Coverage of a cirlce Suppose I have a coordinate system with one main circle and additional circles. I want to determine the area, the main circle is covering, which is not covered by the other circles. Further, it might be important to mention, that the center of a circle is always a grid intersection, so circles cannot be placed randomly. Also, the radius of all circles is equal. In the example below, I am looking for the yellow area.
How can this task be performed? Happy to receive any suggestions for formulas/algorithms/code.

 A: Not an answer but too long for a comment.
I think there is no easy answer to your question.
Your picture suggests that all the circles have the same radius $r$.
If so, start by noting that you can ignore all the gray circles whose distance from the center of the yellow circle is more than $2r$.
Then you will have to loop over the gray circles that matter.
The intersection of one gray circle with the yellow circle is a
lens . You need to subtract its area from the yellow circle. You will face complexities when two such lenses intersect, since that would double count the area to be subtracted. An inclusion-exclusion argument can deal with this. It will require (at least) a nested loop over gray circles.
This related stackexchange question may help:
Intersection of n circles
Edit:
If the centers are in fact grid points and the radii are all $1$ then you can enumerate all the cases in advance. Look at the number and disposition of the (at most $9$) gray circles and calculate the area in each case. Take advantage of the symmetries to reduce the number of cases.
