By half-life

Ten values spanning the range this arithmetic is useful over. No compound is named on any of them: a half-life here is a parameter, and each page is what follows from one value of it.

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

2 hoursAt a 24-hour interval: 0.0% survives the gap and the peaks approach about 1.00 times one amount.
4 hoursAt a 24-hour interval: 1.6% survives the gap and the peaks approach about 1.02 times one amount.
6 hoursAt a 24-hour interval: 6.3% survives the gap and the peaks approach about 1.07 times one amount.
12 hoursAt a 24-hour interval: 25.0% survives the gap and the peaks approach about 1.33 times one amount.
24 hoursAt a 24-hour interval: 50.0% survives the gap and the peaks approach about 2.00 times one amount.
48 hoursAt a 24-hour interval: 70.7% survives the gap and the peaks approach about 3.41 times one amount.
72 hoursAt a 24-hour interval: 79.4% survives the gap and the peaks approach about 4.85 times one amount.
120 hoursAt a 24-hour interval: 87.1% survives the gap and the peaks approach about 7.73 times one amount.
168 hoursAt a 24-hour interval: 90.6% survives the gap and the peaks approach about 10.61 times one amount.
336 hoursAt a 24-hour interval: 95.2% survives the gap and the peaks approach about 20.70 times one amount.

The accumulation limit at three intervals, across all ten half-lives. Each page below carries seven intervals and two further tables; this is the comparison across values.
Half-life	At 24 hours	At 72 hours	At 168 hours
2 hours	1.00x	1.00x	1.00x
4 hours	1.02x	1.00x	1.00x
6 hours	1.07x	1.00x	1.00x
12 hours	1.33x	1.02x	1.00x
24 hours	2.00x	1.14x	1.01x
48 hours	3.41x	1.55x	1.10x
72 hours	4.85x	2.00x	1.25x
120 hours	7.73x	2.94x	1.61x
168 hours	10.61x	3.89x	2.00x
336 hours	20.70x	7.24x	3.41x

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.

Why ten values and not a formula

There is a formula, and the worksheet evaluates it for any pair of figures. These pages exist because a table is faster than a form when somebody wants to see the shape, and because they work without JavaScript.

The ten values are spaced roughly logarithmically - two hours to a fortnight - because that is how published half-lives for peptides are distributed: a handful of minutes to several days, with no clustering that would justify an even spacing.

What the grid above shows at a glance

That the limit depends only on the ratio. Read down the 24-hour column and the limit climbs steadily as the half-life grows, because the same gap is a smaller and smaller fraction of it. Read across any row and it falls, because the same half-life is being given longer to work.

The two cells where the limit is exactly 2 are the ones where the interval equals the half-life: 24 hours at 24 hours and 168 hours at 168 hours. Different clocks, identical arithmetic.

What is deliberately absent

Any half-life attributed to any substance. This site holds no compound data: no names, no molar masses, no potencies and no published half-lives. A figure like that belongs to the study that measured it, with the species, the formulation, the route and the assay attached, and reproducing one here without all four would be worse than not having it.

So the parameter is a parameter. If you have a figure from a source you trust, the worksheet takes it; if you want to see the shape first, these ten pages are the shape.