Dose arithmetic has three parts: concentration from vial content and diluent, volume from dose and concentration, and units from volume and syringe scale.
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 underlying point is that 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.
Published data on syringe dead space quantifies low-dead-space designs as retaining under 2 µL against 35 µL or more for conventional detachable-needle syringes.
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.
Write the arithmetic on the vial label. It costs nothing and removes the step where you reconstruct it from memory.
edited 17 Jul 2025 by kwn_analytical — corrected a unit error in the worked example
3The placebo-arm figure is the part everyone omits. – tess_amankwah 3 months ago add a comment