An interval of 24 hours

The interval held fixed at 24 hours while the half-life varies. At a 24-hour half-life, 50.0% of one amount survives the gap and the peaks approach about 2.00 times one amount.

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

An interval of 24 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	12.00	0.0%	1.00x	1
4 hours	6.00	1.6%	1.02x	2
6 hours	4.00	6.3%	1.07x	2
12 hours	2.00	25.0%	1.33x	4
24 hours	1.00	50.0%	2.00x	7
36 hours	0.67	63.0%	2.70x	10
48 hours	0.50	70.7%	3.41x	14
72 hours	0.33	79.4%	4.85x	20
120 hours	0.20	87.1%	7.73x	34
168 hours	0.14	90.6%	10.61x	47
336 hours	0.07	95.2%	20.70x	94

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	1.07x	1.33x	2.00x
24 hours	1.33x	2.00x	3.41x
48 hours	2.00x	3.41x	6.29x
72 hours	2.70x	4.85x	9.17x
168 hours	5.57x	10.61x	20.70x

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 spacing most of this site's worked examples use, because a day is the unit people already think in. The interesting feature of this page is how fast the limit climbs once the half-life passes the interval: at 24 hours it is 2, at 48 it is 3.41, at 120 it is 8.0, at 336 it is above 21. Nothing about the function is linear.

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 24 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.