Caffeine half-life: how much caffeine is left at bedtime

A half-life is not the time caffeine takes to wear off. It is the time the amount in your body takes to fall by half. After one half-life, half of the dose is left. After two, a quarter is left. After three, an eighth. The amount keeps getting smaller but takes many hours to reach almost zero.

The arithmetic is: caffeine left = dose × 0.5^(hours since the drink ÷ half-life). The ^ sign means “to the power of”. For 100 mg after 10 hours at a 5-hour half-life, 10 ÷ 5 = 2 half-lives, and 100 × 0.5 × 0.5 = 25 mg. A phone calculator with an xʸ key does the same sum for hours that are not a whole number of half-lives.

The table uses the three half-life settings in the caffeine calculator: 3 hours (fast), 5 hours (typical) and 8 hours (slow). It uses the simple formula above, which counts the whole dose from the moment you drink it. Scale the numbers for a different dose: for 200 mg, double each value.

Caffeine left from one 100 mg dose, in mg, rounded to whole numbers. Estimates from the half-life formula, not measurements.

The half-life setting matters more than small changes in timing. Ten hours after a 100 mg drink, the estimate is 10 mg at a 3-hour half-life and 42 mg at an 8-hour half-life. A cup of coffee in the late afternoon can leave very different amounts at bedtime for two different people.

Take a hypothetical day: 100 mg at 8 a.m., 100 mg at 2 p.m., and bedtime at 11 p.m., with a 5-hour half-life. Work out each drink on its own, then add them.

1. First drink: 8 a.m. to 11 p.m. is 15 hours. 15 ÷ 5 = 3 half-lives. 100 × 0.5 × 0.5 × 0.5 = 12.5 mg.
2. Second drink: 2 p.m. to 11 p.m. is 9 hours. 9 ÷ 5 = 1.8 half-lives. 100 × 0.5^1.8 = 28.7 mg.
3. Add them: 12.5 + 28.7 = 41.2 mg, or about 41 mg at bedtime.

The afternoon drink leaves more than twice as much as the morning drink, although both had the same dose. Later drinks count for more at bedtime.

The caffeine calculator gives about 46 mg for the same entries, not 41 mg. It treats each drink as absorbed evenly over 45 minutes and starts the halving after that. Its formula is dose × e^(−0.693 × hours after absorption ÷ half-life). The number 0.693 is the natural logarithm of 2, so this is the same halving rule. In the example, the first drink has 14.25 hours of halving and leaves 13.9 mg. The second has 8.25 hours and leaves 31.9 mg. Both methods are simplified models. The difference shows how much an assumption about absorption can move the result.

Many medicines can also change how caffeine is cleared. If you take a regular medicine, are pregnant or have a liver condition, ask a pharmacist or clinician whether it affects caffeine. You cannot find your own half-life from how alert you feel. The calculator's fast, typical and slow settings show a range of results. Its smoking option halves the selected half-life, and its pregnancy option uses an 11.5-hour value. These are the calculator's own model settings for comparison, not measurements of your body.

The half-life arithmetic helps explain these findings. At a 5-hour half-life, 400 mg taken 6 hours before bed leaves about 174 mg at bedtime, which is more than one 100 mg drink at its peak. The 2013 study also suggests that people may not notice the effect themselves. No source here gives a bedtime amount of caffeine that is safe for sleep. The calculator's note on when one 95 mg serving falls to 50 mg is a timing comparison, not a sleep threshold.

The half-life tells you when caffeine leaves. It does not tell you how much is too much in a day. Public bodies give daily reference amounts for that question.

Drinks vary a lot. The FDA lists 113 to 247 mg for 12 fluid ounces of brewed coffee and 41 to 246 mg for 12 fluid ounces of energy drink. The calculator's presets, such as 95 mg for brewed coffee, are starting values. Use the amount on the label or the café's information when you have it. The reference amounts are for adults and are comparison values, not targets. The FDA page cites the Dietary Guidelines for Americans, which say caffeinated drinks should be avoided for children younger than 2, and notes that medical experts advise against energy drinks for children and teens.