What is the present day radius of the observable universe? The radius of the observable universe is generally taken to be ~45 billion light  years. However, we see distant galaxies as they were many millions of years in the past, so there are two ways I can interpret this radius value:

1) Light that is reaching Earth for the first time today was emitted by ancient galaxies that were initially a lot closer, but are now estimated to be 45 billion light years away from us.

2) Light that is reaching Earth for the first time today was emitted by ancient galaxies that were initially 45 billion light years away, and are now a lot further.

Which interpretation, if they're not both wrong, is correct?
The answer is basically #1. The observable universe contains objects whose light has taken up to the age of the universe to travel to us.

Thanks to the expansion of the universe, the things that emitted that light are about 46 billion light years away now.
The exact figure depends on the details of the cosmological parameters and also whether you take the first time that the light can have started out as being the "epoch of recombination" (when the cosmic microwave background was emitted and the universe became transparent to radiation) or the big-bang itself (which would add about 0.5 billion light years to the figure).

Light emitted just after the epoch of recombination has a redshift of about 1100. That means the scale factor has increased by a similar amount. Thus something that is now 46 billion light years away was about 42 million light years away when the light was emitted (of course neither the Earth or our Galaxy existed then).

The answer cannot be #2 since light from something 45 billion light years away cannot have reached us in the age of the universe.