What these pages assume
A cycle of 90 minutes and 14 minutes to fall asleep. Both are population averages. Real cycles run about 70 to 120 minutes and lengthen through the night, so the six-cycle time is a much looser target than the four-cycle one — treat every answer as the centre of a window of about three quarters of an hour.
Both numbers are editable on the sleep cycle calculator, and moving them is the fastest way to see how much confidence any of these times deserve. Changing the cycle length from 90 to 100 minutes moves a five-cycle wake time by fifty minutes, which is a larger shift than most of the decisions people make on the back of it.
Total sleep beats boundary timing
If the choice is between six cycles at an awkward hour and five at a sensible one, take the one you can keep to every night. Cycle timing is worth using to choose between a 7:15 and an 8:45 alarm. It is not a reason to accept ninety minutes less sleep, and no page on this site will suggest otherwise.
The same applies to consistency. A bedtime you hit every night, including at the weekend, does more for how you feel than landing exactly on a cycle boundary occasionally. The body clock responds to regularity; the arithmetic on these pages is a tie-breaker, not a programme.
Which page you actually want
Going to bed now? The wake-up time calculator works forwards and gives you the alarm options. Alarm fixed by work? The bedtime calculator works backwards from it. Neither fixed? The sleep calculator does both directions in one place. Tired every day? The sleep debt calculator totals a week of short nights, which is usually the real question behind the other three. Need to get through this afternoon? The nap calculator, and read the part about why an hour-long nap is the worst option available.
What none of this is
Clock arithmetic. That is the whole claim. These pages do not diagnose anything, do not measure your sleep, and cannot tell you whether the tiredness you are trying to fix is a scheduling problem or a medical one. Insomnia, sleep apnoea, restless legs and shift-work disorder are all common and all treatable, and none of them are fixed by a better alarm time. If you are sleeping enough hours and still exhausted, that belongs with a doctor rather than with a calculator.