About

The human circadian system operates on an endogenous period of approximately 24.2 hours, entrained daily by light exposure through retinal ganglion cells projecting to the suprachiasmatic nucleus (SCN). Misalignment between your behavioral schedule and this internal oscillator - measured as social jetlag - correlates with metabolic dysfunction, impaired cognitive performance, and elevated cardiovascular risk. A 1-hour chronic misalignment can reduce glucose tolerance by up to 17%. This tool models your personal circadian phase by applying offsets from your anchor sleep/wake times, adjusted for chronotype, to predict cortisol acrophase, core body temperature nadir, melatonin onset (DLMO), and optimal windows for cognitive work, physical performance, and sleep initiation.

The underlying model approximates the Two-Process framework: Process S (homeostatic sleep pressure accumulating during wakefulness) and Process C (the sinusoidal circadian drive). Results assume stable entrainment with consistent light/dark exposure. Shift workers, transmeridian travelers, or individuals with non-24-hour sleep-wake disorder will find predictions less accurate. The tool does not replace polysomnography or actigraphy-based clinical assessment.

Formulas

The circadian alertness curve is modeled as a sinusoidal function of time since wake, combined with a linear homeostatic pressure term. The composite alertness score A(t) at hours t after wake is approximated by:

A(t) = A₀ ⋅ cos(2π(t − φ)T) − k ⋅ t

Where A₀ = baseline circadian amplitude (normalized to 1.0), T = circadian period (24 h), φ = phase offset from wake (approximately 4 h for peak alertness), and k = homeostatic decay constant (~0.04 h⁻¹).

Optimal sleep cycles align with 90-minute ultradian periods. For a target sleep onset at time t_s, recommended wake times are:

t_wake = t_s + 90 ⋅ n min, n ∈ {4, 5, 6}

Where n is the number of complete sleep cycles. Waking between cycles (during N1/N2 light sleep) minimizes sleep inertia. The chronotype adjustment shifts all phase markers by δ:

{

δ = −1 h if Lionδ = 0 h if Bearδ = +1 h if Wolfδ = 0 h if Dolphin

Dim Light Melatonin Onset (DLMO) is estimated at t_sleep − 2 h. Core body temperature nadir occurs at approximately t_sleep + 4.5 h.

Reference Data

Circadian Event	Typical Offset from Wake	Physiological Marker	Practical Implication
Cortisol Awakening Response (CAR)	0 - 1 h	Cortisol peak ~500 - 700 nmol/L	Natural alertness boost; avoid caffeine
Peak Cognitive Alertness	+2 - 4 h	High prefrontal cortex activation	Best window for analytical work
Peak Short-Term Memory	+3 h	Hippocampal theta rhythm peak	Study, memorization tasks
Best Coordination	+6 - 7 h	Motor cortex excitability peak	Skill-based sports, fine motor tasks
Peak Cardiovascular Efficiency	+7 - 8 h	VO₂max plateau, core temp rising	Endurance exercise
Fastest Reaction Time	+8 - 9 h	Core body temperature peak ~37.2 °C	Competitive sports, reflex-dependent tasks
Peak Muscle Strength	+9 - 10 h	Testosterone & grip strength peak	Resistance training optimal
Post-Lunch Dip	+7 - 8 h	Process S pressure + circadian trough	Nap window (20 min max)
Dim Light Melatonin Onset (DLMO)	2 - 3 h before sleep	Melatonin >3 pg/mL	Avoid bright light & screens
Optimal Sleep Gate	0 - 1 h before habitual sleep	Core temp descending, melatonin rising	Easiest time to fall asleep
Core Body Temperature Nadir	~4 - 5 h after sleep onset	Minimum ~36.2 °C	Deepest sleep phase; shift work danger zone
Growth Hormone Pulse	First 90 min of sleep	N3 slow-wave sleep peak	Critical for recovery; alcohol suppresses
REM Predominance	Last 2 - 3 h of sleep	Acetylcholine surge	Memory consolidation; do not truncate sleep
Sleep Inertia Zone	0 - 30 min post-wake	Adenosine clearance lag	Avoid critical decisions immediately after waking
Chronotype: Lion (Early)	Wake shift −1 h	Earlier cortisol peak	Peak performance before noon
Chronotype: Bear (Average)	No shift (0 h)	Population median	Follows solar cycle closely
Chronotype: Wolf (Late)	Wake shift +1 h	Delayed melatonin onset	Peak creativity in evening
Chronotype: Dolphin (Irregular)	Variable	Light sleep, fragmented	Benefits from strict schedule enforcement

Frequently Asked Questions

Chronotype represents genetically-influenced variation in circadian phase preference. Lion (early) types have cortisol peaks approximately 1 hour earlier than the population mean, shifting all downstream windows (peak alertness, exercise optimization, melatonin onset) earlier. Wolf (late) types shift 1 hour later. Dolphin types have irregular patterns and benefit most from strict schedule adherence rather than phase shifting. The calculator applies these offsets to every computed event time.

Cortisol naturally peaks at 500 - 700 nmol/L within 30 - 60 minutes of waking. Consuming caffeine during this window provides diminishing returns because alertness is already at a physiological high. Worse, it accelerates adenosine receptor downregulation, increasing tolerance. Optimal first caffeine intake is 90 - 120 minutes after waking, when cortisol begins its first descent.

Sleep cycles average 90 minutes but vary between 80 - 110 minutes across individuals and across the night (earlier cycles have more N3, later cycles more REM). The calculator uses the 90-minute approximation. If you consistently wake feeling groggy despite aligning to calculated times, your personal cycle length likely deviates. Try shifting wake time by ±10 minutes to calibrate.

Morning bright light (>10,000 lux) within 1 hour of waking advances the circadian phase, making you sleepier earlier at night. Evening light exposure (>100 lux after DLMO) delays the phase. The calculator assumes standard indoor/outdoor light patterns. Shift workers or those with minimal daylight exposure should expect phase drift of 0.5 - 1.5 hours from predicted values.

The model is designed for monophasic sleep (one consolidated block). For biphasic sleep (e.g., core night sleep plus a 20-minute afternoon nap), the main schedule output remains valid and the nap window shown in the results corresponds to the post-lunch circadian dip. True polyphasic schedules (Uberman, Everyman) violate the underlying sinusoidal model assumptions and predictions will be unreliable.

Alcohol suppresses REM sleep in the first half of the night and causes rebound wakefulness in the second half. It also suppresses growth hormone release during the initial N3 slow-wave period by up to 75%. While the circadian oscillator timing itself is not substantially shifted by moderate alcohol, the quality of sleep within the predicted windows degrades. The calculator does not model alcohol effects.