How Doppio calculates caffeine

Doppio models caffeine the way pharmacology does: as exponential decay with a half-life. Here is each step, so you can judge the numbers for yourself.

1. The level in your body right now

Every logged drink has an amount in milligrams and a time. The caffeine still in your system from one drink is:

remaining = amount × 0.5^{(hours since drink ÷ half-life)}

Doppio sums this over every recent drink. After one half-life, half of a drink's caffeine is left; after two, a quarter. The Home gauge shows that sum, next to today's total intake against your daily ceiling.

2. The half-life

The default half-life is 5 hours. Real half-lives vary between people, so a short questionnaire in the app estimates your caffeine sensitivity and sets a personalised half-life. That value then drives every chart, widget and forecast.

3. Drink amounts

Doppio includes 21 built-in drinks plus custom entries, with adjustable serving sizes. The brew calculator estimates caffeine for 11 brewing methods from the coffee dose, grind, roast, brew time and temperature, and is kept consistent with the drink table on a milligrams-per-millilitre basis.

4. Bedtime forecast

The forecast applies the same decay to your estimated bedtime. Bedtime is taken from your Apple Health sleep data when you allow it, with 23:00 as the fallback. The result is compared with a threshold that depends on sensitivity:

High sensitivity: 35 mg
Normal sensitivity: 50 mg
Low sensitivity: 65 mg

5. The last-coffee time

Doppio starts from a caffeine-free window of about 6 hours before bed. A study of caffeine taken 0, 3 or 6 hours before bedtime found that even the 6-hour dose measurably disturbed sleep (Drake et al., 2013). Doppio then adjusts the window between about 4 and 8 hours using your half-life, your sensitivity, your own caffeine-and-sleep history and how you slept last night. The recommended last-coffee time is the earlier of that cutoff and the time at which your projected bedtime level would reach the threshold.

6. What the numbers are not

These are estimates from a standard model adjusted by your answers, not measurements from your body. Doppio is not a medical device and does not give medical advice.

Source

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.