What time should I go to bed if I wake up at 6:45 am?

Set for 6:45 am? Lights out at 11:00 pm gives five cycles (7 h 30 min); 9:30 pm gives six (9 h).

Why three times and not one

The middle option, 11:00 pm, is five cycles and 7 h 30 min of actual sleep; 9:30 pm is six cycles and 9 h. Both sit inside the adult range. The 12:30 am option is 6 h: enough to get through the day, not enough to do it twice.

A cycle is one trip through light sleep, deep sleep and REM. The 90-minute figure is an average from NIH material; your own cycles could run 70 to 120 minutes, so treat each time as the middle of a 15-minute window.

Here is the shape of the night. You settle at 11:00 pm and are asleep by 11:15 pm; the first and deepest slow-wave stretch arrives near 11:35 pm; by 3:00 am you are halfway through; from about 6:10 am the final REM period runs up to the 6:45 am alarm. Cut the night short and that last REM block is what goes.

All bedtimes for a 6:45 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 11:00 pm

Build in the fifteen minutes honestly: lights out at 11:00 pm means phone down at 11:00 pm, not "in bed, scrolling". If sleep has not come by 11:20 pm, the guidance from sleep medicine is to leave the bed, do something dull in dim light, and return when sleepy — the next clean boundary is 12:30 am.

Try a different time