Caffeine halves about every five hours: a coffee at 3 pm is still about half in you at 8 pm, a quarter at 1 am and an eighth at 6 am.
The body clears a fixed share of the caffeine each hour, so the amount falls by half over each half-life of about 5 hours. After 5 hours 51 percent of a dose is left (a little over half, because some was still being absorbed), after 10 hours 26 percent and after 15 hours 13 percent.
The half-life is anywhere from about 2 to 8 hours in a healthy adult: smoking shortens it, and the contraceptive pill and pregnancy lengthen it, to as much as 16 hours late in pregnancy. A drink also takes about 45 minutes to reach its peak, so the amount in you is still rising for the first hour.
Estimate with the rule, then check it against the calculator that models it properly.
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