Reconstitution Math from First Principles

This guide is the math version of the reconstitution process — written out in slow motion so that anyone who wants to verify a calculator output by hand can do so. If you already trust the calculator and just want a number, the calculator on the homepage will give it to you in real time. This guide is for the careful user who wants to know exactly what every step is doing and why.

Nothing here is medical advice. The math is just dimensional analysis applied to a particular practical problem.

The problem in plain language

You have a vial. The vial contains a certain mass of dry peptide, expressed in milligrams (mg). You add a certain volume of bacteriostatic water, expressed in milliliters (mL). The mixture becomes a solution with a particular concentration — a certain mass of peptide per unit volume of liquid.

You also have a target dose. That target dose is a mass — typically expressed in micrograms (mcg) for most peptide protocols, sometimes expressed in milligrams.

The question the calculator answers: how much volume of the solution do I need to draw, in order to deliver the target mass?

That’s it. Everything else is unit conversion.

Conversion 1: peptide mass to concentration

Concentration in chemistry is mass per unit volume. The formula is:

concentration = mass ÷ volume

If you put 5 mg of peptide into 1 mL of bacteriostatic water, you have:

concentration = 5 mg ÷ 1 mL = 5 mg/mL

That is the concentration of your solution, expressed in mg per mL.

Most peptide doses are expressed in micrograms, not milligrams. To convert mg/mL to mcg/mL, multiply by 1,000 (because 1 mg = 1,000 mcg):

5 mg/mL × 1,000 mcg/mg = 5,000 mcg/mL

So the concentration of your solution, expressed in mcg per mL, is 5,000.

Concentration is a property of the solution. It does not depend on the dose you want to draw, the syringe you’re using, or anything else. It depends only on the mass of peptide and the volume of water you mixed it with.

Conversion 2: dose mass to draw volume

Now you know your concentration in mcg/mL. You have a target dose expressed as a mass in mcg. The volume you need to draw is:

volume = dose ÷ concentration

Make sure both numbers are in the same mass unit. If your dose is in mg, convert it to mcg first by multiplying by 1,000.

Continuing the example: suppose your target dose is 250 mcg. Your concentration is 5,000 mcg/mL. The volume you need is:

volume = 250 mcg ÷ 5,000 mcg/mL = 0.05 mL

The units cancel correctly: mcg ÷ (mcg/mL) = mcg × (mL/mcg) = mL. We end up with milliliters, which is what we wanted.

Sanity check: if your concentration is 5,000 mcg per mL, then 1/5,000th of an mL contains 1 mcg. To get 250 mcg, you need 250 of those 1/5,000th-mL portions, which is 250/5,000 = 0.05 mL. Same answer.

Conversion 3: draw volume to syringe units

You have the answer in milliliters. Now you need to translate that into the marked units on the syringe you’re holding. This step depends entirely on which type of insulin syringe you have. (See the U-100 vs U-40 guide for the deeper explanation of why two scales exist.)

For a U-100 insulin syringe (the standard in the United States), the printed scale assumes 100 units per mL of solution. So:

units = volume_mL × 100

In our example, 0.05 mL × 100 = 5 units. You draw to the “5 unit” mark on a U-100 insulin syringe.

For a U-40 insulin syringe, the printed scale assumes 40 units per mL of solution. So:

units = volume_mL × 40

In our example, 0.05 mL × 40 = 2 units. You draw to the “2 unit” mark on a U-40 syringe.

The physical volume drawn is identical in both cases — 0.05 mL. The number printed on the syringe scale is different because the scale is different.

Putting it all together

Here is the entire calculation in one go, with all units explicit:

draw_units = (target_dose_mcg ÷ ((peptide_mg × 1000) ÷ bac_water_mL)) × syringe_factor

where syringe_factor = 100 for U-100, 40 for U-40

For our example: 250 mcg target dose, 5 mg peptide vial, 1 mL bac water, U-100 syringe.

draw_units = (250 ÷ ((5 × 1000) ÷ 1)) × 100 = (250 ÷ 5000) × 100 = 0.05 × 100 = 5 units

The calculator on the homepage performs exactly this computation for every input you give it. The source code is straightforward and the test suite verifies it against multiple worked cases. There is no hidden complexity.

A second worked example with different numbers

Let’s run a different scenario end to end. Suppose you have a 10 mg peptide vial, you reconstitute with 2 mL of bacteriostatic water, your target dose is 2 mg (you decided to express your dose in mg this time instead of mcg), and you’re using a U-100 0.5 mL insulin syringe.

Step 1: concentration.

10 mg ÷ 2 mL = 5 mg/mL = 5,000 mcg/mL

Step 2: dose in consistent units.

2 mg × 1,000 mcg/mg = 2,000 mcg

Step 3: draw volume.

2,000 mcg ÷ 5,000 mcg/mL = 0.4 mL

Step 4: syringe units.

0.4 mL × 100 units/mL = 40 units

Sanity check on capacity: a U-100 0.5 mL syringe holds 50 units (because 0.5 mL × 100 units/mL = 50). 40 units is below the 50-unit capacity, so the draw fits in this syringe. Good.

Final answer: draw to the 40-unit mark on a U-100 0.5 mL insulin syringe.

A third example, this time with U-40

Same 10 mg vial, same 2 mL of bacteriostatic water, same 2 mg target dose, but now we’re using a U-40 1 mL insulin syringe instead of a U-100.

