The Modified Bavarian Formula Explained

What the formula does

The German scale runs from 1.0 (best) to 4.0 (lowest pass); anything worse is a fail. The modified Bavarian formula maps your grade onto that scale by position: if your grade sits 80% of the way from the lowest passing grade to the best possible one, it lands 80% of the way from 4.0 to 1.0. It is based on a resolution of the Kultusministerkonferenz and is used in the conversion tools of universities such as TUM.

The formula

X = 1 + 3 × (Nmax − Nd) ÷ (Nmax − Nmin)

• X — the German grade you want
• Nmax — the best possible grade in your system (not the best grade you personally received)
• Nmin — the lowest passing grade in your system
• Nd — the grade you want to convert, for instance your overall GPA or percentage

Worked examples

Check the first row: 1 + 3 × (100 − 75) ÷ (100 − 40) = 1 + 3 × 25 ÷ 60 = 2.25. Because 2.25 sits between 2.2 and 2.3, the final rounding depends on the university — some cut off after the first decimal, some round.

Step by step: converting your own grade

1. Write down the grading scale of your university: the best possible grade (Nmax) and the lowest passing grade (Nmin).
2. Decide which grade to convert — usually your overall result, as stated on the transcript or certificate (Nd).
3. Insert the three values into the formula and calculate.
4. Check the plausibility: the result should lie between 1.0 and 4.0 for a passing grade.
5. Round following the target university’s rule, or give two decimals and state that the value is unrounded.

Letter grades

When your grades are letters, number them from the best grade upwards. TUM’s example: A+ = 1, A = 2, B = 3, C = 4, D = 5, E = 6 (fail). Then Nmax = 1, Nmin = 5 (the lowest passing letter, D) and Nd is the number of your overall grade. The formula works for scales that run in either direction.

Here is TUM’s letter-grade example worked through with the formula (Nmax = 1, Nmin = 5):

A D is the lowest passing grade, so it maps to the German 4.0. Your own overall letter grade is usually an average, so convert the average, not each letter on its own.

Where it can mislead

• It is linear. It cannot know that a 75% at one university is rarer than at another, or that an A is awarded to 40% of students at some schools and 5% at others.
• Nmin is the passing grade, not the lowest possible mark. Using 0 instead of 40 or 60 changes the result a lot.
• Many programs use their own tables. Admissions offices may convert your grades differently from the formula, and official conversions follow the program’s examination regulations.
• The result is non-binding. University converters, including TUM’s, say so explicitly.

What German results look like

Individual exams at German universities are usually graded in steps — 1.0, 1.3, 1.7, 2.0, 2.3, 2.7, 3.0, 3.3, 3.7 and 4.0 — while overall grades are often shown with one decimal. A converted value such as 2.25 therefore does not have to match one of these steps; it is a reference figure that lets admissions staff compare you with German applicants.

Going the other way

To see what a German grade means on your own scale, reverse the formula: Nd = Nmax − (X − 1) × (Nmax − Nmin) ÷ 3. A German 2.0, for example, is 80% on a 100/40 scale. Use the German grade converter for either direction.

Frequently asked questions