Denmark uses an unusual seven-value numeric grading scale known as the 7-trinsskala (7-point scale): 12, 10, 7, 4, 02, 00, and -3. Despite the numbers, it is not a continuous scale from 0 to 12 — only these seven specific values exist, each tied to a fixed official description of performance, and 02 is the lowest passing grade.
The Danish 7-point scale
| Grade | Official Description | Status |
|---|---|---|
| 12 | An excellent performance with no or only a few minor flaws | Pass |
| 10 | A very good performance with a number of minor flaws | Pass |
| 7 | A good performance with some flaws | Pass |
| 4 | A fair performance with several flaws | Pass |
| 02 | An adequate performance meeting only the minimum requirements | Pass |
| 00 | An inadequate performance not meeting the minimum requirements | Fail |
| -3 | An unacceptable performance | Fail |
Notice that the numbers 1, 2, 3, 5, 6, 8, 9, and 11 simply don't exist on this scale — there's no partial credit "between" 7 and 10, for example. A grade is always exactly one of these seven fixed values.
Why the scale is structured this way
The 7-point scale replaced Denmark's older 13-point scale (which ran from -3 to 13 with more intermediate values) in the mid-2000s, partly to make Danish grades easier to map onto the ECTS grading scale used across Europe. Each of the seven grades was deliberately designed to correspond to one of the ECTS grade bands (A through F), giving Danish universities a built-in, standardized way to translate local grades into the European framework used for exchange and credit transfer.
Because there are only seven possible values, don't try to interpret gaps between them as if points were missing — a jump from a 4 to a 7, for instance, represents a full step up to the next qualitative performance band, not a partial score.
Passing thresholds and credit structure
02 is the minimum grade needed to pass an individual course or exam in the Danish system. 00 and -3 are both failing grades, with -3 specifically reserved for work considered unacceptable in a way that goes beyond simply "not meeting requirements" (00). Denmark uses the ECTS credit system, with a full academic year typically equal to 60 ECTS credits. If your Danish transcript reports ECTS credits, the ECTS Calculator can help with the credit-weighting side of a conversion.
Converting Danish grades to a US 4.0 GPA
There's no single official Danish government formula for converting the 7-point scale into a US GPA, but because the scale was explicitly designed to align with ECTS grade bands, a commonly referenced approximate mapping looks like this:
| Danish Grade | Approx. ECTS Grade | Approx. US Letter | Approx. GPA Points |
|---|---|---|---|
| 12 | A | A | 4.0 |
| 10 | B | A- | 3.7 |
| 7 | C | B | 3.0 |
| 4 | D | C | 2.0 |
| 02 | E | D | 1.0 |
| 00 / -3 | F / Fx | F | 0.0 |
Worked example: A student completes an exchange semester at a Danish university with the following results:
| Course | ECTS Credits | Danish Grade | Approx. GPA Points |
|---|---|---|---|
| International Marketing | 7.5 | 12 | 4.0 |
| Danish Society and Culture | 7.5 | 10 | 3.7 |
| Supply Chain Management | 7.5 | 7 | 3.0 |
| Applied Statistics | 7.5 | 4 | 2.0 |
Weighted GPA = ((4.0×7.5) + (3.7×7.5) + (3.0×7.5) + (2.0×7.5)) ÷ 30 = (30.0 + 27.75 + 22.5 + 15.0) ÷ 30 = 95.25 ÷ 30 ≈ 3.18
Once you've mapped each Danish grade to an estimated GPA point value, you can plug the converted grades and credit hours directly into a GPA Calculator.
Common edge cases
- A 4 is a real pass, not a near-fail: Despite being numerically close to 02 (the minimum pass) and far from 12, a grade of 4 in Denmark represents a "fair" performance and is a comfortable, unambiguous pass — it should not be read as a near-failing grade.
- Grade distribution guidance: Danish grading regulations have historically referenced an expected distribution across a cohort (with 12s intended to be relatively rare), though individual course examiners assess against the qualitative descriptions first and foremost, not a forced curve.
- 7-point scale replaced the 13-point scale: Older Danish transcripts or credential documents (generally pre-2007) may still reference the previous 13-point scale, which used different numeric values entirely — don't apply the 7-point conversion table above to an older document without checking which scale was used.
- Not the same as Norway or Sweden: Denmark's numeric 7-point scale, Norway's A-F letters, and Sweden's mixed A-F/U-G-VG system are all different frameworks — geographic proximity doesn't mean grading compatibility.
Try it yourself
If you have Danish grades and ECTS credit values you need to convert into an estimated US GPA, the GPA Calculator and ECTS Calculator handle the math instantly in your browser, with no account required.
