How the German grade formula works
The formula places your grade on the German scale from three numbers: X = 1 + 3 × (Nmax − Nd) ÷ (Nmax − Nmin), where X is the German grade, Nd your average grade, Nmax the upper reference value, which university converters such as TUM’s call the maximum grade, and Nmin the lower reference value. The Standing Conference of education ministers (KMK, the Kultusministerkonferenz) names it the modified Bavarian formula in its agreement of 15 March 1991 (amended on 12 September 2013) and takes both reference values from the evaluation proposals of the ZAB, the Central Office for Foreign Education.
Strictly, that agreement sets the overall grade of foreign school-leaving certificates. German universities also use its formula for foreign degree grades, and TUM, Heidelberg and Hamburg cite the KMK resolution when they do.
Read it as a share: how far your grade sits below the best grade, out of the whole distance down to the minimum, spread over the three steps from 1.0 to 4.0. Your best possible grade gives 1.0; the minimum gives 4.0.
Nmin is your degree minimum, not your course pass mark
For an overall degree grade, Nmin is the lowest CGPA or percentage your university requires to award the degree, not the pass mark for a single course. Many converters and search answers fill in a course pass instead: 4 on a 10-point CGPA, 40%, a D. uni-assist, which converts grades for its member universities, rules that out on its India page: “The minimum grade required for passing individual courses is not relevant and cannot be accepted.” Its Pakistan and Bangladesh pages also ask for the minimum CGPA for the award of the degree, and Bayreuth’s converter gives the same instruction for an overall degree grade.
The choice moves the result. A 7.5 on a 10-point scale converts to 2.2 with Nmin 4, 2.5 with Nmin 5 and 2.8 with Nmin 6.
uni-assist points to the grading system printed on the back of your transcript of records; your university’s academic regulations state the degree minimum too.
Truncated or rounded: why tools give different results
The KMK agreement, whose formula universities also use for degree grades, sets the converted grade to one decimal without rounding: “es wird nicht gerundet” (it is not rounded), a rule written for school-leaving certificates. On the admission side, Münster cuts a master’s applicant’s result after the first decimal, and TUM’s own converter does the same; Bamberg truncates as well when it recognises modules taken abroad. HAW Landshut and Marburg round, also for recognition, but to whole grades or whole points, so their results do not line up with a one-decimal figure.
Most online converters round half up to one decimal, which no official text we read prescribes. The two methods part whenever the exact value’s second decimal is 5 or more. Take 8.5 on a 10-point scale with Nmin 4, where the exact value is 1.75:
| Method | Who uses it | 8.5 on 10, Nmin 4 |
|---|---|---|
| Truncate to one decimal | KMK text (entrance certificates), Münster, TUM converter (admission); Bamberg (recognition) | 1.7 |
| Round half up to one decimal | most online converters (not an official rule) | 1.8 |
| Round to whole grades or points | HAW Landshut, Marburg (recognition) | not comparable |
This calculator leads with the truncated grade and shows the figure rounded half up beside it, labelled as unofficial.
German grade bands: sehr gut to ausreichend
An overall German grade falls into one of five bands. TUM’s table and HTW Dresden’s assessment rules agree on them, from sehr gut at 1.0 to 1.5 down to ausreichend at 3.6 to 4.0, with a fail from 4.1. They are how universities name an overall grade, not a national statute. Module grades move in steps instead: HTW Dresden lists 1.0, 1.3, 1.7 and so on to 4.0, then 5.0 for a fail.
| German grade | German term | English |
|---|---|---|
| 1.0–1.5 | sehr gut | very good |
| 1.6–2.5 | gut | good |
| 2.6–3.5 | befriedigend | satisfactory |
| 3.6–4.0 | ausreichend | sufficient |
| from 4.1 | nicht ausreichend | fail |
Worked examples: CGPA, percentage and US GPA
A converted grade is only as good as the two endpoints behind it, so every example below states them. Nmax is the best grade on the scale. Nmin is given as “if your degree minimum is …”, because the minimum differs between universities and only your own transcript or regulations can supply it.
Say a US college awards the degree from a cumulative GPA of 2.0. A graduate with a 3.0 enters 4.0, 2.0 and 3.0 and reads 2.5. Entering the D’s 1.0, a course pass, would give 2.0 instead, a better German grade than the degree minimum supports.
- Find Nmax, the best overall grade your scale allows.
- Find your degree minimum in your transcript’s grading system or your university’s regulations.
- Enter both, then your grade.
