Can I determine ABV after beer is bottled?

You would at least need to know the OG, then you could. Or you could send your beer to a lab if that is worth it to you.

But if you just want to know so you can tell your friends, I say taste it, then tell them it is a full point or two higher than what it tastes like. Expect comments like "Wow, really clean fermentation man. Great job! The ABV is masterfully concealed."

 

Only if you know your OG

 

FG calculation is dependent on OG value. no way around that.

you can estimate if you know the recipe. estimates can vary quite a bit if you are all grain because of variables. if this is an extract brew than you should be able to get fairly close. use an online recipe program like brewtoad (or brewfrog?)
Cheers.

 

If you have a refractometer and hydrometer, you can use them together to make some estimates for OG and ABV. This BYO article discusses it a bit: http://byo.com/stories/item/1313-refractometers

I have used this method in the past to and it has worked well to confirm my OG numbers.

 

Like others said, need to have OG to know abv.

Make sure you degas your bottled sample though. Get a hydrometer worth of beer and let sit for about 30 minutes, then get two larger containers (beakers, pint glasses, etc) and pour the sample back and forth for a good minute or two, let sit another 10 mins or and then read.

 

There are beer analyzers that can do that, but we can't afford those.

 

White Labs will test your sample for ABV and IBUs (and maybe some other things) for < $40. If it's that important to you.