Coffee Kick Calculator

Background.

Can a coffee at three in the afternoon still be in you at eleven at night? Mostly, yes. In the average adult, caffeine's half-life is about five hours, so after ten hours roughly a quarter of it is still circulating. Two mugs of brewed coffee at 3 pm can leave around 61 mg in your body at an 11 pm bedtime, more than the 30 to 50 mg the FDA gives for an 8 oz cup of black or green tea.

The calculator follows one sitting of coffee, tea or energy drink through the hours after you finish it, using the one-compartment model pharmacology applies to drugs taken by mouth: caffeine enters the blood from the gut at one rate and is cleared by the liver at another. It reports the peak and when it arrives, what is left at bedtime, how long it takes to fall below a level you choose, and what remains a day later.

Your own elimination half-life sets the shape of the whole curve, and people differ widely: a review by Cappelletti and colleagues gives 2 to 12 hours. Smoking speeds clearance; pregnancy and oral contraceptives slow it substantially.

No health authority publishes a safe bedtime level of caffeine, so the comparison point comes from a sleep study. Drake and colleagues gave volunteers 400 mg six hours before their usual bedtime, and they lost more than an hour of sleep. Your bedtime figure is shown against what that dose leaves in the same model, alongside a threshold you set yourself.

What is coffee kick calculator?

Caffeine moves through the body in two overlapping stages. After you swallow it, it passes from the gut into the bloodstream over roughly the first hour, and essentially all of it gets there. Meanwhile the liver, mainly through the enzyme CYP1A2, removes it at a first-order rate: a constant fraction each hour rather than a fixed number of milligrams. Together those produce a curve that climbs steeply to a peak, typically 30 to 60 minutes after the drink, then decays exponentially. The calculator gives that curve as the amount of caffeine in your body in milligrams. It does not give a blood concentration, which would need your weight and a volume of distribution, about 0.6 L/kg in adults, and would imply more precision than a two-parameter model can deliver.

How to use this calculator.

1. 01Enter the caffeine in one serving. The FDA gives 80 to 100 mg for an 8 oz cup of brewed coffee (the 90 mg default is the midpoint), 30 to 50 mg for 8 oz of tea, 30 to 40 mg for a 12 oz soft drink and 40 to 250 mg per 8 fl oz for energy drinks.
2. 02Enter the number of servings drunk at that sitting. They are treated as one dose finished at the same moment.
3. 03Set your caffeine half-life. Start at 5 hours; go higher if you are pregnant, take oral contraceptives, or find that an afternoon coffee reliably keeps you awake, and lower if you smoke.
4. 04Leave the absorption half-life at 10 minutes unless you have a reason to change it, and check that the time to the peak stays in the 30 to 60 minute range. It has to be shorter than the elimination half-life.
5. 05Enter the hours from finishing this drink to bedtime and the most caffeine you are willing to have on board at lights-out. The 50 mg default is a Quanta choice, not a published limit.
6. 06Read "Hours until below your threshold" as your cut-off: the last cup needs to be at least that long before you plan to sleep.

The formula.

The amount in the body t hours after you finish drinking is A(t) = D × ka ÷ (ka − ke) × (e^(−ke·t) − e^(−ka·t)), the Bateman function. D is the dose in milligrams, and ka and ke are the absorption and elimination rate constants, each ln 2 divided by the corresponding half-life in hours. With the defaults, ke = 0.6931 ÷ 5 = 0.1386 per hour and ka = 0.6931 ÷ (10 ÷ 60) = 4.1589 per hour, exactly 30 times faster.

At t = 0 both exponentials equal 1 and A is zero. Because ka is so much larger, the e^(−ka·t) term fades within an hour or two, and after that the curve is plain exponential decay at your elimination half-life. The peak comes at t_max = ln(ka ÷ ke) ÷ (ka − ke), which depends on the two half-lives but not on the dose. Bioavailability is taken as 1, the usual assumption for caffeine.

The 10-minute absorption half-life is not a measured figure. Studies report time to peak instead, 30 to 60 minutes in Cappelletti's review, and 10 minutes puts this model's peak at 50.8 minutes; across elimination half-lives of 2 to 12 hours the derived peak stays between about 39 and 63 minutes.

The time to fall below your threshold has no closed form, so it is found numerically on the falling side of the curve, and reads 0 if the peak never reaches the threshold. The Drake reference is A(6) for D = 400 mg at your half-life.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Evans J, Richards JR, Battisti AS. "Caffeine." In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; last update 29 May 2024 — "the half-life of caffeine in the average adult is approximately 5 hours", volume of distribution about 0.6 L/kg in adults, and "daily doses of up to 400 mg are considered safe".
2. [2]Cappelletti S, Piacentino D, Sani G, Aromatario M (2015). "Caffeine: Cognitive and Physical Performance Enhancer or Psychoactive Drug?" Current Neuropharmacology 13(1):71–88, doi:10.2174/1570159X13666141210215655 — "The maximum plasma concentration is reached after 30-60 minutes from consumption", with "maximum plasma concentrations reached between 15 and 120 min" reported, and "Caffeine's half-life in humans ranges from a minimum of 2 to a maximum of 12 hours".
3. [3]Drake C, Roehrs T, Shambroom J, Roth T (2013). "Caffeine Effects on Sleep Taken 0, 3, or 6 Hours before Going to Bed." Journal of Clinical Sleep Medicine 9(11):1195–1200, doi:10.5664/jcsm.3170 — 400 mg of caffeine in pill form at 0, 3 and 6 hours before habitual bedtime; "reducing TST between 1.1 to 1.2 hours" at every administration time; "provides empirical support for sleep hygiene recommendations to refrain from substantial caffeine use for a minimum of 6 hours prior to bedtime".
4. [4]U.S. Food and Drug Administration (Consumer Updates). "Spilling the Beans: How Much Caffeine is Too Much?" — an 8-ounce cup of coffee is "closer to 80 to 100 milligrams", 8 oz green or black tea 30–50 mg, a 12-ounce caffeinated soft drink 30–40 mg, energy drinks 40–250 mg per 8 fl oz; 400 mg a day cited as an amount not generally associated with negative effects for most healthy adults, with "too much" varying by body weight, medications, medical conditions and individual sensitivity.
5. [5]Grogan S, Preuss CV. "Pharmacokinetics." In: StatPearls [Internet]. StatPearls Publishing; last update 30 July 2023 — first-order kinetics is "the major elimination model of most medications", and half-life is "the amount of time for serum drug concentrations to decrease by 50%". The basis for deriving both rate constants as ln 2 divided by a half-life.