By interval

Six spacings. Each page sweeps the half-life rather than the interval, and each carries the sensitivity table: what the answer does if the half-life you relied on is out by half.

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

Every 8 hoursAt a 24-hour half-life: 79.4% survives the gap and the limit is about 4.85 times one amount.
Every 12 hoursAt a 24-hour half-life: 70.7% survives the gap and the limit is about 3.41 times one amount.
Every 24 hoursAt a 24-hour half-life: 50.0% survives the gap and the limit is about 2.00 times one amount.
Every 48 hoursAt a 24-hour half-life: 25.0% survives the gap and the limit is about 1.33 times one amount.
Every 72 hoursAt a 24-hour half-life: 12.5% survives the gap and the limit is about 1.14 times one amount.
Every 168 hoursAt a 24-hour half-life: 0.8% survives the gap and the limit is about 1.01 times one amount.

The accumulation limit across five half-lives and all six intervals. Every cell is one over one minus the fraction surviving the gap, and the fraction surviving the gap depends only on the ratio of the two figures in its row and column headings.
Half-life	8 h	12 h	24 h	48 h	72 h	168 h
12 hours	2.70x	2.00x	1.33x	1.07x	1.02x	1.00x
24 hours	4.85x	3.41x	2.00x	1.33x	1.14x	1.01x
48 hours	9.17x	6.29x	3.41x	2.00x	1.55x	1.10x
72 hours	13.49x	9.17x	4.85x	2.70x	2.00x	1.25x
168 hours	30.80x	20.70x	10.61x	5.57x	3.89x	2.00x

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.

The diagonal in the grid above

Read it along the cells where the interval equals the half-life - 12 hours at 12, 24 at 24, 48 at 48, 72 at 72, 168 at 168 - and every one of them is exactly 2.00. Those five cells are the same calculation performed on five different clocks, which is the clearest demonstration available that only the ratio of the two figures matters.

Above that diagonal the gap is longer than the half-life and the limit falls towards one. Below it the gap is shorter and the limit climbs without bound. Nothing in either direction is linear.

Why this family exists as well as the half-life pages

Because the two directions answer different questions. "I have a half-life from a source and want to see what different spacings do" is the half-life pages. "I know the spacing and want to see how much the answer depends on a half-life I am unsure of" is these. The second question is the more honest one, and it is the one that almost never gets asked.

Which is why every page in this family carries a sensitivity table that the half-life pages do not. Two projections of one function, each with the table its own direction makes useful.

An interval is a parameter

Six values appear here because six points make the shape of the function visible across the range it is useful over. None of them is a recommendation, none is presented as common or typical, and nothing on this site says how often anything should happen.

That restraint is structural rather than editorial: there is no function behind this site that could produce such a figure, because every worksheet takes its interval from a form. What this does not do is explicit about it.