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Discover how your daily habits affect your rest.
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Research & Statistics
Calculations based on scientific research, studies, and primarily statistics of average people.
Key Insight
Caffeine has a half-life of 4-6 hours (average ~5 hours). After 5 hours, about 50% of caffeine remains in your body. For optimal sleep, caffeine levels should drop below ~15-25mg – this typically means having your last coffee 10+ hours before bedtime.
Key Insight
Late eating elevates heart rate due to digestive processes. Your heart rate should be low when falling asleep. A gap of 3+ hours between your last meal and bedtime is optimal.
Key Insight
After intense exercise, your body needs a few hours to recover and calm down. Morning workouts allow complete recovery before sleep and maintain a healthy heart rate throughout the day. Exercising close to bedtime can compromise sleep quality.
Caffeine Pharmacokinetics
Based on Grzegorzewski et al. 2022 & Puri et al. 2020. One-compartment model with oral absorption.
// Absorption phase (t ≤ 45min):
C(t) = C₀ × (t / t_peak)
// Elimination phase (t > 45min):
C(t) = C₀ × e^(-(t - t_peak) × ln(2) / t½)
t_peak = 0.75h | t½ = 4.5h (male) / 5.0h (female)
Melatonin Circadian Rhythm
Based on Brown et al. 1997, Zeitzer et al. 2007 & Gunn et al. 2016. Gaussian approximation with fixed circadian peak.
// Gaussian circadian model:
M(t) = M_base + (M_peak - M_base) × e^(-Δt² / 2σ²)
// Caffeine suppression effect:
M_final = M(t) × (1 - min(0.6, caffeine × 0.005))
t_peak = 3:00 (female) / 3:30 (male) | σ = 3.0h
Heart Rate Model
Based on Speed et al. 2023, Khalid et al. 2025 & Chikwetu et al. 2024. Sinusoidal circadian baseline with meal/workout modulations.
// Circadian baseline:
HR_base(t) = HR_mean - A × cos(2π × Δt / 24)
// Final HR with modulations:
HR(t) = HR_base + ΔHR_meal + ΔHR_workout + ΔHR_caffeine
HR_mean = 63 (male) / 67 (female) | A = 7 BPM | ΔHR_caffeine = 3 × (C/100mg)
Optimal Bedtime Calculation
Based on Drake et al. 2013 (caffeine threshold) and DLMO research. Finds the earliest time after 8 PM where all conditions are met.
// All conditions must be true:
1. Caffeine < 25mg // Sleep-safe threshold
2. Melatonin ≥ 20% // DLMO onset
3. HR < HR_baseline + 5 // Near resting
// Result:
Optimal = min(t) where t ≥ 20:00 AND all conditions true
Misconceptions & Good to Know
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