The first three steps are identical because the peptide, water, and dose haven’t changed:

concentration = 5,000 mcg/mL draw volume = 0.4 mL

The only thing that changes is the unit conversion at the end:

0.4 mL × 40 units/mL = 16 units on a U-40 syringe

Same physical 0.4 mL of liquid in the barrel, different printed number because the syringe scale is different. If you had habitually used U-100 and now switched to U-40 without redoing the math, you might draw to the “40” mark on the U-40 — which would be 1.0 mL of solution, or 5 mg of peptide, instead of the intended 2 mg. That’s 2.5× the intended dose.

A capacity warning example

Suppose you have a 2 mg vial reconstituted with 0.5 mL of bacteriostatic water, you want a 1 mg dose, and you want to use a U-100 0.3 mL insulin syringe.

Step 1: 2 mg ÷ 0.5 mL = 4 mg/mL = 4,000 mcg/mL. Step 2: 1 mg = 1,000 mcg. Step 3: 1,000 mcg ÷ 4,000 mcg/mL = 0.25 mL. Step 4: 0.25 mL × 100 units/mL = 25 units.

A U-100 0.3 mL syringe has a capacity of 30 units (0.3 mL × 100). Our draw is 25 units. That fits — it’s tight, but it fits. The calculator would not flag this as exceeding capacity.

Now suppose instead you wanted a 2 mg dose with the same vial:

Step 3: 2,000 mcg ÷ 4,000 mcg/mL = 0.5 mL. Step 4: 0.5 mL × 100 units/mL = 50 units.

A U-100 0.3 mL syringe holds only 30 units. We need 50. This dose exceeds the syringe’s capacity. The calculator flags this with an “exceeds capacity” warning, telling you to either split the dose across two draws or use a larger syringe. Switching to a U-100 1 mL syringe (which holds 100 units) would resolve the warning — 50 units fits in a 100-unit barrel just fine.

A too-small-to-measure example

Suppose you have a 10 mg vial reconstituted with only 1 mL of bacteriostatic water, your target dose is 50 mcg, and you’re on a U-100 1 mL insulin syringe.

Step 1: 10 mg ÷ 1 mL = 10 mg/mL = 10,000 mcg/mL. Step 2: dose is already in mcg. Step 3: 50 mcg ÷ 10,000 mcg/mL = 0.005 mL. Step 4: 0.005 mL × 100 = 0.5 units.

A 0.5-unit draw on a U-100 1 mL insulin syringe is below the practical resolution of the printed scale. The calculator flags this with the “too small to measure accurately” warning. The practical fix is to add more bacteriostatic water next time — a more dilute solution requires a larger physical draw for the same dose:

If you reconstitute the same 10 mg vial with 5 mL of bacteriostatic water instead of 1 mL:

concentration = 10 mg ÷ 5 mL = 2 mg/mL = 2,000 mcg/mL draw volume = 50 mcg ÷ 2,000 mcg/mL = 0.025 mL syringe units = 0.025 × 100 = 2.5 units

2.5 units is now measurable (though still on the small side). You could push the dilution further — reconstituting with 10 mL gives a 1,000 mcg/mL solution, where a 50 mcg dose is 0.05 mL = 5 units, very comfortable to read.

The lesson: dilution is a free variable. Choose it to put your typical draw in a comfortable range on your chosen syringe.

Why “first principles” matters

You don’t need to derive the math by hand for every dose — that’s what the calculator is for. But if you can derive it by hand, you can verify the calculator’s output, catch input errors before they become dosing errors, and reason about edge cases (like the capacity and too-small warnings) with confidence. The math is genuinely simple. It’s two division operations and one multiplication, with one unit conversion (mg to mcg) sprinkled in.

If you ever find yourself uncertain about a calculator output — say, the number looks higher or lower than you expected — pause and walk through the steps by hand. The discrepancy is almost always either a unit confusion (mg vs mcg) or a syringe-type confusion (U-100 vs U-40).

Common mistakes (math edition)

• Mixing units mid-calculation. Pick mcg or mg and stay there. Convert at the boundaries, never in the middle.
• Forgetting that 1 mg = 1,000 mcg, not 100. This is a factor-of-ten error and will show up immediately as a way-off draw amount. If your computed draw seems crazy, check this conversion first.
• Multiplying by 100 when you should be dividing, or vice versa. Sanity-check by checking units. If your formula gives you mL × units/mL, the units cancel to “units,” which is what you want. If your formula gives you mL × mL, you’ve made an error.
• Reading the wrong syringe scale at the end. U-100 multiplies by 100. U-40 multiplies by 40. Read your syringe label every time.

Further reading on this site

• How to reconstitute peptides — the physical process this math feeds into.
• Insulin syringe units explained — why “a unit” is not a volume.
• U-100 vs U-40 syringes — the deeper version of the syringe-type distinction.
• The calculator on the homepage — does the same math in real time and shows the step-by-step breakdown when you expand “show the math”.

Wrapping up

The reconstitution calculation is two divisions, one multiplication, and one unit conversion. You can run it on a napkin if you have to. The calculator on this site automates it and adds the safety checks for capacity and measurability, but the math is no harder than a high-school dimensional analysis problem. If you can derive it by hand, you can use the calculator with confidence — and that confidence is worth the ten minutes it takes to walk through the worked examples in this guide.