Bedtimes for a wake-up time, or wake-up times for a bedtime, counted in 90-minute sleep cycles plus the time it takes to fall asleep.
To wake at 07:00 after 5 full cycles (7 h 30 min of sleep), get into bed at 23:15.
| Cycles | Sleep | Go to bed at |
|---|---|---|
| 6 | 9 h | 21:45 |
| 5 | 7 h 30 min | 23:15 |
| 4 | 6 h | 00:45 |
| 3 | 4 h 30 min | 02:15 |
Clock arithmetic wraps around midnight.
The calculator counts back from a wake-up time, or forward from a bedtime, in whole sleep cycles plus the time it takes to fall asleep: bedtime = wake-up time − cycles × cycle length − time to fall asleep. Each night's sleep runs through non-REM stages and REM sleep in repeating cycles; the first lasts about 70 to 100 minutes and later ones about 90 to 120, so the default cycle is 90 minutes.
People use it to choose a bedtime or an alarm time that falls between cycles. With the defaults, waking at 07:00 after 5 cycles and 15 minutes to fall asleep means getting into bed at 23:15, for 7 h 30 min of sleep. The table lists the times for 3 to 6 cycles.
Real cycles vary from night to night, so the times are estimates. The American Academy of Sleep Medicine recommends at least 7 hours a night for adults, which 5 or more 90-minute cycles provide and 4 cycles (6 hours) do not.
Checked against: Python 3.8 datetime: 07:00 − (15 + 5 × 90) min = 23:15 the evening before
Checked against: Python 3.8 datetime: 06:00 − 555 min = 20:45
Checked against: Python 3.8 datetime: 23:30 + 465 min = 07:15 next day
Checked against: Python 3.8 datetime: 00:30 + 360 min
About 90 minutes on average. The US Institute of Medicine's 2006 report on sleep disorders, citing Carskadon and Dement, gives 70 to 100 minutes for the first cycle of non-REM and REM sleep and 90 to 120 minutes for later cycles. The National Institute of Neurological Disorders and Stroke says REM sleep first occurs about 90 minutes after falling asleep. You can change the cycle length under More options.
At least 7 hours a night on a regular basis, according to the 2015 consensus statement of the American Academy of Sleep Medicine and the Sleep Research Society. Regularly sleeping less is linked to weight gain, diabetes, high blood pressure, heart disease, stroke, depression and a higher risk of death. Five 90-minute cycles give 7 h 30 min; four give 6 hours, which falls short.
The American Academy of Sleep Medicine's 2016 consensus recommends 8 to 10 hours per 24 hours for teenagers aged 13 to 18 and 9 to 12 hours for children aged 6 to 12. For a 15-year-old who must get up at 06:30, six 90-minute cycles (9 hours) plus 15 minutes to fall asleep put bedtime at 21:15.
It can, but the timing is an estimate. Grogginess on waking, called sleep inertia, is strongest after waking from deep slow-wave sleep, weakest after stage 1 or 2 sleep and in between after REM, and without major sleep loss it rarely lasts beyond 30 minutes (Tassi and Muzet, Sleep Medicine Reviews, 2000). Because real cycles run 70 to 120 minutes, five counted 90-minute cycles can end half an hour or more away from your actual cycle boundary.
30 minutes or less. The National Sleep Foundation lists falling asleep within 30 minutes as one of four signs of good sleep quality, from its 2017 expert consensus (Ohayon et al., Sleep Health). The calculator's default is 15 minutes; enter your usual time, because every extra 15 minutes moves the suggested bedtime 15 minutes earlier.
Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 5 worked examples whose answers come from independent sources; for example, “Wake at 07:00, 5 cycles, 15 min to fall asleep” is checked against Python 3.8 datetime: 07:00 − (15 + 5 × 90) min = 23:15 the evening before.
Carskadon MA, Dement WC. Normal human sleep: an overview. In: Principles and Practice of Sleep Medicine (NREM–REM cycle of about 90 minutes); Watson NF et al. Recommended amount of sleep for a healthy adult: AASM and SRS joint consensus statement. Sleep 2015;38(6):843–4; NINDS — Brain basics: understanding sleep (REM sleep first occurs about 90 minutes after falling asleep; reviewed 2025); Paruthi S et al. Recommended amount of sleep for pediatric populations: AASM consensus statement. J Clin Sleep Med 2016;12(6):785–6.
5 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.
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