# German Grade Calculator — Modified Bavarian Formula

> Convert your GPA, percentage or foreign grade to the German 1.0–4.0 scale with the official modified Bavarian formula used by German universities. Free.

- **Category:** Education & Grades
- **Interactive calculator:** https://youcalc.com/en/education-grades/german-grade-calculator/
- **Price:** Free, no sign-up required

## Overview

German universities and the central application service uni-assist convert a foreign overall grade into the German 1.0–4.0 scale using one official method: the modified Bavarian formula, set out in the Kultusministerkonferenz (KMK) resolution. This calculator applies that formula. Pick your home grading system to fill in its best and lowest-pass marks, enter the grade you want to convert, and read the German equivalent — where 1.0 is the best grade and 4.0 is the lowest pass. Use it when applying to a German university, comparing transcripts, or estimating where your results land before uni-assist evaluates them.

## How to read your result

The headline is your German grade, given to one decimal place (1.0 is best, 4.0 is the lowest pass, and anything worse is a 5.0 fail). The coloured band beneath it shows where the grade sits on the German scale from 1.0 to 5.0 and names the official descriptor — sehr gut (very good), gut (good), befriedigend (satisfactory), ausreichend (sufficient) or nicht ausreichend (fail). The formula card echoes the exact calculation with your numbers substituted, and the reference table lists every German band. A source grade below your system’s pass mark cannot be expressed on the German passing scale, so it is reported as a 5.0 fail.

## Method

The modified Bavarian formula (KMK) converts a foreign grade Nd into the German grade x as x = 1 + 3 × (Nmax − Nd) / (Nmax − Nmin), where Nmax is the best attainable grade in the source system and Nmin is the lowest passing grade. The result is determined to one decimal place and is NOT rounded — the second decimal is simply dropped (for example 3.25 becomes 3.2, not 3.3). The best grade maps to 1.0, the lowest pass to 4.0, and a grade below the source pass mark is treated as a 5.0 fail. The formula is direction-agnostic as long as you enter the best grade as Nmax and the lowest pass as Nmin. One important caveat: the binding Nmax and Nmin are the country-specific benchmark values (Eckwerte) published in the KMK/ZAB anabin database, which can differ from the raw extremes of a scale, so the presets here are sensible defaults you should confirm against anabin and your university. The result is indicative; the receiving university or uni-assist makes the final decision.

**German grade scale (1.0 best → 5.0 fail)**

| German grade | Descriptor | Meaning |
| --- | --- | --- |
| 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 (lowest pass) |
| 4.1 – 5.0 | nicht ausreichend | Fail |


**Default best (Nmax) and lowest-pass (Nmin) marks by source system**

| Source system | Best (Nmax) | Lowest pass (Nmin) |
| --- | --- | --- |
| Percentage | 100 | 50 |
| US GPA 4.0 | 4.0 | 2.0 |
| India CGPA 10 | 10 | 4 |
| Pakistan CGPA 4 | 4.0 | 2.0 |
| UK percentage | 100 | 40 |
| France /20 | 20 | 10 |
| Italy /30 | 30 | 18 |
| Scale /10 | 10 | 5 |


## Example

- **Setup:** You scored 85% in a system where 100 is the best mark and 50 is the lowest pass. Keep "Percentage" selected (best 100, pass 50) and enter 85.
- **Result:** The calculator returns a German grade of 1.9 — gut (good) — from 1 + 3 × (100 − 85) / (100 − 50) = 1.9. It is a pass, and the scale strip highlights the "gut" band (1.6–2.5).

## Frequently asked questions

### What is the modified Bavarian formula?

It is the official method German states (the KMK) prescribe for converting a foreign overall grade to the German 1.0–4.0 scale: x = 1 + 3 × (Nmax − Nd) / (Nmax − Nmin). German universities and uni-assist use it, which is why it produces an exact, reproducible number rather than a rough band.

### What should I enter for Nmax and Nmin?

Nmax is the best grade attainable in your system and Nmin is the lowest passing grade. Picking your system from the list fills sensible defaults (for example a US 4.0 GPA uses Nmax 4.0 and Nmin 2.0). The values that are actually binding are the country-specific benchmark values (Eckwerte) in the KMK anabin database, so check anabin.kmk.org and edit the fields if your country’s benchmarks differ.

### Why is the grade not rounded?

The KMK resolution states the converted grade is determined to one decimal place and is not rounded ("es wird nicht gerundet"). The calculator therefore truncates: 3.25 becomes 3.2, not 3.3. This matches what German universities apply.

### What do the German grades mean?

On the German scale 1.0 is the best grade and 4.0 is the lowest pass: 1.0–1.5 is sehr gut (very good), 1.6–2.5 gut (good), 2.6–3.5 befriedigend (satisfactory), 3.6–4.0 ausreichend (sufficient), and anything above 4.0 is nicht ausreichend (a 5.0 fail).

### Is this result official?

No. The formula is the official method, but the conversion is indicative: the receiving university or uni-assist performs the binding evaluation, using the country-specific anabin benchmarks and any subject-specific rules. Treat the result as a reliable estimate for planning, not a final decision.

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- [GPA Equivalence Converter](https://youcalc.com/en/education-grades/gpa-equivalence-converter/)
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- [ECTS Grade Converter](https://youcalc.com/en/education-grades/ects-grade-converter/)
- [CGPA to Percentage Calculator](https://youcalc.com/en/education-grades/cgpa-to-percentage/)
- [Grade Percentage to Letter Grade & GPA Calculator](https://youcalc.com/en/education-grades/grade-percentage-letter/)
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- [Cumulative GPA Calculator](https://youcalc.com/en/education-grades/cumulative-gpa-calculator/)

## Sources

- https://www.kmk.org/fileadmin/Dateien/pdf/ZAB/Hochschulzugang_Beschluesse_der_KMK/GesNot04.pdf
- https://www.tum.de/en/studies/application/application-info-portal/grade-conversion-formula-for-grades-earned-outside-germany
- https://anabin.kmk.org

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