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What is the arithmetic to convert 15 mg in 5 mL into units on a U-100 scale?

Asked 30 May 2026Modified 2 months agoViewed 8.1k times
19

For reference: 15 mg · 5 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?

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MI
askedmicron2236k13830 May 2026
8Related: the same reasoning applies to the counter-ion question. – RP_C18 4 months ago
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4 Answers

Accepted answer first, then by votes
21

Accepted answer

Specifically, 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.

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.

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

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.

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answered · acceptedcake_intact18k281 Jun 2026
Do you have a reference for the last claim? Not disputing it, just want to read it. – micron22 3 months ago
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8

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

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.

Specifically, 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 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.

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 12 Jun 2026 by sian_llewellyn — added a caveat about sampling

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answeredsian_llewellyn85k2481 Jun 2026
5

It helps to be literal here: dose arithmetic has three parts: concentration from vial content and diluent, volume from dose and concentration, and units from volume and syringe scale.

Room temperature before drawing is worth the ten minutes. Cold solution is more viscous, draws slower, and condensation on a cold barrel makes it harder to read the meniscus.

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.

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.

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DA
answeredDr_Rosalind_Achebe90k1581 Jun 2026
4

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

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.

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

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answeredDr_Ravi_Selvarajah42k1381 Jun 2026
7Thank you — the worked example is what makes this usable. – bea_castellanos 3 months ago
8Related: the same reasoning applies to the counter-ion question. – m_haraldsen 5 months ago
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