The modified Bavarian formula estimates a German grade from three values on the original grading scale: the best possible grade, the lowest passing grade and your achieved grade. TUM publishes this formula for a conversion context; it is not a universal rule for marking every German exam.
Use the German grade calculator when the original scale increases with better performance and the receiving institution accepts this method.
The formula and its inputs
German estimate = 1 + 3 × (best − achieved) ÷ (best − passing)
In the calculator, Maximum Points means the best possible value on the original scale. Minimum Points means its published minimum passing value. These are scale boundaries, not necessarily the highest and lowest scores earned by your classmates.
The best value must be greater than the passing value. Your achieved value must lie between them for this calculator’s passing-grade estimate.
Example one: a 100-point scale
Suppose the documented best result is 100, the passing threshold is 50 and your result is 80.
- Best minus achieved: 100 − 80 = 20.
- Best minus passing: 100 − 50 = 50.
- Divide and scale: 3 × 20 ÷ 50 = 1.2.
- Add one: 1 + 1.2 = 2.2.
This is an invented example of the arithmetic. It does not establish that a particular institution uses 50 as its passing threshold.
Example two: why the passing threshold matters
Keep the best result at 100 and the achieved result at 80, but use a documented passing threshold of 40.
The formula becomes 1 + 3 × 20 ÷ 60 = 2.0. The achieved mark has not changed, yet the estimate differs from the first example. Using a guessed passing threshold would therefore change the answer.
At the endpoints, the formula gives 1.0 for the best possible result and 4.0 for a result exactly at the passing threshold. Those checks help catch reversed inputs.
When the calculator cannot give this estimate
- Best and passing are equal: the denominator is zero, so the formula is undefined.
- The achieved score exceeds the best value: check the source scale or whether extra credit needs separate treatment.
- The achieved score is below the passing value: this calculator shows a message instead of extrapolating or capping a failing result.
- Lower source numbers mean better performance: this form’s increasing-scale assumptions do not fit that input directly.
The calculator updates while you type. It displays the estimate to one decimal place. A university may specify different rounding or a different evaluation method; follow its instructions for an official submission.
Keep conversion separate from admission
A calculated number does not decide whether a qualification is recognized or whether admission requirements are met. Keep your original transcript, the grade key and the receiving institution’s conversion instructions together.
For a comparison with a US-style table, read German grades and US GPA. That page uses an illustrative lookup, which is a different operation from the formula here.
Save a reproducible scenario
Record the three inputs and where the grade boundaries came from. Save separate assumptions in separate workspaces, then export a backup if you need to move the calculation to another browser.
Before changing a boundary merely because the result looks unexpected, verify it against the published rule. The international grading guide explains why similarly named grades can need different treatment.
