What is the arithmetic to convert 40 mg in 5 mL into units on a U-100 scale?

Concretely: 40 mg · 5 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?

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

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.

On the detail: 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.

One qualification: if your arithmetic and someone else's disagree by a factor of ten, one of you has made a unit error, and writing out the units at every step is the diagnostic.

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

The relevant detail is that the single most useful thing to do is write the arithmetic on the vial label, because you will reconstruct it from memory at an inconvenient moment if you do not.

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.

Concretely, the concentration you actually work with is label claim times content fraction divided by actual diluent volume, which is usually not the same as the nominal concentration because content is usually not 100 per cent and you rarely measure the diluent volume to 0.1 mL precision.

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.

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

Write the units at every step, because units errors are the failure mode that catches everyone eventually.

Air bubbles at these volumes are a measurement problem rather than a safety one. A 2 mm bubble in a 0.3 mL syringe is roughly 4 µL, which at 10 units drawn is a four per cent error.

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.

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.

edited 13 Apr 2026 by tabular_nums — fixed an arithmetic slip in the third paragraph

The relevant detail is that 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 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.