[an/the] hour

If you say "Within the hour" and it's 2:50, I'd assume you'd have it done within 60 minutes, or by 3:50. I would hear "the hour" as "the hour that starts now."

But I understand your reasoning. If someone said "by the end of the hour" I would think by 3.

However, this could be one of those things like "next Friday" in which a listener might hear a different meaning than the speake

#1 Not necessarily. You could be saying "It is now 2.50pm; I will complete within the hour - say, by 3.30pm." It is "within [the/a] hour from now".

#2 "I will finish the report within an hour" = it will take me about an hour to finish the report >> possibly an hour from now, possibly just indicating it will take an hour to do it.

The context of the use should make it

Thank you, Feebs and GG.

I'll complete the report within the hour.
If the time now is 2:50, I'm saying I'll get the report done before 3:00. Am I right? I would have an hour to finish the report if I said 'within an hour'. Is that right?If it's any consolation to you, that's precisely how I would understand those expressions. Obviously, not everyone makes the same interpretations.

Thank you, CalifJim. It does make me feel better