A half-life of 72 hours

Every figure on this page is a function of one number: 72 hours. Five of those is 15 days, and down to one percent takes about 478 hours. No compound is named here and none is implied.

Educational arithmetic only. Not medical advice and not a dosing protocol.

Whole multiples of a 72-hour half-life. The percentage column is exact: one half to the power n is a rational number and is computed as one, so these figures are not rounded decimals.
Half-lives elapsed	Remaining, exactly	Elapsed	Which is
1	50.0000%	72 hours	3 days
2	25.0000%	144 hours	6 days
3	12.5000%	216 hours	9 days
4	6.2500%	288 hours	12 days
5	3.1250%	360 hours	15 days
6	1.5625%	432 hours	18 days
7	0.7813%	504 hours	21 days

Clock time to five remaining fractions. These are approximate: the exponent is fractional except at whole multiples of the half-life, so the value is irrational and is rounded for display.
To	Remaining	Hours, about	Which is about
Down to a half	50%	72.0 hours	3 days
Down to a quarter	25%	144.0 hours	6 days
Down to a tenth	10%	239.2 hours	9 days 23.2 hours
Down to a twentieth	5.0%	311.2 hours	12 days 23.2 hours
Down to a hundredth	1.0%	478.4 hours	19 days 22.4 hours

A 72-hour half-life against seven intervals. The interval is a parameter in this table and nothing more: no row is a suggestion, and the second column is the only thing that determines the rest of the row.
Interval	Intervals per half-life	Surviving the gap	Limit the peaks approach	Intervals to within 1%
8 hours	0.11	92.6%	13.49x	60
12 hours	0.17	89.1%	9.17x	40
24 hours	0.33	79.4%	4.85x	20
48 hours	0.67	63.0%	2.70x	10
72 hours	1.00	50.0%	2.00x	7
168 hours	2.33	19.8%	1.25x	3
336 hours	4.67	3.9%	1.04x	2

What this figure is not

This is educational arithmetic on figures entered by the reader. It is not medical advice, not a dosing protocol, and not a recommendation that anything be prepared, obtained or administered.

Nothing here states what quantity is appropriate for anyone, and there is no function in it that produces an amount to administer. A question about anyone’s health belongs with a licensed clinician who can examine the person asking.

Compounds of the kind this arithmetic is used on are largely research chemicals that are not approved by the FDA for human use. An exact calculation is not an accurate measurement: what is actually in a syringe depends on the preparation and the device, neither of which this page can see.

A half-life belongs to the population, formulation and route it was measured in. Carrying one anywhere else is an assumption rather than a calculation, and this site holds no half-life for any compound: the figure is whatever was typed into the form.

An interval on this site is a parameter, never a proposal. No page here suggests how often anything should happen, and a geometric series evaluated at a spacing somebody chose is not a schedule.

No qualified clinical reviewer is recorded against this site, and no credential is claimed anywhere on it. the full version.

What is particular to this half-life

Three days, and the first value where a weekly interval does something interesting: 168 hours is about 2.3 half-lives, so a fifth of one amount survives the week and the limit is about 1.25. The daily column, by contrast, is up at about 4.8. The spread across one row of this table is the clearest illustration on the site that only the ratio matters.

Reading the third table

The second column is the whole story. It is the interval divided by the half-life, and it is the only input to the three columns after it: the fraction surviving a gap is 0.5 to that power, and the limit is one over one minus that fraction. Two rows with the same figure in column two have identical arithmetic however different the clock times are.

At a 72-hour half-life and a 24-hour interval, 0.33 half-lives pass between repeats, about 79.4% of one amount survives the gap, and the peaks approach about 4.85 times one amount after roughly 20 intervals. Every one of those four figures comes from the ratio and from nothing else.

Why the first table is exact and the other two are not

At whole multiples of a half-life the exponent is a whole number, so the remaining fraction is exactly one half to the power n - a rational number, computed as one. That is why the first table has figures like 3.1250% in it rather than 3.13%.

Everywhere else the exponent is fractional and the value is irrational. There is no exact decimal to print, so those tables are computed in floating point and labelled approximate. Exact and approximate sets out which figures across this whole site are which, and why the distinction is worth making rather than papering over.

What this page is not

It is not about a compound. No substance has a 72-hour half-life as far as this page is concerned; 72 hours is a number, chosen as one of ten points spanning the range this arithmetic is useful over. A published half-life belongs to the species, formulation, route and assay that measured it, and this site holds no such figure for anything.

It is also not a schedule. The intervals in the third table are parameters swept across a plausible range so that the shape of the function is visible. None of them is a proposal, and what this does not do is explicit about that.

Elsewhere on this site

The worksheetAny half-life and any interval, rather than the seven tabulated here.
The other nine half-life valuesSame three tables, a different number at the top.
The same grid by intervalHold the interval fixed and sweep the half-life instead.