What a half-life is
One number, and four things attached to it that usually get dropped when it is quoted. This site asks for the number and says plainly that it does not know the four.
Educational arithmetic only. Not medical advice and not a dosing protocol.
The definition, and what follows from it
A half-life is the time for a quantity decaying at a constant proportional rate to fall to half of its value. Constant proportional rate is the whole content of the idea: the same fraction goes in each equal slice of time, which is why the absolute amount lost per hour shrinks as the quantity does.
Mathematically that gives remaining = 0.5t ÷ t½, and two
useful consequences. Whole multiples of the half-life give exact rational fractions - a
half, a quarter, an eighth. And the time to fall to any given fraction is the same whatever
you start with, which is why "five half-lives" is a rule of thumb rather than a figure that
has to be recomputed.
| Half-lives elapsed | Remaining, exactly |
|---|---|
| 1 | 50.0000% |
| 2 | 25.0000% |
| 3 | 12.5000% |
| 4 | 6.2500% |
| 5 | 3.1250% |
| 6 | 1.5625% |
| 7 | 0.7813% |
The four things that travel with a published figure
The species
A half-life measured in one species is a measurement about that species. It is often the only figure available, and carrying it anywhere else is an assumption.
The formulation
The same molecule in a different preparation can clear at a different rate, because what is being measured is the behaviour of the preparation in a body rather than a property of the molecule on its own.
The route
A subcutaneous injection has to be absorbed before it can be cleared, and absorption competes with elimination. A figure measured intravenously describes a different curve from the same compound given subcutaneously.
The assay
What was being counted, how sensitively, and over what period. A short sampling window can miss a slow terminal phase entirely and report a half-life that is too short.
Why this site holds no half-life for anything
Because a table of them would drop all four of the things above and keep only the number. Published values for one compound can differ between studies by more than the precision anyone would quote them to, and a lookup that picks one and presents it as the figure has made an editorial judgement without saying so or standing behind it.
So the half-life is a field on every worksheet here, and the ten half-life pages are a parameter sweep rather than a catalogue: ten values spanning the range this arithmetic is useful over, with no substance attached to any of them.
What to do with a figure you are unsure of
Put it in and then put in half of it and double it, and look at how much the answer moves. Every page in the by interval family carries that comparison as a table, because the spread is usually much wider than people expect: at an eight-hour spacing, a half-life of 24 hours against 48 hours is the difference between a limit of about 4.3 and one of about 7.8.
An answer that changes a lot when a parameter is doubled is an answer whose uncertainty lives in the parameter rather than in the arithmetic, and knowing which of those two you are looking at is most of what this site is for.
Related
- Where the series comes fromWhat follows when an amount decaying like this is repeated.
- The decay curveOne half-life plotted, with the exact points marked.
- The ten half-life pagesThe parameter swept across its useful range.