Strength of a mixed vial

Mass of solid in, volume of liquid in, strength out - as a ceiling rather than a measurement until a finished volume is entered.

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

Solid in the vial Unit for solid in the vial

Diluent put in Unit for diluent put in

Finished volume, if measured Unit for finished volume, if measured With this the strength is a measurement. Without it, a ceiling.

Amount you want to draw Unit for amount you want to draw

Which barrel Required. The printed numbers mean a different volume on each of these.

Fill the fields in and the answer appears here.

What the bench will not tell you

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 limits of this bench.

The arithmetic, step by step

Strength is the mass divided by the volume of the finished solution: c = m / V.
The finished solution is bigger than the diluent, because the solid takes up room once it dissolves. With that displacement unmeasured, V ≥ diluent, so dividing by the diluent gives the highest the strength can possibly be.
The tool therefore prints at most on the figure until a finished volume is entered, and prints at least on any volume derived from it.
Five milligrams in 2 mL is 5 / 2 = 2.5 mg/mL at the ceiling, which is 2,500 mcg/mL, which is 250 mcg in each tenth of a millilitre - the same figures the fields above start with, so the worked example and the answer agree rather than offering a reader two plausible numbers.

What the finished-volume field buys

Mark the barrel after mixing, read the finished volume off it, and type that in. The strength stops being a bound and becomes a division of two measured quantities, so the label changes from at most to a plain figure. What that removes is one specific assumption - that the finished volume equals the diluent added. It removes nothing else: whether the vial held what the label claimed, whether the solid fully dissolved and whether the volume was read correctly are all still unknown, and all still larger in effect than the assumption that has gone.

For a few milligrams of solid the gap is usually small against the error of reading a 1 mL barrel. Small is not zero, and the direction matters: the ceiling always errs towards a stronger solution than you have, which means towards a smaller draw than you need.

Why the strength is printed three ways

Milligrams per millilitre is how vials get labelled. Micrograms per millilitre is the unit most amounts are discussed in, and the factor of a thousand between them is the single most common error in this arithmetic. Micrograms per tenth of a millilitre is the figure that matters at the barrel, because a tenth of a millilitre is ten units on a U-100 and it is the increment anyone actually draws in.

All three are the same number in different clothes. Printing one and leaving the reader to shift the decimal point is where the factor of a thousand gets introduced.

Next to this on the bench

Volume for an amount
Starts from a strength you already know rather than from the vial.
Diluent for a strength
The same identity solved for the volume instead of the strength.
The eight vial strengths
Every common vial worked through at every diluent volume.