Calculating extruder motor steps for 1 mm I would like to calculate the amount of steps to turn the motor to have 1 mm of the filament.

I did the following (using approximate values):

The gear on the outside of the teeth as a diameter of 11mm.
Therefore the circumference is 34.56mm. Divided into one degree i get 0.096mm / degree. The stepper does 1.8 degree per step which results in 0.1728mm per step.

To get 1mm of filament pushed into the extruder I will have to do 5.787 steps.

The same extruder is in a Geeetech i3. The firmware there is configured to do 93 steps per millimeter.

I don't have any experience in working with stepper motors but in theory, this would be my approach with a huge difference to an existing firmware.

Where is my mistake?
Microstepping. Your board likely has 16x microstepping, so that each step is divided up into 16 parts. Your 5.787 figure, when multiplied by 16, comes out to 92.6 steps/mm - matching the value in your firmware.