Whole draws in a vial
Two numbers in: what is in the vial, and how much comes out per draw. The count, the exact ratio and the leftover out. Add an interval and the span those draws cover comes with it.
Educational arithmetic only. Not medical advice and not a dosing protocol.
Enter the figures above.
Where that comes from
- The exact ratio is one mass divided by the other, both converted to the same unit first. A 5 mg vial at 250 mcg a draw is
5000 ÷ 250 = 20. - The whole count is that ratio with the fractional part dropped, because two thirds of a draw is not a draw. The same vial at 300 mcg gives 16.67, which is sixteen.
- The remainder is what those whole draws leave:
5000 - 16 × 300 = 200 mcg. It is always smaller than one draw, or there would be another draw in it. - The span, when an interval is given, is the interval repeated ONE FEWER time than there are draws. Twenty draws separated by three and a half days span nineteen gaps, which is 66.5 days rather than 70. Getting that wrong overstates the span by a whole interval, and it is the commonest error in this particular calculation.
The count is a ceiling, and the gap is not small
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 this figure or fewer, never more.
How much fewer depends on the volume, the needle and the vial, none of which this worksheet can see. What it can do is be clear that the number it prints is the arithmetic maximum rather than a yield anybody measured.
Why the remainder is printed rather than rounded away
Because the interesting case is the one where the leftover is nearly a draw. A 10 mg vial at 700 mcg gives fourteen draws with 200 mcg left: not close. The same vial at 1,100 mcg gives nine with 100 mcg left. Knowing which of those two you are in is most of the value of the calculation, and a count on its own does not say.
A vial that divides exactly says so, which is worth knowing too: it means the arithmetic has no slack in it at all, so every bit of unrecoverable liquid comes straight off the last draw.
What the interval field does and does not do
It multiplies. Given a count and a gap, the span is one fewer gap than there are draws, and that is the whole operation - the same arithmetic as working out how many weeks forty-two days is. The figure comes from the form and nowhere else.
What it does not do is suggest a value. There is no default, no placeholder figure, no list of common intervals and no page on this site that proposes one. An interval here is a parameter, and what this does not do says so at length.
The other arithmetic on this site
- Repeat-interval arithmeticWhat a half-life you supply implies when an amount repeats at an interval you supply.
- The decay curveA single half-life plotted, with the exact fractions at whole multiples.
- All six worksheetsIncluding the three that convert between an amount, a volume and a barrel reading.