Work in the order concentration, then volume, then units, and the arithmetic stops being confusing. Concentration is milligrams per millilitre and comes from the vial contents and the diluent volume. Volume per dose is dose divided by concentration. Units on a U-100 syringe are volume in millilitres multiplied by one hundred.
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.
In practice, 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 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 removes the step where you reconstruct it from memory.
2Useful. I have added the accept threshold suggestion to my own notes. – dead_volume 40 days ago add a comment