What is the arithmetic to convert 10 mg in 2 mL into units on a U-100 scale?

Conditions: 10 mg · 2 mL.

I want the working, not the result — I need to be able to redo it with different numbers.

I care about the precision as well as the value — I want to know how many figures are real.

Is my approach right even if my number is wrong?

Rounding to the nearest whole syringe unit is usually the right error to make, but understanding which direction it is and why matters.

On filtration: a 0.22 µm syringe filter will remove particulates and organisms, and it will also adsorb a fraction of your peptide onto the membrane — with a low-binding PVDF or PES membrane the loss is typically a few per cent.

On the detail: number of stopper piercings matters less than the gauge doing the piercing. A 30G or 31G needle through a butyl stopper leaves a track that reseals; a 21G or 18G drawing needle punches a core and can drop it into the solution.

The limitation is that technique reduces risk, it does not remove it, and nothing you can do outside a controlled environment makes a non-sterile preparation sterile.

Write the arithmetic on the vial label. It costs nothing and removes the step where you reconstruct it from memory.

The part that matters: two people working through the same arithmetic independently should get the same answer, and if they do not, someone has made a unit error.

Room temperature before drawing is worth the ten minutes. Cold solution is more viscous, draws slower, and condensation on a cold barrel makes it harder to read the meniscus.

Do not use the same needle to pierce the stopper and to administer. The tip is blunted by the stopper, and the hub now contains a dose you are about to lose to dead space anyway.

The content assay results from major testing services show that nominal vial claim and measured content differ by one to ten per cent, making content a driver of dose error.

I would flag the obvious failure mode: people get the concentration right, get the volume right, and then read the syringe against the wrong scale.

Do the arithmetic twice, ideally with someone else doing it independently.

edited 4 Dec 2025 by lyoph_cake — added the citation requested in comments

Concretely, this is one of those calculations where checking your work takes two minutes and prevents a very consequential error.

Rotation of injection site is a tolerability measure, not a pharmacokinetic one, but if you are going to do it you might as well do it right.

Write the arithmetic on the vial label. It costs nothing and it removes the step where you reconstruct it from memory at an inconvenient moment.

The part that matters: the arithmetic only stops being confusing once you work it through once and see that it is straightforward.

Worked example, because the general form is easier to trust once you have seen it once. Take a 10 mg vial and add 2 mL of diluent: the concentration is 10 ÷ 2 = 5 mg/mL. A 0.5 mg dose is 0.5 ÷ 5 = 0.1 mL. On a U-100 syringe, where 1 unit = 0.01 mL, that is 0.1 ÷ 0.01 = 10 units. Change the diluent to 1 mL and the same dose becomes 5 units — same dose, half the resolution.

The insulin-unit standard U-100 means 100 units per millilitre, so one unit is 0.01 mL — this is the conversion that trips up more people here than any other single piece of arithmetic.

The caveat is that this assumes the vial contains what the label says, and if the content assay has not been done, the arithmetic is precise about an unknown quantity.

The practical summary: fine gauge, gentle swirl, diluent down the wall, room temperature before drawing, and check the syringe scale against the barrel rather than against your assumption.