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Reconstitution: The Arithmetic, Not the Advice

Concentration is mass divided by volume — except the naive division is wrong, and an FDA label's own numbers prove it. The maths, and what it cannot tell you.

By Grant Delaney, Research Editor

What this page is and is not

This page explains the arithmetic of reconstitution: how a mass of powder and a volume of liquid become a concentration, and how a concentration and a volume become a number on a syringe barrel.

It contains no dose, no suggested dose, and no example intended to be followed. Every quantity below is either a statement quoted from an FDA label or the result of dividing two such statements.

What quantity of anything is appropriate for a particular person is a prescribing decision, and no amount of arithmetic produces it.

The equation

Reconstitution means adding liquid to a freeze-dried — lyophilised — powder to produce a solution.

Concentration equals mass divided by volume. If a container holds M milligrams dissolved in V millilitres, the concentration is M ÷ V milligrams per millilitre.

Then volume equals mass divided by concentration. To find what volume contains a given mass, divide that mass by the concentration.

Two divisions. That is the whole of it — and one of them is routinely done wrong.

Why the obvious division gives the wrong answer

The powder is not weightless and it is not volumeless. When it dissolves it occupies space, so the final volume of solution is larger than the volume of diluent added.

An FDA label demonstrates this with its own published numbers. The following are quoted statements from the EGRIFTA WR label for tesamorelin, an approved product for reduction of excess abdominal fat in adults with HIV-associated lipodystrophy — quoted here as an arithmetic worked example, not as a protocol for anything.

The label states that each single-patient-use vial contains 11.6 mg of tesamorelin as a lyophilised powder1.

The label directs reconstituting one vial with 1.3 mL of diluent1.

The label states that one dose is 1.28 mg in 0.16 mL of the reconstituted solution1.

Now run the numbers backwards. 1.28 mg ÷ 0.16 mL = 8.0 mg/mL. That is the concentration the label's own figures imply.

If the concentration is 8.0 mg/mL and the vial holds 11.6 mg, the final volume must be 11.6 ÷ 8.0 = 1.45 mL.

But only 1.3 mL of diluent went in. The missing 0.15 mL is the dissolved powder's own volume plus the vial's overfill.

Do the naive division instead — 11.6 mg ÷ 1.3 mL — and you get 8.923 mg/mL. That is 11.5% higher than the concentration the label actually implies. An 11.5% error, from an arithmetic step that looks obviously correct.

This is the single most useful thing on this page. Where a label publishes both the diluent volume and the delivered dose volume, those two numbers, not the division, define the concentration.

Converting a volume into syringe units

Syringe barrels for this kind of injection are marked in units rather than millilitres, and the scale is a property of the product, not a universal.

An insulin label states its strengths as 100 units/mL (U-100) and 200 units/mL (U-200)2. On a U-100 scale, 1 mL is 100 units, so 1 unit is 0.01 mL. On a U-200 scale the same barrel marking means half the volume.

Applying the U-100 scale to the label figure above: 0.16 mL × 100 units/mL = 16 units.

The conversion is a multiplication. It carries no information about whether that volume is appropriate for anyone.

What the vial does not deliver

Two cross-checks on the same label, which should agree — and do.

By mass: the label states one reconstituted vial provides daily doses for 7 consecutive days at 1.28 mg each1. 7 × 1.28 mg = 8.96 mg, out of the 11.6 mg the vial contains. That is 77.2%.

By volume: 7 × 0.16 mL = 1.12 mL, out of the 1.45 mL of solution the arithmetic above implies. Also 77.2%.

The two routes agreeing is how you know the arithmetic held. Roughly 23% of the vial's labelled content is never delivered — overfill, residual volume, and the dead space in the needle hub. A calculation that assumes a vial delivers its full labelled mass will overstate what is available.

What the diluent is, per its own label

Bacteriostatic Water for Injection, USP is described on its label as a sterile, nonpyrogenic preparation containing 0.9% (9 mg/mL) or 1.1% (11 mg/mL) of benzyl alcohol added as a bacteriostatic preservative, supplied in a multiple-dose container from which repeated withdrawals may be made3.

The same label carries a boxed statement: NOT FOR USE IN NEONATES. Its contraindications section states that due to the potential toxicity of benzyl alcohol in neonates, solutions containing benzyl alcohol must not be used in that population, and that preparations containing benzyl alcohol should not be used in epidural or spinal anaesthesia procedures3.

The label also states that it must be made approximately isotonic prior to use, that administration without a solute may result in haemolysis, and — the line most relevant here — that the manufacturer's instructions should be consulted for choice of vehicle and appropriate dilution or volume for the drug being dissolved3.