- Read the truncated result and its band.
| Your grade | Nmax | If your degree minimum is | Exact value | German grade (truncated) | Band |
|---|---|---|---|---|---|
| 7.5 CGPA | 10 | 4 | 2.25 | 2.2 | gut |
| 7.5 CGPA | 10 | 5 | 2.5 | 2.5 | gut |
| 7.5 CGPA | 10 | 6 | 2.875 | 2.8 | befriedigend |
| 70% | 100 | 40% | 2.5 | 2.5 | gut |
| 70% | 100 | 50% | 2.8 | 2.8 | befriedigend |
| 3.0 GPA | 4.0 | 1.0 | 2.0 | 2.0 | gut |
| 3.0 GPA | 4.0 | 2.0 | 2.5 | 2.5 | gut |
Two official examples to check the arithmetic against: LMU’s page converts 5.32, on a scale whose best grade is 6 and minimum 4, into 2.02, which truncates to 2.0. Wuppertal’s converts 6.08 between 10 and 5 into 3.352, printed to three decimals; truncated, that is 3.3.
When your grade is outside your scale’s range
A grade better than your scale’s best grade or worse than your degree minimum is not converted here. TUM’s converter refuses such grades too: your grade must lie between the lowest pass and the maximum. Refusing them is our rule, following TUM; no source we read gives an official rule for them. Put through the formula anyway, a grade worse than the minimum lands above 4.0: 2.5 on a 10-point CGPA with Nmin 4 gives 4.75, no German pass. For a grade better than the best one, check the maximum against your transcript. Nmax equal to Nmin is refused too, and Marburg notes that a scale with only two pass levels cannot go through the formula at all.
Not every university converts the same way
The formula is common ground, but universities differ on which numbers go into it and on when they use it. Most of the variants below come from rules for recognising modules that enrolled students took abroad, not from admission: no admission source we read sets a country-specific Nmax other than the ZAB’s. On the admission side, Münster and TUM ask for the best grade of your own scale.
Where the lower number is the better grade, the formula is used unchanged: Nmax is the best grade and Nmin the lowest pass, whichever number is larger. The ZAB can also fix an endpoint for a whole country, as uni-assist reports for some Iranian degrees. The KMK text, Münster, Heidelberg and HAW Landshut point to the anabin database for each country’s best grade and lower pass mark.
| Variant | Example | Context | Source |
|---|---|---|---|
| A lower practical Nmax | Bamberg’s country list (UK 70%, France 16, Netherlands 9.5); Weimar’s highest mark typically awarded; Erfurt’s below 20 for French grades; Marburg’s maximum actually achievable | recognition | Bamberg, Weimar, Erfurt, Marburg |
| Lower number is better | a 1-to-5 scale with 1 best: formula unchanged | admission (TUM’s converter accepts both orders) | TUM |
| A country value from the ZAB | Iran: Nmin = 12 | Kardani and Karshenasi degrees from accredited universities, from 1 January 2015 | uni-assist |
| anabin or a table first | Weimar applies the formula where anabin does not help; HAW Landshut transfers grades directly where the systems are comparable | recognition | Weimar, HAW Landshut |
| A 15-point form | NP = 15 − 10 × (Nmax − N) ÷ (Nmax − Nmin), rounded to whole points | recognition (not final degree grades) | Marburg |
| Letter grades | number the levels from 1 for the best: A+ = 1 … D = 5 | admission (TUM, Bayreuth); Heidelberg’s is a scholarship form | TUM, Bayreuth, Heidelberg |
Who makes the official conversion: uni-assist and your university
The binding German grade comes from uni-assist or from the university you apply to, never from an online calculator, this one included. uni-assist states it plainly: “We convert your grades to the German grading system.” For its member universities it issues a VPD (preliminary review documentation), which records how uni-assist rates your grade in the German system; you then upload the VPD to the university before its deadline.
Universities that publish their own converters treat the result as orientation. TUM says its results “are for reference only and are not binding”, and that official conversions follow each programme’s academic and examination regulations. Bayreuth, HS Düsseldorf and Hamburg describe theirs the same way.
None of the uni-assist pages we read publishes the formula itself, its rounding, or how Nmax and Nmin are chosen beyond asking for your grading system. A VPD can therefore differ from the figure here, for example where the ZAB fixes a country’s Nmin, as in the Iranian case above.
Pick your university: what we prefill and what we don’t
Choose your university and the calculator fills in Nmax from its verified grading scale on GPAWise, with a link to the scale’s source; you can still change it. Of the 1,372 verified scales, all but 6 have a top grade equal to the scale’s maximum. For those 6, such as an A+ worth 4.33 on a 4.00 scale, nothing is prefilled: whether an A+ can lift a cumulative GPA above 4.00 is each university’s rule, so you enter the highest overall grade your transcript prints.
Nmin stays empty. Our scales record course grades, and the minimum for the award of a degree is a different number, so you enter it yourself. To convert to a 4.0 GPA instead of the German scale, use the GPA converter.