Convert a foreign grade with the modified Bavarian formula, handle higher- or lower-is-better scales, compare rounding, or reverse-solve a German target.
Bavarian Formula
The modified Bavarian formula maps passing foreign grades between the best attainable grade and the lowest passing grade to German grades from 1.0 to 4.0. A lower German grade is better. This calculator does not extrapolate failing grades.
- x = converted German grade
- Nmax = best attainable grade, maximum score, or best rank
- Nmin = minimum passing grade, minimum passing score, or lowest passing rank
- Nd = your grade, score, or rank
For number grades, enter the best possible value, the minimum passing value, and your achieved value. The same formula works for systems where higher numbers are better, such as 100-point scores, and systems where lower numbers are better, such as 1 to 4 grade scales.
For letter grades, first convert letters into institution-approved numeric ranks from best to worst and enter those ranks with the lower-is-better direction. The best letter is rank 1. For example, on the scale A+, A, B, C, D, E, the ranks are A+ = 1, A = 2, B = 3, C = 4, D = 5, and E = 6. Enter those numeric ranks in the same Bavarian formula.
German Grade Ranges and Result Meaning
| German grade range | Meaning | Typical status |
|---|---|---|
| 1.0 to 1.5 | Very good | Passing |
| 1.6 to 2.5 | Good | Passing |
| 2.6 to 3.5 | Satisfactory | Passing |
| 3.6 to 4.0 | Sufficient | Passing |
| 4.1 to 5.0 | Fail | Failing |
| Input type | Nmax example | Nmin example | Nd example |
|---|---|---|---|
| 100-point score, higher is better | 100 | 50 | 82 |
| 1 to 4 scale, lower is better | 1 | 4 | 2.3 |
| Letter scale ranked best to worst | 1 | Lowest passing rank | Your letter rank |
Example Problems
Example 1: 100-point score
You have a score of 82, the best attainable score is 100, and the minimum passing score is 50.
Rounded to one decimal, the German grade is 2.1, which is in the Good range.
Example 2: Letter grade
Your letter scale is A+, A, B, C, D, E. The lowest passing letter is D, and your grade is B. The ranks are A+ = 1, A = 2, B = 3, C = 4, D = 5, E = 6.
The German grade is 2.5, which is in the Good range.
FAQ
What should I enter for Nmax in the Bavarian formula?
Enter the best attainable result in your original grading system. If your system uses scores where higher is better, Nmax might be 100. If your system uses lower numerical grades as better grades, Nmax might be 1. If you are using letter grades, the best letter is treated as rank 1.
What should I enter for Nmin?
Enter the minimum passing result in the original grading system. For a 100-point system, this may be 50, 60, or another pass mark set by your institution. For a letter scale, enter the numeric rank of the lowest passing letter, such as the rank assigned to D on an A to F scale.
Why can a result above 4.0 show as failing?
On the German grading scale, 4.0 is usually the lowest passing grade. A calculated result above 4.0 falls into the failing range. This calculator accepts only the declared passing interval and displays results from 1.0 to 4.0. Choose the formula result, nearest tenth, or truncated tenth; official institutional rounding may differ.
