative, it does not merely fail to add to a weighted average, it subtracts from one, so a single −3 moves a Danish average further than a zero moves an average anywhere else in Europe. To put your own marks through the ECTS-weighted arithmetic, use the Danish grade calculator. To see the 7-point scale beside other countries' systems, use the grading scale comparison.

What is the Danish 7-point grading scale?

Seven fixed grades: 12, 10, 7, 4, 02, 00 and minus 3. There is nothing between them, so no 11, no 8 and no 5. It has applied across state-regulated Danish education since August 2007, and each grade carries an official ECTS letter running from A down to F.

What is the lowest passing grade in Denmark?

02. The ministry states plainly that 02 is the minimum grade for passing an exam. Both 00 and minus 3 are failing grades and they are not the same thing: 00 marks a performance that does not meet the minimum requirements, while minus 3 is reserved for one that is unacceptable in all respects.

What do Danish grades convert to in ECTS?

12 = A, 10 = B, 7 = C, 4 = D, 02 = E, 00 = Fx and minus 3 = F. That is the official correspondence published by the Danish ministry, and it is the only conversion Denmark itself publishes.

How do old Danish 13-scale grades convert to the 7-point scale?

The ministry publishes the correspondence directly: 13 and 11 become 12, 10 stays 10, 9 and 8 become 7, 7 becomes 4, 6 becomes 02, 5 and 03 become 00, and 00 becomes minus 3. The 13-scale ran until 2007, so it is what appears on older Danish transcripts.

Does Denmark use a GPA?

No. Danish institutions record grades on the 7-point scale, and the official equivalence is to ECTS letters rather than to any grade point average. A 4.0-scale figure for a Danish transcript is always somebody's after-the-fact conversion, so quote your average on the 7-point scale and name the scale beside it.

Is there a grade between 4 and 7 in Denmark?

No. The scale has exactly seven values and the gaps are deliberate: the numbers were chosen so each one lines up with an ECTS letter, not to form a continuous run. An examiner awards one of the seven and never a value in between.

What is the minus 3 grade in Denmark?

The lowest grade on the scale, awarded for a performance which is unacceptable in all respects, and the ECTS equivalent of F. It is unusual among European grades in being negative, which means it pulls a weighted average down rather than simply contributing nothing to it.

How is a Danish grade average calculated?

Each grade is multiplied by the course's ECTS points, those products are added together, and the total is divided by the total ECTS. Because minus 3 is negative it subtracts from the numerator rather than contributing zero. The Danish grade calculator on this site runs exactly that arithmetic in your browser.