# Why does the number of filters does not determine the output size in the CNN layer?

The formula to determine the output size is [(W−K+2P)/S]+1. Here the number of filters used is not significant for determining the ouput size, I was wondering why?

Is it because Each filter is separately applied to the input to obtain a feature map and the output of the that part is considered as dimension size?

The formula you've given is for 1 filter. If you have $$N$$ filters, then you have $$N$$ outputs of the size you describe.