When radio signals leave earth, they propagate out in a wave form. But how far they can “spread out” over distance until they become indistinguishable from background noise?
There's a lot of factors in this question, but it really comes down to a link budget. With a fixed power, gain (gain = 1 for omnidirectional antennas), wavelength etc. it really just comes down to running the numbers.
The real equation of note here is the free space path loss equation:
That equation will give the the loss at a given distance. You can use the temperature of the background radiation in you link budget, and quickly come up with a distance at which the signal strength is less than the noise. Although it's typical when designing communications system to require a S/N ration of greater than 3, so that might be a more practical target.