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What is the arithmetic to convert 5 mg in 1 mL into units on a U-100 scale?

Asked 15 Feb 2025Modified 14 months agoViewed 25k times
34

What I am working with: 5 mg · 1 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.

How many significant figures are actually justified here?

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GW
askedgel_pack_warm13k1815 Feb 2025
3For what it is worth, my own result was within half a per cent of this. – dead_volume 36 days ago
2Any reason this would differ for a longer peptide? – swirl_dont_shake 9 months ago
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5 Answers

Accepted answer first, then by votes
-2

Accepted answer

On the detail: this is arithmetic, so let us do the arithmetic rather than argue about it.

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.

Dead space by syringe type

ConfigurationDead volumeLoss at 5 mg/mLOver 20 draws
Fixed-needle insulin syringe3–5 µL15–25 µg0.3–0.5 mg
Low-dead-space, detachable<2 µL<10 µg<0.2 mg
Standard luer-lock + 30G35–60 µL175–300 µg3.5–6 mg
Luer-lock + 21G drawing needle70–100 µL350–500 µg7–10 mg

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.

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.

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.

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

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answered · acceptedcharge_state_339k4817 Feb 2025
4Adding for future readers: the certificate should carry the lot number, not just a batch code. – thermal_mass 4 months ago
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72

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.

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 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.

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.

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DV
answeredDr_Ilse_Vandenberg78k2486 Jun 2025
3Does this hold at lower concentrations, or does adsorption dominate? – e_dziedzic 7 months ago
4Worth flagging that this changed in 2025, so older answers on the site are out of date. – otto_brenner 9 months ago
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38

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.

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.

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

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.

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BD
answeredb_delacroix48k3828 Feb 2025
30

This is one of those calculations where checking your work takes two minutes and prevents a very consequential 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.

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 28 Mar 2025 by amara_nwachukwu — corrected a unit error in the worked example

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AN
answeredamara_nwachukwu41k3811 Mar 2025
27

The relevant detail is that the arithmetic only stops being confusing once you work it through once and see that it is straightforward.

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.

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

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PM
answeredp_mkhize41k13823 Apr 2025
6This is the first explanation of that which has actually made sense to me. – Dr_Nadia_Farsi 9 days ago
5Note that the label instructions differ between agents on precisely this point. – low_dead_space 9 months ago
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