Sources & Methodology
This page lists the published sources behind SleepyClock's calculators and reference articles. Where a calculation is based on a specific formula, the formula and its source are described below.
Sleep cycle calculator (90-minute cycles)
Formula: A standard sleep cycle is approximated as 90 minutes. Recommended bedtimes are computed by:
bedtime = wake_time − (90 × cycles + 15 minutes)
The 15 minutes accounts for average time-to-sleep onset.
Sources:
- Feinberg, I. (1974). Changes in sleep cycle patterns with age. Journal of Psychiatric Research.
- Carskadon, M. A., & Dement, W. C. (2011). Monitoring and staging human sleep. In: Kryger et al., Principles and Practice of Sleep Medicine (5th ed.).
- American Academy of Sleep Medicine (AASM). Sleep Duration Recommendations.
Limitations: Individual sleep cycle length varies from about 70 to 110 minutes. The 90-minute figure is an average used for population-level guidance.
Nap length calculator (25 / 60 / 90 minutes)
Formula: Three nap lengths are recommended based on goal:
- 20 minutes — limits slow-wave sleep, avoids sleep inertia.
- 60 minutes — includes slow-wave sleep; some grogginess for ~30 minutes after.
- 90 minutes — completes a full cycle; wake at end = minimal inertia.
Sources:
- Waterhouse, J., Reilly, T., Atkinson, G., & Edwards, B. (2007). Jet lag: trends and coping strategies. The Lancet.
- Dhand, R., & Sohal, H. (2006). Good sleep, good learning, good life. Pilot study on nap length and cognitive performance.
Limitations: Nap recommendations assume the napper is well-rested otherwise. Naps late in the day may impact nighttime sleep.
Caffeine calculator (half-life model)
Formula: Caffeine plasma concentration is modeled with a one-compartment exponential decay:
C(t) = C₀ × 0.5 ^ (t / T_half)
where T_half = 5 hours (population mean).
Sources:
- Gardiner, C. L., et al. (2024). A systematic review of caffeine half-life in healthy adults.
- Drake, C., et al. (2013). Caffeine effects on sleep taken 0, 3, or 6 hours before going to bed. Journal of Clinical Sleep Medicine.
Limitations: Real caffeine metabolism is influenced by genetics (CYP1A2 polymorphisms), pregnancy, oral contraceptives, smoking, and liver function. The calculator uses a population mean — for personalized advice, see a clinician.
Jet lag calculator (timezone adjustment)
Formula: The calculator uses a per-day adjustment of 1 hour for westward travel and 1 hour for eastward travel, applying pre-flight adjustment tips. Daylight Saving Time (DST) transitions are applied per the IANA timezone database.
Sources:
- Waterhouse, J., Reilly, T., Atkinson, G., & Edwards, B. (2007). Jet lag: trends and coping strategies. The Lancet.
- IANA tz database (2026 release).
Magnesium glycinate for sleep
Recommendation: Magnesium glycinate is a commonly used supplement. The evidence base is mixed. Some studies show small improvements in subjective sleep quality; others show none.
Sources:
- Abbasi, B., et al. (2012). The effect of magnesium supplementation on primary insomnia in elderly. Journal of Research in Medical Sciences.
- Held, K., et al. (2002). Oral Mg²⁺ supplementation reverses age-related neuroendocrine and sleep EEG changes. Pharmacopsychiatry.
- NIH Office of Dietary Supplements. Magnesium Fact Sheet for Health Professionals.
Caveats: Magnesium glycinate is generally well-tolerated, but high doses may cause diarrhea. People with kidney disease should consult a doctor before supplementing.
How to read a reference
Each entry follows this format: Author(s) (Year). Title. Source.
For example: Carskadon, M. A., & Dement, W. C. (2011). Monitoring and staging human sleep. Principles and Practice of Sleep Medicine, 5th ed.
Where a reference is a website rather than a peer-reviewed paper, we note the publisher (e.g. CDC, NHS).
What we don't do
- We do not cite studies that have been retracted.
- We do not cite blog posts or unsourced listicles as authority.
- We do not cite a study whose findings contradict the broader literature without saying so.
If you spot a reference that doesn't meet these standards, please email hello@sleepyclock.top.