How many vial-days does a 5 mg vial give at 2 mg/mL on a weekly schedule?

Setup, so nobody has to ask: 5 mg · 2 mg/mL.

The units are where I keep going wrong, so please be explicit about them.

I have sanity-checked the order of magnitude and it seems right, which is not the same as being right.

Where is my error, and what is the correct working?

The common error is getting the concentration right but then misreading the syringe scale, which is why checking the barrel marking rather than your memory matters.

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 relevant detail is that 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.

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.

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

The rounding error accumulates if you round too many times — rounding concentration to 5.0, rounding the dose volume to 0.1 mL, rounding the unit reading to 10 — and the safest approach is to work the full precision and round only the final answer.

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.

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

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.

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.

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 it removes the step where you reconstruct it from memory at an inconvenient moment.

edited 21 Mar 2026 by orla_ferriter — corrected a unit error in the worked example

Stated carefully, two people working through the same arithmetic independently should get the same answer, and if they do not, someone has made a unit error.

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 Arrhenius relationship for drawing kinetics means that cold solution takes noticeably longer to draw than room-temperature solution.

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.