The cost of public insurance is based on your (pre-tax) income—and your employer pays for half. The general contribution amount is 14.6% of pre-tax salary. After that, you may need to pay an additional contribution as determined by the public insurer. (For TK this is 0,7%, while others may be lower or higher.) In nearly all cases, you will also need to pay long-term care insurance (Pflegeversicherung) of around 1.8%. This means that for most insurers, you will end up paying around 17-18% of your pre-tax salary toward insurance.
To figure out your monthly contribution to TK, enter your pre-tax income in this calculator.