How many units on a 1 mL luer-lock syringe is a 20 mg dose at 20 mg/mL?

For reference: a 1 mL luer-lock syringe · 20 mg · 20 mg/mL.

I would rather understand the derivation than memorise the outcome.

Two people I asked gave two answers that differ by a factor of ten, which is suggestive.

Can someone walk through the arithmetic step by step?

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

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 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 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.

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.

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

Dose arithmetic has three parts: concentration from vial content and diluent, volume from dose and concentration, and units from volume and syringe scale.

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.

It helps to be literal here: 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 Arrhenius relationship for drawing kinetics means that cold solution takes noticeably longer to draw than room-temperature solution.

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.

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

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.

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.

Worth noting: the concentration after reconstitution is not the same as the label claim, and most people do not account for the difference.

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

edited 27 Jan 2026 by ines_brandt — added the citation requested in comments

To be exact about it, the arithmetic only stops being confusing once you work it through once and see that it is straightforward.

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.

edited 10 May 2026 by Dr_Nadia_Farsi — corrected a unit error in the worked example

The distinction that resolves most of these questions is understanding what concentration actually means and why it is not the same as label claim.

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.