On a total GDP basis it would be GDP divided by labor hours, no more no less. A national economy is complex, and especially one like the US or Europe, in which a lot of financial services are involved. So typically it is done on a sector basis (labor force productivity in steelmaking or construction, or mining, or office work).

Sometimes it's quite tricky: when the "output" of a given person goes up a lot it could lead to a different product (e.g. when the spreadsheet meant one person could do financial analysis that had previously required multiple people and a lot of time, it didn't mean less time doing analysis but instead significantly more sophisticated analysis in the same time, with the objective (at least) of finding better deals or avoiding worse ones).

> How does unemployment factor in?

It doesn't. It's simply output divided by input. Don't mix the two.

The same output with half the people means a doubling in productivity for that activity. What happens to the other half of people? Orthodox economics says they find some other job, perhaps a more productive one or more likely less so. Pragmatics says some never work again, some find a (often but not always) better job.

That's harsh, but the "lump of labor" fallacy is indeed a fallacy.