What a cycle is
Across a night you move repeatedly through a sequence: light sleep, deeper slow-wave sleep, then REM, and back out again. One full pass is a cycle. Most adults complete four to six of them a night. Waking at the end of one means waking out of light sleep, which generally feels considerably better than an alarm going off in the middle of deep sleep — that difference is real, and it is the entire idea the sleep calculators on this site are built on.
Where 90 minutes comes from
It is a population average, and a rounded one. Measured cycle lengths in sleep laboratories cluster somewhere around 90 minutes but range roughly from 70 to 120 across individuals. Ninety is a convenient middle that happens to divide neatly into a night: five cycles is 7 hours 30 minutes, six is 9 hours. That tidiness is part of why the figure spread, and it is worth being clear that it is a planning number, not a measurement of you.
Cycles are not all the same length
This is the part most sleep calculators leave out. Early in the night your cycles are weighted towards deep slow-wave sleep; later they carry proportionally more REM, and they tend to lengthen. So the blocks are not interchangeable, and the arithmetic gets looser as the night goes on.
The practical consequence: the four-cycle boundary is a reasonably tight target, and the six-cycle one is a wide one. Six × 90 assumes a precision that is not there. Treat any of these times as the centre of a window of about three quarters of an hour rather than as a moment.
Fourteen minutes to fall asleep
Every sleep calculator adds an allowance for sleep onset, and the common figure is around 14 minutes for adults. It shifts every answer by exactly the same amount, so it is the easiest assumption to correct: if you reliably drop off in two minutes, subtract twelve from every time; if you lie awake for forty, add twenty-six. Sites that add nothing will give you times about a quarter of an hour earlier than this one, and that difference — not cycle length — is why sleep calculators disagree with each other.
What this is worth, honestly
Less than getting enough sleep. If the choice is between six cycles at an awkward hour and five at a sensible one, take the option you can actually keep to every night. Cycle timing is a refinement worth using to choose between a 7:15 and an 8:45 alarm; it is not a reason to accept an hour and a half less sleep in exchange for better timing, and waking mid-cycle occasionally is not a problem worth engineering around.
Two things that do more for how you feel on waking than any of this: a consistent schedule, including at weekends, and light exposure in the first hour after getting up.
Napping is a different problem
A nap is usually either much shorter than a cycle — twenty minutes, staying in light sleep — or one full cycle at about ninety. The awkward zone is 40 to 70 minutes, which tends to land the alarm in deep sleep and produces the grogginess people blame on napping in general.