What time should I go to bed if I wake up at 1:30 pm?

A 1:30 pm wake-up means sleeping through the morning: lights out at 5:45 am for 7 hours 30 minutes.

Why three times and not one

The middle option, 5:45 am, is five cycles and 7 h 30 min of actual sleep; 4:15 am is six cycles and 9 h. Both sit inside the adult range. The 7:15 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 5:45 am lights-out: asleep by about 6:00 am, into the first stretch of deep sleep around 6:20 am, first REM period near 7:15 am, the halfway point of the night at 9:45 am, and the longest REM period of the night starting around 12:55 pm — which is what a 1:30 pm alarm at the end of cycle 5 lets you finish.

All bedtimes for a 1:30 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 5:45 am

Build in the fifteen minutes honestly: lights out at 5:45 am means phone down at 5:45 am, not "in bed, scrolling". If sleep has not come by 6:05 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 7:15 am.

Try a different time