Diluent for a strength

The vial identity solved the other way round: strength named, volume solved. The answer is a finished volume, which is not the same thing as the liquid you pour in.

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

Fill the fields in and the answer appears here.

This tool does its arithmetic in the browser, so it needs JavaScript switched on. The vial pages can be read backwards: find the strength, read off the diluent.

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

Rearranging c = m / V gives V = m / c. Ten milligrams at a target of 2 mg/mL needs 5 mL of finished solution.
That is the FINISHED volume. The diluent to pour in is that figure minus the room the solid itself occupies, which is unknown unless it has been measured.
Pouring in the full figure therefore lands a little below the target strength. The direction is always the same: slightly weaker than asked for, never stronger.

Why the answer is a solution volume rather than an amount to pour

The identity solves for the volume of liquid the solid ends up dissolved in. Pour that much diluent and you end up with marginally more liquid than that, because the solid contributes its own volume, and so with a marginally weaker solution than the one you asked for.

There are two honest ways round it. Mix first, measure the finished volume, and use the vial strength tool with that figure, which removes the uncertainty completely. Or accept being a little under the target and know which way the error runs. What is not honest is treating the two volumes as one number, which is the standard behaviour in this category.

Picking a target that produces a readable draw

A strength is only useful if the volumes it produces can be read on the barrel in hand. At 10 mg/mL a 100 mcg amount is 0.01 mL, which is one single unit on a U-100 and sits in the range where the reading error is a large share of what is being measured. The same amount in a more dilute preparation is a longer draw and a smaller relative error.

That trade-off is arithmetic, and it is worked through on rounding to the nearest mark, which puts a percentage on half a graduation at each volume.

Next to this on the bench

Strength of a mixed vial
The same identity, solved forwards.
Thinning a solution
For a solution already mixed that needs to be weaker.
Displacement and the ceiling
Why the two volumes differ and by how little.