SyllabusCalc

German grade calculator (modified Bavarian formula)

A grade on any foreign scale, converted to the German 1.0 to 4.0 scale with the formula every source starts from, then finished four ways, because German offices do not finish it the same way.

Reviewed by C. B. Zakarian on

Enter the best grade on your scale, the lowest passing grade and your own grade. The scale can run either way: a best grade of 18 with a pass line of 10, or a best grade of 1 with a pass line of 5. Each preset loads values one German office publishes, not a national standard.

Your grade under each finishing rule

The formula gives one exact value; a German grade has one decimal at most. These are the four ways the offices that publish their rule get from one to the other.

Finishing rulePublished byYour grade
Cut to one decimal, not roundedThe KMK resolution on foreign school-leaving certificates; TUM's converter; Passau's School of Business; the University of Erfurt—
Rounded to one decimal (an exact half goes up)Hochschule Osnabrück; LMU Munich's pharmacy admissions—
Nearest German grade step, an exact tie to the better gradeLeuphana University Lüneburg, for free movers—
Cut to one decimal, then the better neighbouring stepPassau's humanities and social-sciences faculties, for outgoing cohorts before 2025/26—

Every grade on your scale

The ladder from your best grade to your pass line, each grade converted and finished all four ways. It steps in tenths on a scale spanning 2 units or less, in whole grades up to 20 units, in fives up to 100, and in twenty equal steps beyond that, always ending on the pass line.

Your scaleExactCutRoundedNearest stepCut, then better step

Where the rules and the values come from

The formula is printed in the annex to the KMK's agreement on the overall grade of foreign school-leaving certificates (adopted 15 March 1991, in the version of 12 September 2013), which also rules that the grade is “auf eine Stelle nach dem Komma bestimmt; es wird nicht gerundet”: set to one decimal place, not rounded. TUM's formula sheet (July 2020) and Heidelberg University's (May 2023) state the same formula, and both print the letter-grade example loaded above. The French, Dutch and UK presets are rows of the TUM School of Computation, Information and Technology list dated 3 June 2026. The grade steps, 1.0, 1.3, 1.7, 2.0, 2.3, 2.7, 3.0, 3.3, 3.7 and 4.0, are the passing grades in Passau's own grade table, and Leuphana's six worked examples all land on them. Neither Osnabrück nor LMU says which way an exact half goes; the calculator rounds it up. Every source was read on October 6, 2026. The converting office's own values and rule win — type them in.

Where the arithmetic ends

This page converts one grade at a time. It does not know which office will read your transcript, which best grade and pass line that office uses, or which of the four rules it applies, and it does not average a transcript for you: the KMK resolution, for one, averages the foreign grades first and converts the average. A scale whose steps are not evenly spaced, or a letter scale, has to be numbered before the formula means anything. And an office can use a table instead of the formula, or decide a case by hand. The four readings are the range the published rules produce, not a promise of the grade on your record.

Questions

What is the modified Bavarian formula?

A straight line from a foreign scale to the German one: x = 1 + 3 × (Nmax − Nd) / (Nmax − Nmin), where Nmax is the best grade on the foreign scale, Nmin the lowest passing grade and Nd the grade being converted. The best grade becomes 1.0 and the pass line 4.0, the best and the lowest passing German grades. The KMK prescribes it for foreign school-leaving certificates, and TUM, Heidelberg, Passau, Leuphana, Erfurt, Osnabrück and LMU publish the same formula for grades earned abroad.

Why are four grades shown?

Because the exact value usually has more decimals than a German grade, and the offices that publish their rule finish it in four different ways. The KMK resolution sets the grade to one decimal without rounding, and TUM, Passau's School of Business and Erfurt cut the same way. Hochschule Osnabrück and LMU's pharmacy admissions round to one decimal. Leuphana moves it to the nearest German grade step, an exact tie going to the better grade. Passau's humanities and social-sciences faculties cut to one decimal and then took the better of the two neighbouring steps, a rule their German pages say ends with the 2025/26 outgoing cohort. The calculator shows all four and does not choose.

Which best grade should I enter?

The one the converting office uses, which is not always the top of your scale. TUM's School of Computation, Information and Technology lists 18 rather than 20 for French grades and 9 rather than 10 for Dutch ones, and says its best grade can differ from the one the foreign university states. Passau's School of Business used 9 for the Netherlands and 80 for UK marks until the winter semester 2025/26; for students going abroad from then on, it takes both values from the host university's transcript of records. Where an office states nothing, ask it: the KMK resolution takes both values from the assessment proposals of Germany's Central Office for Foreign Education.

How do I convert letter grades?

Number them first. TUM and Heidelberg print the same example: A+ = 1, A = 2, B = 3, C = 4, D = 5 and E = 6, a fail, so 1 is the best grade and 5 the lowest pass, and a B converts to 2.5. A scale whose steps are not evenly spaced has to be numbered the same way: TUM's School of CIT reads the Danish 12, 10, 7, 4 and 2 as 1 to 5 and lists a 10 as 1.7 and a 4 as 3.2. Typing the Danish numbers in directly would give 1.6 and 3.4.

What if my grade is above the best grade or below the pass line?

The formula maps only the stretch between them. Past the best grade it returns less than 1.0, better than any German grade; past the pass line it returns more than 4.0, a fail. TUM's own converter refuses both, and none of the sources read for this page says what an office records for a mark above a best grade it has capped, so the calculator prints the exact value and no reading.

Can I share a result?

Yes. The best grade, the lowest passing grade and your grade are stored in the page URL, and the copy-link button copies it.

Calculator, not counselor: this page does arithmetic on the values you give it. How a grade earned abroad is recognized, which values and which rule convert it, and what the result counts toward are decided by the institution reading it, so confirm anything that depends on it with that office.