On this page
The Modified Bavarian Formula
The exact formula used to estimate how a foreign grade maps to the German 1.0 to 4.0 passing scale.
Updated
2 min read
At a glance
1.0
Best German grade
4.0
Lowest German pass
3
Inputs needed
German grade = 1 + 3 × ((best possible grade − your grade) ÷ (best possible grade − lowest passing grade)). A German 1.0 is the best result and 4.0 is the lowest pass. For example, 8.0 on a 10-point scale with 4.0 as the pass mark converts to 2.0.
- Official result
- University or VPD
- Sources checked
- 27 July 2026
The formula and what each value means
German grade = 1 + 3 × ((Nmax − Nd) ÷ (Nmax − Nmin))
- Nmax is the best possible grade in your grading system.
- Nd is the grade you obtained.
- Nmin is the lowest grade that still passes in your grading system.
Nmax means the best result, even when the best result is the smallest number. This is why the same formula can also handle a letter scale after the letters are given numerical positions.
TUM publishes this formula for grades earned outside Germany and states that it gives a non-binding first estimate. Your target program’s rules and official document review decide the grade used in an application.
Worked examples
| Your grade | Calculation | German estimate |
|---|---|---|
| 9.0 | 1 + 3 × (1 ÷ 6) | 1.5 |
| 8.0 | 1 + 3 × (2 ÷ 6) | 2.0 |
| 7.0 | 1 + 3 × (3 ÷ 6) | 2.5 |
| 6.0 | 1 + 3 × (4 ÷ 6) | 3.0 |
| 4.0 | 1 + 3 × (6 ÷ 6) | 4.0 |
The pass mark matters as much as the maximum. If two universities both use a 10-point scale but one passes at 4.0 and the other at 5.0, the same 8.0 result produces a different German estimate.
Use the right values
- Copy the best possible grade from your transcript or official grading rules.
- Copy the lowest passing grade for the degree, not the admission cut-off for your next program.
- Enter your final overall grade exactly as it appears on the transcript.
- Treat the result as an estimate until the university or uni-assist checks your documents.
If your university uses a country-specific table, a non-linear scale, or different rules for the degree award, the plain formula may not match the official result. Use the VPD grade calculator for a planning estimate, then rely on your issued VPD or university decision.
Frequently asked questions
It is a linear formula that maps a foreign grade between that system's best grade and lowest passing grade onto the German range from 1.0 to 4.0. The formula is 1 + 3 × ((best grade − obtained grade) ÷ (best grade − lowest passing grade)).
No. It is a planning estimate. The target university, examination rules, or uni-assist document review decides which values and conversion method apply to your application.
The formula measures where your result sits between the best possible grade and the lowest pass. A different pass mark changes that range, so the same CGPA can convert to a different German grade.
Ready to apply for your Master's?
Create a free account to keep your shortlist, documents and deadlines in one place. Or ask a counsellor to call you.