What time should I go to bed if I wake up at 2:45 am?

Waking at 2:45 am is a night-shift or early-flight schedule, and the arithmetic does not care: five cycles still means lights out at 7:00 pm, which for most people is the previous afternoon.

Why three times and not one

The middle option, 7:00 pm, is five cycles and 7 h 30 min of actual sleep; 5:30 pm is six cycles and 9 h. Both sit inside the adult range. The 8:30 pm option is 6 h: enough to get through the day, not enough to do it twice.

Sleep moves from light sleep into deep sleep and then REM, and one pass takes about 90 minutes — anywhere from 70 to 120 depending on the person and the point in the night. That spread is why these are windows, not appointments.

Here is the shape of the night. You settle at 7:00 pm and are asleep by 7:15 pm; the first and deepest slow-wave stretch arrives near 7:35 pm; by 11:00 pm you are halfway through; from about 2:10 am the final REM period runs up to the 2:45 am alarm. Cut the night short and that last REM block is what goes.

All bedtimes for a 2:45 am alarm

Formula: bedtime = wake time − (cycles × 90 min) − 15 min · adult range from the NSF 2015 panel and the AASM/SRS 2015 consensus · methodology

If you can't fall asleep by 7:00 pm

If 7:00 pm comes and your mind is still running, aim for the next cycle boundary at 8:30 pm instead of counting the minutes. Ten to twenty minutes to fall asleep is normal; much longer, repeatedly, is worth a conversation with a clinician rather than a calculator.

Try a different time