Vial yield is a division

The simplest arithmetic on this site and the one with the most ways to be read wrongly. Three of them are worth a paragraph each.

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

The division

Convert both masses to the same unit and divide. A 5 mg vial at 250 mcg a draw is 5000 ÷ 250 = 20 exactly. The same vial at 300 mcg is 5000 ÷ 300 = 16.667, and the whole count is the floor of that: sixteen, because two thirds of a draw is not a draw.

The remainder is what those whole draws leave behind: 5000 - 16 × 300 = 200 mcg. It is always smaller than one draw, or there would be another draw in it, and that property is one of the things the test suite asserts rather than assumes.

A 10 mg vial at seven amounts. The leftover column is the point of the table: two of these rows leave almost a whole draw behind and two leave nothing at all.
Amount per draw	Whole draws	Exact ratio	Left over
250 mcg	40	40.00	nothing
300 mcg	33	33.33	100 mcg
500 mcg	20	20.00	nothing
700 mcg	14	14.29	200 mcg
1 mg	10	10.00	nothing
1.1 mg	9	9.09	100 mcg
3 mg	3	3.33	1,000 mcg

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.

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

One: the count is a ceiling, not a yield

Arithmetic says a 5 mg vial holds twenty 250 mcg draws. A vial does not. Liquid stays in the needle, in the hub of the syringe and in the shoulder of the vial where a needle cannot reach, and none of it is recoverable. The real number of full draws is the computed figure or fewer, never more.

How much fewer depends on the volume, the needle and the vial, none of which software can see. What it can do is say that the number is an arithmetic maximum rather than something somebody measured, which is what the note under every answer does.

Two: the span is one interval shorter than you think

Twenty draws separated by three and a half days do not span seventy days. They span nineteen gaps, which is 66.5. Four fence posts hold three panels, and this is the same off-by-one in a different costume - it is the commonest error in this particular calculation and it always overstates the span.

The vial yield worksheet computes (count - 1) × interval for that reason and says so in the note beside the figure.

Three: the count says nothing about measurability

A 10 mg vial holds a hundred 100 mcg draws. At 10 mg/mL each of those is ten microlitres, which is one single unit on a U-100 barrel, where half a graduation is half the measurement. The count is correct and the draw is unusable.

Those two properties are independent and both have to work, which is why amount to volume and barrel units are on this site at all. The division tells you how many; the conversion tells you whether any one of them can be drawn.