How the cutoff is worked out

The one piece of math

Caffeine leaves the body by halves. If your half-life is five hours, then whatever is on board now is halved five hours from now, halved again five hours after that, and so on. As a formula, the amount left after t hours is:

left = dose × 0.5^{t / half-life}

The cutoff calculator runs that same line backward. You give it a bedtime and a drink; it asks how many hours of halving the drink needs before what's left at bedtime fits under your line, and turns that many hours into a clock time. That's the whole trick — the answer you see stamped on the curve.

The four-to-six-hour range

The FDA puts the typical caffeine half-life at four to six hours, and we run the middle of that range — five — unless you nudge it on the half-life page. The spread is real: the liver enzyme that handles caffeine runs at different speeds in different people. Smoking speeds it up. Pregnancy and some medications slow it down considerably. Age and genes account for most of the rest. A range presented as a range is honest; one exact number for everyone wouldn't be.

The bedtime line

"Out of your system" is the wrong test for sleep — trace amounts linger for a day. What matters is being low enough, so the tool solves to a bedtime line instead of zero. The default is 50 mg — about half a small cup of drip — which is modest enough that most people sleep normally under it. Light sleepers can tighten the line to 25 mg, and the well-seasoned can loosen it to 100. The line is a preference, not a prescription: pick the one that matches your nights.

Answers round to the earlier five minutes. A cutoff of 3:19 pm shows as 3:15 — per-minute precision would promise more than half-life arithmetic can deliver.

What the tool leaves out, on purpose

• The ramp-up. Caffeine takes roughly half an hour to peak after you finish a drink. The tool treats the full dose as landing when you finish it, which errs a few minutes on the careful side.
• Your personal chemistry. The tool assumes a typical healthy adult on the published range. If you're pregnant or on medication, your half-life can be far longer — ask your doctor, not a calculator.
• Sleep advice. Timing arithmetic is all this site does. It won't diagnose why you sleep badly, and it doesn't sell anything that claims to fix it.

Sources

• The half-life range and the 400 mg daily guide: the FDA's consumer page, "Spilling the Beans: How Much Caffeine is Too Much?"
• Coffee, tea, and chocolate figures: USDA FoodData Central
• Branded drinks: each maker's own published number — Starbucks' menu figures, Coca-Cola and PepsiCo's product pages, and the energy-drink labels themselves. The drinks table names the source on every row.