That last sentence is the diluent's own label saying that the diluent does not decide the arithmetic. The product being dissolved does.

What arithmetic cannot resolve

Rounding. If a division produces 13.7 units on a barrel whose smallest gradation is a whole unit, no further arithmetic tells you which way to go. That is a measurement limit, not a maths problem.

Stability. The tesamorelin label directs storing the reconstituted solution at 20°C to 25°C and discarding unused solution 7 days after mixing, and not freezing it1. Concentration maths says nothing about how long a molecule survives in solution; only the product's own label or stability data does.

Sterility. Nothing in a calculation addresses whether a preparation is sterile.

And the dose itself. Every equation on this page takes a target quantity as an *input*. None of them produces one. Our reconstitution calculator is built the same way: it converts a figure you already have into syringe units and shows every step, and it will not suggest a figure.

Where this fits

Reconstitution exists because many peptides are supplied as lyophilised powder — they are more stable dry than wet. Why they are injected at all is covered in oral vs injectable peptides, and how long they last once they are in is covered in half-life and dosing frequency.

For the compound records themselves, start at the research index.

Frequently asked questions

How do I calculate concentration after reconstitution?

Concentration is mass divided by volume — but the volume is the final volume of solution, not the volume of diluent added, because the dissolved powder occupies space. On the EGRIFTA WR label, 1.3 mL of diluent goes into an 11.6 mg vial, and the label's own dose figures (1.28 mg in 0.16 mL) imply 8.0 mg/mL and therefore a final volume of 1.45 mL. Dividing 11.6 by 1.3 instead gives 8.923 mg/mL — 11.5% too high.

How many millilitres is one unit on an insulin syringe?

On a U-100 scale, 0.01 mL — because U-100 means 100 units per millilitre. An insulin label lists both 100 units/mL (U-100) and 200 units/mL (U-200) strengths, so the scale is a property of the specific product and barrel rather than a universal constant.

Does a vial deliver all the milligrams printed on it?

No. On the EGRIFTA WR label, one reconstituted vial provides 7 daily doses of 1.28 mg — 8.96 mg out of 11.6 mg, or 77.2%. The same figure comes out by volume: 7 × 0.16 mL is 1.12 mL of the 1.45 mL the arithmetic implies. The remainder is overfill, residual volume and dead space.

What is bacteriostatic water?

Its label describes it as a sterile, nonpyrogenic preparation of water for injection containing 0.9% (9 mg/mL) or 1.1% (11 mg/mL) benzyl alcohol as a bacteriostatic preservative, supplied in a multiple-dose container. The label carries the statement NOT FOR USE IN NEONATES, and directs consulting the manufacturer's instructions of the drug being dissolved for choice of vehicle and appropriate volume.

Does this arithmetic tell me what dose to use?

No. Every equation here takes a target quantity as an input and converts it into a concentration or a volume. None of them produces one. What quantity is appropriate for a particular person is a prescribing decision that arithmetic cannot reach.

How long does a reconstituted vial last?

That is set by the specific product's stability data, not by any calculation. As an example of what a label states: the EGRIFTA WR label directs storing the reconstituted solution at 20°C to 25°C, not freezing it, and discarding unused solution 7 days after mixing.

References

  1. DailyMed, U.S. National Library of Medicine (2026). EGRIFTA WR (tesamorelin) for injection — prescribing information, Dosage and Administration. DailyMed Structured Product Label. https://dailymed.nlm.nih.gov/dailymed/drugInfo.cfm?setid=839334d3-8c1d-4c26-9036-2ab524a6ea75
  2. DailyMed, U.S. National Library of Medicine (2026). HUMALOG (insulin lispro) injection, solution — prescribing information, Dosage Forms and Strengths. DailyMed Structured Product Label. https://dailymed.nlm.nih.gov/dailymed/drugInfo.cfm?setid=c8ecbd7a-0e22-4fc7-a503-faa58c1b6f3f
  3. DailyMed, U.S. National Library of Medicine (2026). BACTERIOSTATIC WATER for Injection, USP — prescribing information. DailyMed Structured Product Label. https://dailymed.nlm.nih.gov/dailymed/drugInfo.cfm?setid=87d6e9dc-fe3b-4593-ac9a-d7493d1959c7

Medical disclaimer: This content is for general educational purposes only and is not medical advice, diagnosis, or treatment. Always consult a licensed healthcare professional before starting, stopping, or changing any treatment.

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