What is the arithmetic to convert 8 mg in 3 mL into units on a U-100 scale?

Numbers first: 8 mg · 3 mL.

This should be a straightforward calculation and I keep getting two different answers.

The numbers are arbitrary; the method is what I am after.

What is the general form of this calculation?

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

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.

Specifically, 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.

edited 4 Dec 2024 by dead_volume — expanded the table to cover the lower concentration

Specifically, the arithmetic only stops being confusing once you work it through once and see that it is straightforward.

Breaking it down further: if a 10 mg vial has 96.5 per cent content, you have 9.65 mg of peptide. Divide that by 2.00 mL and your concentration is 4.825 mg/mL, not 5.00 mg/mL, which is a 3.5 per cent systematic error in every dose calculation.

More usefully, dead space quantified: a fixed-needle insulin syringe holds roughly 3 to 5 µL in the hub and needle after the plunger bottoms out. A luer-lock syringe with a detachable needle holds 35 to 100 µL depending on the hub design. At 5 mg/mL that is 15 to 25 µg lost per draw on the insulin syringe and 175 to 500 µg on the luer-lock — which over ten draws is the difference between losing a rounding error and losing half a milligram.

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

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

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.

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

If in doubt, use more diluent and accept the shorter usable window.

Worth being precise here: 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 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.

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