Sleep Cycle Formula (90-Min)
Sleep proceeds in ~90-minute cycles (Carskadon & Dement). Each cycle progresses through light → deep → REM sleep. Waking at a cycle end (early in light sleep) feels easier than waking mid-deep-sleep. Plan bedtime as wake_time minus N×90 min minus a sleep latency buffer (typically 10-20 min). 5-6 cycles per night is optimal for most adults; 4 cycles is the minimum below which performance erodes per Watson 2015.
Formula
Copy the exact expression or work through it step by step below.
bedtime = wake_time − (cycles × 90 minutes) − sleep_latency_minutes
cycles: integer, typically 4-6 per night for adults
sleep_latency: 10-20 min typical (time from lying down to sleep onset)
total_sleep_duration = cycles × 90 minutes
4 cycles = 6.0 hours (minimum)
5 cycles = 7.5 hours (recommended)
6 cycles = 9.0 hours (athletes, recovery focus) Variables
wake_time
Target wake time
When you need to be awake. Anchor backward from this. For shift workers or irregular schedules, anchor each 'sleep block' separately.
cycles
Number of sleep cycles
Whole cycles (90 min each). 4 = minimum for cognitive function; 5 = AASM consensus 7-9h adult target midpoint; 6 = athlete / recovery.
sleep_latency
Sleep latency
Time to fall asleep after lying down. Normal range 5-20 min. Above 30 min often indicates sleep-onset insomnia; below 5 min indicates sleep deprivation (Iber et al. 2007 AASM).
Step By Step
- 1
Identify wake time required.
Wake at 06:30 for 07:30 workout.
- 2
Choose target cycles. 5 cycles = 7.5h sleep is the practical default.
5 cycles.
- 3
Compute backward: wake − (cycles × 90 min) = sleep start.
06:30 − 7.5h = 23:00 sleep start (in bed asleep).
- 4
Subtract sleep latency to get target bedtime.
Average 15 min latency: bedtime 22:45.
- 5
If you miss bedtime by 15-30 min, drop to next-lower cycle count (4 instead of 5) rather than waking mid-cycle.
Couldn't fall asleep until 00:00? Better to wake at 06:00 (4 cycles) than 06:30 (3.5 cycles, mid-cycle wake → grogginess).
Worked Example
Athlete needs 6:30 wake-up time, average 15 min sleep latency
Wake time
06:30
Target cycles
5 (7.5h sleep)
Sleep latency
15 min
Sleep start: 06:30 − 7.5h = 23:00 Bedtime (in bed, lights out): 23:00 − 15 min = 22:45 Alternative cycles (same wake time): 4 cycles (6h): 00:30 sleep, 00:15 bedtime 5 cycles (7.5h): 23:00 sleep, 22:45 bedtime (RECOMMENDED) 6 cycles (9h): 21:30 sleep, 21:15 bedtime
Lights out 22:45. Important context: the 90-min cycle is an average — individual cycles range 70-110 min, so this is approximate. Tracking actual REM cycle endings (Oura, Garmin, Apple Watch sleep staging) gives personalized data. The formula is the planning anchor; biology adjusts.
Common Variations
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Sources & References
- Carskadon & Dement (2017). Normal Human Sleep: An Overview (in Principles and Practice of Sleep Medicine, 6th ed.). — Elsevier — canonical sleep-cycle reference
- Watson et al. (2015). Recommended Amount of Sleep for a Healthy Adult: A Joint Consensus Statement of AASM and SRS. — Sleep — adult sleep duration consensus
- Iber et al. (2007). The AASM Manual for the Scoring of Sleep and Associated Events. — American Academy of Sleep Medicine — sleep latency norms
- Roenneberg et al. (2007). Epidemiology of the human circadian clock. — Sleep Medicine Reviews — chronotype variation