Health📅 18 March 2025⏱ 4 min read
How to Calculate Caffeine Half-Life and the Best Cut-Off Time
Caffeine has a half-life of 5-7 hours — meaning a 3pm coffee still has 50% of its caffeine in your system at 9pm. Here is the calculation and what it means for sleep quality.
JW
James WhitfieldPersonal Finance & Maths WriterJames has written about personal finance, health metrics, and everyday mathematics for over six years. He holds a BSc in Mathematics from the University of Leeds.
Most people know that late coffee disrupts sleep. Fewer people know how to calculate when specific doses fall below sleep-affecting thresholds — and it's often earlier than intuition suggests.
Caffeine Half-Life Basics
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
Sleep-Disrupting Caffeine Threshold
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 in Common Drinks
DrinkServing SizeCaffeine (mg)
Espresso (single)30ml60-75mg
Filter coffee250ml80-140mg
Instant coffee250ml60-80mg
Tea (black, brewed)250ml40-70mg
Green tea250ml20-45mg
Cola330ml can30-40mg
Energy drink (standard)250ml75-80mg
Dark chocolate (50g)50g20-50mg
Adenosine and Why Timing Matters
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