If you stay awake for one whole night, does this mean you need to compensate for exactly one night?

Let's say that you normally sleep for 8 hours a night.
Now, imagine that this person stays awake one full night without sleeping at all, and then goes to bed the next night.
Does this mean that (s)he will now need to sleep for 16 hours that night, or sleep longer than normal until the 8 hours are fully compensated?

I am a little confused about this, because I once heard of a guy who stayed awake for about 11 days and then slept for 16 hours (not sure about those numbers, but it was something like that), and seemed to have recovered after that.
So what's going on there?

No, once your energy level is empty, it doesn't get any emptier. Once it's full, it doesn't get any more full. I figure one who get's 8 hours of sleep a night doesn't regularly pass out on the way to bed, so they must be going to sleep on more than an empty energy level. How much sleep would it take to get from an empty energy level to a full energy level? 16 hours maybe?

No it doesn't work like that. If it did, I'm sure many people would love to work on their sleep debt. Unfortunately sleep debt doesn't work like that. To recover from one full night of staying up, you would need to sleep 8 or more hours each night for a few consecutive nights. For some reason that debt can only be fixed through a period of days and not overnight.

Meth freaks who stay awake 7 days will be able to stay in deep sleep for around 3 days. That is extreme abuse to the system, and they are basically critically ill. Lets say you are moderate and get only 4 hours sleep for 7 nights running, you could be almost fully recovered by sleeping just 10 hours a night for 2 nights. I agree with one up, that serious sleep debt takes a little extra sleep for more than one night to balance. However, simply to function, regardless of how much you have run yourself down, you would regain much function from 12 hours of uninterrupted sleep, even if the deprivation was over a week or so by shorting your sleep a few hours each night.

The proper method is to increase sleep quantity without disturbing sleep quality, and the best way to go about this is to increase your night's sleep for 1-2 hours a night, no more. Ideally, you want to go to bed earlier, and still get up at about the same time.

Do notice that some studies point that sleep recovery is not a generalized "recover sleep" process, some aspects of the sleep debt seem to never be recovered.
Effects of recovery sleep after one work week of mild sleep restriction on interleukin-6 and cortisol secretion and daytime sleepiness and performance.

Quote:

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(...)Extended recovery sleep over the weekend reverses the impact of one work week of mild sleep restriction on daytime sleepiness, fatigue, and IL-6 levels, reduces cortisol levels, but does not correct performance deficits. The long-term effects of a repeated sleep restriction/sleep recovery weekly cycle in humans remain unknown.(...)

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