How to Calculate Caffeine Half-Life and the Best Cut-Off Time

Half-life: the time for blood caffeine concentration to halve. Average adult half-life: 5-6 hours (range: 1.5-10 hours) (Smoking: shorter half-life ~3-4h | Pregnancy: much longer ~15h) Caffeine remaining = Starting dose x (0.5)^(hours elapsed / half-life) Example: 200mg caffeine (2 espressos) at 3pm, half-life = 5 hours: At 8pm (5 hours later): 200 x 0.5^1 = 100mg At 11pm (8 hours later): 200 x 0.5^(8/5) = 200 x 0.5^1.6 = 200 x 0.330 = 66mg At 1am (10 hours later): 200 x 0.5^2 = 50mg

Research suggests sleep is disrupted when caffeine exceeds: approximately 50-100mg in the bloodstream at bedtime For a 10pm bedtime, tolerable residual caffeine: ~50mg Work backwards to find the safe cut-off time: 200mg coffee, half-life 5h: Time to reach 50mg: t = 5 x log2(200/50) = 5 x log2(4) = 5 x 2 = 10 hours Drink at most 10 hours before 10pm = 12pm (noon) 100mg coffee (single espresso), half-life 5h: Time to reach 50mg: t = 5 x log2(100/50) = 5 x 1 = 5 hours Safe cut-off: 5pm for 10pm bedtime This explains why sensitivity varies so much: Slow metaboliser (half-life 8h) and 200mg at 3pm: At 10pm (7h later): 200 x 0.5^(7/8) = 200 x 0.544 = 109mg -- above threshold

Caffeine works by blocking adenosine receptors. Adenosine builds up during wakefulness (sleep pressure). Caffeine doesn't eliminate adenosine -- it just blocks the receptor. When caffeine clears, the built-up adenosine hits all at once. This is the "caffeine crash" -- not a shortage of caffeine, but all the blocked adenosine suddenly binding. Optimal morning caffeine timing: Cortisol peaks 30-45 minutes after waking. Caffeine has diminished effect when cortisol is high. Delaying coffee 90-120 minutes after waking: - Allows cortisol peak to pass - Caffeine effect is stronger and longer-lasting - Reduces afternoon energy crash