An interval of 8 hours

The interval held fixed at 8 hours while the half-life varies. At a 24-hour half-life, 79.4% of one amount survives the gap and the peaks approach about 4.85 times one amount.

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

An interval of 8 hours against eleven half-lives. The interval is held fixed and the half-life is the variable, which is the useful direction when the half-life is the figure you are least sure of.
Half-life	Intervals per half-life	Surviving the gap	Limit the peaks approach	Intervals to within 1%
2 hours	4.00	6.3%	1.07x	2
4 hours	2.00	25.0%	1.33x	4
6 hours	1.33	39.7%	1.66x	5
12 hours	0.67	63.0%	2.70x	10
24 hours	0.33	79.4%	4.85x	20
36 hours	0.22	85.7%	7.00x	30
48 hours	0.17	89.1%	9.17x	40
72 hours	0.11	92.6%	13.49x	60
120 hours	0.07	95.5%	22.14x	100
168 hours	0.05	96.8%	30.80x	140
336 hours	0.02	98.4%	61.09x	280

How much the limit moves if the half-life you relied on is out by a factor of two either way. Published half-lives for one compound often differ by more than this between studies, so the spread across a row is the honest uncertainty in the figure.
Assumed half-life	If it is half that	As assumed	If it is double
12 hours	1.66x	2.70x	4.85x
24 hours	2.70x	4.85x	9.17x
48 hours	4.85x	9.17x	17.82x
72 hours	7.00x	13.49x	26.47x
168 hours	15.65x	30.80x	61.09x

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.

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.

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.

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 interval

The shortest spacing here, and the one where the half-life matters most. Across the eleven rows below the limit runs from essentially one to above twenty-nine: a factor of thirty, driven entirely by a parameter somebody read in a paper. If there were ever a case for checking which half-life a figure came from, this page is it.

Why the second table is the more useful one

Because the half-life is almost always the figure you are least sure of. A spacing is something you chose and know exactly; a half-life came out of a paper, belongs to the population and formulation that paper measured, and can differ between studies by more than the precision anyone quotes it to.

So the second table asks what happens if the figure is wrong by a factor of two either way, which is well within the range published values for one compound can disagree by. The spread across a row is the honest uncertainty in the accumulation figure, and it is usually much larger than anybody expects.

The ratio is the only thing that matters

Only the interval divided by the half-life appears in the arithmetic. The fraction surviving a gap is 0.5 to that power, and the limit is one over one minus that fraction. Which means a 24-hour interval at a 24-hour half-life and a weekly interval at a weekly half-life are the same calculation on a different clock: both give half surviving and a limit of exactly 2.

The half-life pages are the same grid read the other way. If the figure you are confident about is the half-life, start there; if it is the spacing, start here.

What this page is not

It is not a suggestion that anything happen every 8 hours. The figure is one of six spacings swept so that the shape of the function is visible across the range it is useful over, and every row of every table here is a parameter rather than a proposal.

It is also not about a compound: no substance is named on this page or anywhere on this site. What this does not do sets out that boundary in full, and it is the longest page here for a reason.

Elsewhere on this site

The worksheetAny interval and any half-life, rather than the eleven tabulated here.
The other five intervalsSame two tables, a different spacing held fixed.
Where the series comes fromThe derivation, in four lines, with nothing hidden.