German Grade Calculator (Modified Bavarian Formula)
Your grade on the German 1.0–4.0 scale by the KMK formula, with the working.
Working
What do you need?
Every German grade for this scale
Each German grade and the band of your scale’s grades that gives it.
| German grade | Your grade above | up to and including |
|---|
Source: KMK — Vereinbarung über die Festsetzung der Gesamtnote bei ausländischen Hochschulzugangszeugnissen (PDF) · anabin — assessment proposals for foreign qualifications (KMK)
About the German Grade Calculator (Modified Bavarian Formula)
German grades run from 1.0 (best) to 4.0 (the lowest pass), and foreign grades are converted to that scale with the modified Bavarian formula, x = 1 + 3 × (Nmax − Nd) ÷ (Nmax − Nmin): Nmax is the best grade of your scale, Nmin its lowest pass grade and Nd your grade. Pick your scale — a percentage, a 10-point CGPA, a 4.0 GPA or any other — check the pass mark against your transcript and type your grade.
The result follows the KMK agreement that sets out the formula: the grade is worked out to one decimal and cut off, never rounded, so an exact 2.25 is a 2.2, not a 2.3. You see the working, what rounding would have given, the grade you must beat for the German grade a programme asks for, and a table of every German grade from 1.0 to 4.0 for your scale.
How to use it
- Choose your grading scale. The best grade (Nmax) and the pass mark (Nmin) fill in; change them to what your transcript or certificate says.
- Type your grade (Nd) — your average, such as 75, 7.5 or 3.2.
- Read your German grade and the working. When the cut-off changed it, the result also says what rounding would have given.
- Pick the German grade you need — 2.5, say — to see the grade you must beat; the table underneath lists every German grade for your scale.
- Copy result keeps the grade with its working; Download table saves the table as CSV.
Examples
75 · Nmax 100 · Nmin 40
1 + 3 × 25 ÷ 60 = 2.25 → German grade 2.2
Cut off, not rounded: 2.25 becomes 2.2.
CGPA 8.1 · Nmax 10 · Nmin 4
1 + 3 × 1.9 ÷ 6 = 1.95 → German grade 1.9
GPA 3.2 · Nmax 4 · Nmin 1
1 + 3 × 0.8 ÷ 3 = 1.8 → German grade 1.8
Percentage · Nmax 100 · Nmin 40 · target 2.5
A grade above 68 — exactly 68 gives 2.6
Grade 2 · Nmax 1 · Nmin 4
1 + 3 × (1 − 2) ÷ (1 − 4) = 2.0
The formula and its two reference values
The formula is a straight line: your scale’s best grade becomes 1.0, its lowest pass grade becomes 4.0, and every grade in between is placed proportionally. The KMK text calls Nmax and Nmin the upper and lower reference values “according to the assessment proposals of the ZAB”, the KMK’s Central Office for Foreign Education, which publishes its assessment proposals in the anabin database. uni-assist’s glossary describes a grading system the same way: the maximum grade and the minimum passing grade of your degree.
The pass mark changes the result more than people expect: 75% is a 2.2 with a pass mark of 40 (exactly 2.25), a 2.1 with 35 (2.153…) and a 2.5 with 50. Use the values printed on your marksheet or transcript, or the ones the university gives for your certificate.
Cut off at one decimal, never rounded
Section 4(4) of the KMK agreement: “Bei der Umrechnung wird die zu ermittelnde Note auf eine Stelle nach dem Komma bestimmt; es wird nicht gerundet” — the grade is set to one decimal place and is not rounded. So 1.95 is a 1.9 and 2.29 is a 2.2. The converter works with exact decimals, so a result such as 2.3 is never shown as 2.2 because of a computer’s rounding error.
The agreement is written for foreign university-entrance certificates. For other qualifications — a bachelor’s degree in a master’s application, for example — the university’s own admission rules say how it converts, and they may use other reference values or round.
Grades from several certificates or subjects
The same agreement says what goes into Nd. If a certificate lists only subject grades, the overall grade is their arithmetic mean, keeping the weighting. Several overall grades that all count are averaged with equal weight and then converted; if they come from different grading systems, each is converted first. Work out such an average before you type it here — the GPA calculator and the CGPA calculator help with weighted averages.
Scales where 1 is the best grade
Some countries grade the other way round, with 1 as the best grade. The formula still works: type 1 as the best grade (Nmax) and the lowest pass grade (say 4) as Nmin. A 2 then gives 1 + 3 × (1 − 2) ÷ (1 − 4) = 2.0, and the table shows the grades you must stay below.
Sources
- KMK, Vereinbarung über die Festsetzung der Gesamtnote bei ausländischen Hochschulzugangszeugnissen — the formula (Anlage), the one-decimal cut-off (4(4)) and the averaging rules (2 and 4)
- KMK Central Office for Foreign Education, anabin — the assessment proposals for foreign qualifications
- uni-assist, Glossary of terms — a grading system: the maximum grade and the minimum passing grade of a degree
Limitations
- The university or uni-assist decides which reference values and rules apply to your certificate; this page applies the formula to the values you enter.
- A grade below the pass mark is a fail and is not converted.
- Letter grades have to be given as numbers on your scale first (for a 4.0 GPA, the GPA calculator turns letters into grade points).
- The result is a calculation for orientation, not an evaluation of your certificate.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
How do I convert my percentage to a German grade?
Use the modified Bavarian formula with 100 as the best grade and your pass mark as the lowest pass grade. With a pass mark of 40, 75% gives 1 + 3 × 25 ÷ 60 = 2.25, which is a German 2.2.
Why is an exact 2.25 shown as 2.2 and not 2.3?
The KMK agreement says the grade is set to one decimal and not rounded, so everything after the first decimal is cut off.
Which pass mark (Nmin) should I use?
The lowest passing grade of your certificate’s grading system — usually printed on the marksheet or transcript. The KMK’s anabin database holds the assessment proposals for foreign qualifications, and uni-assist’s glossary describes a grading system as the maximum grade and the minimum passing grade of your degree.
What CGPA do I need for a German 2.5?
On a 10-point scale with 4 as the pass grade, a CGPA above 6.8: exactly 6.8 gives 2.6, and anything higher gives 2.5 or better. With another pass grade the figure changes — the table under the result shows it for your scale.
Is this what my university or uni-assist will calculate?
If they use the same best grade and pass mark, the formula gives the same German grade. They apply the reference values and rules for your certificate, so use this result as a check, not as their decision.
Can I convert a scale where 1 is the best grade?
Yes. Type 1 as the best grade and your lowest pass grade as Nmin; the formula and the table work the same way, with lower grades being better.