The ‘formula’ would be the transfer function of your filter, in the context of the frequency content of your signal.
For example, of you are using a lowpass filter with a 2kHz cutoff, and the frequency of your signal was 1kHz, you would expect essentially no attenuation. If you signal frequency was 3kHz, the output would be reduced by whatever the the filter stopband attenuation is. If your signal consisted of both, the 1kHz output would be essentially the same as the input, and the 3kHz signal would be significantly reduced.
