· Vincenzo Lambiase · 4 min read
Caffeine’s half-life in adults is five hours, according to the US prescribing information for caffeine citrate. In a 1983 study of ten healthy young men it ranged from 2.7 to 9.9 hours. A half-life printed on a label is a figure for a population, with a spread behind it.
What it measures is simpler than the drugs it is printed for. Under first-order elimination the body removes the same fraction of what is left in every equal stretch of time. The amount halves, then halves again, and the time each halving takes is the half-life. After five half-lives about 3% is left; after ten, about 0.1%.
Three clocks, one curve.
I built Half-Life around three substances whose half-lives sit far apart: esmolol, a beta blocker given into a vein, at about nine minutes; caffeine at five hours; pembrolizumab, an antibody used against cancer, at twenty-two days. Twenty-two days is 3,520 times nine minutes.
Write what is left as a share of the starting amount and the substance appears in one place only, its half-life. Count time in half-lives and it drops out of the sum: the three curves become one. That is the whole idea of the instrument. Its dial is a clock that turns once per half-life; the point on its hand comes halfway to the centre with every turn, so the spiral it draws is the curve, wound up. The numbers on the rim change with the substance, minutes, hours or days, and nothing else does.
Three slips of pink paper draw the same curve flat, each on its own clock, one large square to a half-life. Put the three on one clock and they come apart: esmolol’s curve has reached the floor before pembrolizumab’s has visibly moved. Switch to a logarithmic scale and each curve becomes a straight line, its slope set by the natural logarithm of 2 divided by the half-life.
The labels, checked against each other.
The labels print more than half-lives. For curves like these, the half-life also follows from two other numbers on the same documents: the natural logarithm of 2, times the volume of distribution, divided by the clearance. Esmolol’s 3.4 litres per kilogram and 285 millilitres per kilogram per minute give 8.3 minutes, against the 9 printed. Pembrolizumab’s 6.0 litres and 195 millilitres a day give 21.3 days, against 22. Close, not equal: labels round, and a body is not one well-stirred tank.
What it leaves out.
Each curve starts when the whole dose has entered the body and spread through it, and shows elimination only. Real curves also rise while a drug is absorbed, and fall fast at first while it spreads into tissues; esmolol’s early fall has its own half-life of about two minutes. The vertical axis is a percentage of the starting amount, not a concentration, and no dose appears anywhere on the page.
Why there is nothing to type.
Half-Life has no field: not for a dose, a weight, an age or a time of day, and it never shows the real clock. That is a rule. Under the EU Medical Device Regulation, what makes software a medical device is what it is intended for and what it actually does, and taking one person’s data to compute something for their treatment can be enough. A page that only draws fixed curves from published values, the same for everyone, is built to stay on the other side of that line. A short check runs before every deploy of this site and stops it if the page ever grows a field, a dose, a stored value or the real clock.
So the page explains a mechanism and decides nothing. If you came with a question about your own medicine, or someone else’s, it can’t answer it. A doctor or a pharmacist can.
How it is built.
A model of 74 lines with no page in it, 500 lines that draw the dial and the slips in your browser, and a 92-line check of 34 assertions: the model, every number printed in the table, and the rule above, in both editions. Every value is copied from US prescribing information on DailyMed, an Irish summary of product characteristics and one paper, all read on 6 October 2026, and each is cited on the page beside its curve.
One thing to try.
Set the time to five half-lives and tap the three slips in turn. The hand stays where it is; only the rim changes: 45 minutes, 25 hours, 110 days.
To hear when the next instrument is out, write to me from the correspondence page.
entry no. 7