What time should I go to bed if I wake up at 11:30 am?

With a 11:30 am alarm you can go to bed at 3:45 am and still get 7 hours 30 minutes, or at 2:15 am for a sixth cycle.

Why three times and not one

The middle option, 3:45 am, is five cycles and 7 h 30 min of actual sleep; 2:15 am is six cycles and 9 h. Both sit inside the adult range. The 5:15 am option is 6 h: enough to get through the day, not enough to do it twice.

Why cycles at all? Because what you wake from matters more than how long you slept: an alarm in deep sleep leaves ten to thirty minutes of fog, an alarm in light sleep does not. Cycles average 90 minutes but range from 70 to 120, so aim for the window rather than the minute.

In clock terms: lights out 3:45 am, asleep around 4:00 am, deepest sleep of the night between roughly 4:20 am and 5:30 am, the night's midpoint at 7:45 am, and REM building toward 10:55 am. The 11:30 am alarm lands as cycle 5 closes, so you are likely in light sleep rather than deep.

All bedtimes for a 11:30 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 3:45 am

Fifteen minutes is the average time a healthy sleeper takes to drop off; ten to twenty is normal. If you are still awake twenty minutes after 3:45 am, sleep-medicine guidance is to get up, do something dull in dim light, and return when sleepy — lying there teaches the brain that bed is for being awake. Miss the window and the next one, 5:15 am, is only a cycle away.

Try a different time