What is the arithmetic to convert 2 mg in 1.5 mL into units on a U-100 scale?

What I have: 2 mg · 1.5 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.

Can someone show the working rather than just the answer?

The underlying point is that write the units at every step, because units errors are the failure mode that catches everyone eventually.

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 part that matters: 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 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.

The part that matters: the arithmetic only stops being confusing once you work it through once and see that it is straightforward.

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.

Mechanically, 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.

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.

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

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

It helps to be literal here: the single most useful thing to do is write the arithmetic on the vial label, because you will reconstruct it from memory at an inconvenient moment if you do not.

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.

In practice, 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.

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.

edited 3 Mar 2026 by ruaidhri_o_shea — added the placebo-arm figures

Rounding to the nearest whole syringe unit is usually the right error to make, but understanding which direction it is and why matters.

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.

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.

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

edited 1 Jul 2026 by kwn_analytical — fixed an arithmetic slip in the third paragraph

It helps to be literal here: 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.

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.

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.

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