What time should I go to bed if I wake up at 3:00 pm?

A 3:00 pm wake-up means sleeping through the morning: lights out at 7:15 am for 7 hours 30 minutes.

Why three times and not one

The middle option, 7:15 am, is five cycles and 7 h 30 min of actual sleep; 5:45 am is six cycles and 9 h. Both sit inside the adult range. The 8:45 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.

Walk through the night from a 7:15 am lights-out: asleep by about 7:30 am, into the first stretch of deep sleep around 7:50 am, first REM period near 8:45 am, the halfway point of the night at 11:15 am, and the longest REM period of the night starting around 2:25 pm — which is what a 3:00 pm alarm at the end of cycle 5 lets you finish.

All bedtimes for a 3:00 pm 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 7:15 am

Build in the fifteen minutes honestly: lights out at 7:15 am means phone down at 7:15 am, not "in bed, scrolling". If sleep has not come by 7:35 am, 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 8:45 am.

Try a different time