The formula
Bedtime equals wake-up time, minus a whole number of 90-minute cycles, minus about 15 minutes to fall asleep. Five cycles is 7.5 hours of sleep; six cycles is 9 hours. Subtract the total from your alarm and you get two candidate bedtimes.
Counting backward from the alarm, rather than guessing a bedtime, is the whole trick. It guarantees the hours in bed land as whole cycles instead of ending mid-cycle.
Worked example: wake at 6:30 AM
Start with 6:30 AM. For 5 cycles: 5 times 90 minutes is 450 minutes (7 hours 30 minutes), plus the 15-minute buffer, for a total of 7 hours 45 minutes. 6:30 AM minus 7 hours 45 minutes is 10:45 PM.
For 6 cycles: 6 times 90 minutes is 540 minutes (9 hours), plus 15 minutes, for a total of 9 hours 15 minutes. 6:30 AM minus 9 hours 15 minutes is 9:15 PM. So a 6:30 alarm gives two bedtimes: 10:45 PM or 9:15 PM.
More wake-up times, worked the same way
Wake at 5:30 AM: minus 7 hours 45 minutes is 9:45 PM; minus 9 hours 15 minutes is 8:15 PM. Options: 9:45 PM or 8:15 PM.
Wake at 7:00 AM: minus 7 hours 45 minutes is 11:15 PM; minus 9 hours 15 minutes is 9:45 PM. Options: 11:15 PM or 9:45 PM.
Wake at 8:00 AM: minus 7 hours 45 minutes is 12:15 AM; minus 9 hours 15 minutes is 10:45 PM. Options: 12:15 AM or 10:45 PM.
Notice the pattern: moving your alarm one hour later moves both bedtime options one hour later. Once you know your pair, the schedule scales.
Why the 15-minute buffer belongs in the math
Most people take around 15 minutes to fall asleep, and cycles are counted from sleep onset, not from lights-out. Skipping the buffer means your first cycle starts late and your alarm lands 15 minutes into what should have been a between-cycle wake. If you typically lie awake longer, use 20 or 30 minutes; the formula works the same.
Bedtime also means lights out, screens off, in bed. Scrolling for 40 minutes after your "bedtime" silently deletes half a cycle from the plan.
Which option should you pick?
Choose based on how much sleep you need. Most adults do well on 5 cycles (7.5 hours); people who train hard, are recovering from illness, or simply feel better on more sleep should take the 6-cycle option (9 hours). If you are unsure, try the 5-cycle bedtime for a week: if you wake before the alarm feeling clear, it is enough; if you sleep through it groggy, move to 6 cycles.
Teenagers should default to the 6-cycle option or later bedtimes overall, since ages 13 to 17 need 8 to 10 hours.
Keep the bedtime consistent
The same bedtime every night, weekends included, trains your circadian rhythm to start winding down on schedule. A bedtime that swings by two hours between weeknights and weekends creates the same drag as jet lag. Protect the bedtime the way you protect the alarm: it is the other half of the same appointment.
Run your exact wake-up time
A bedtime calculator takes any alarm time and returns both bedtime options instantly, with the fall-asleep buffer included, so you do not have to do the subtraction by hand.