Reconstitution Math: 10 Worked Examples

Reconstitution math looks scary the first time, but it is only three steps of division and multiplication. Below are 10 worked examples, from the most common setups to a few tricky ones, so you can see the pattern and check your own numbers.

These examples show arithmetic only. The dose itself always comes from your prescriber or pharmacy label, and PepSteady does not recommend doses.

Key takeaways

• Concentration (mg/mL) = peptide in the vial (mg) ÷ water added (mL).
• Volume to draw (mL) = your prescribed dose (mg) ÷ concentration (mg/mL).
• On a U-100 insulin syringe, units = mL × 100. On a U-40 syringe, units = mL × 40.
• Always convert mcg to mg first: 1 mg = 1,000 mcg.
• Have your pharmacist confirm your numbers, especially the first time.

The three formulas

If your dose is written in mcg, divide by 1,000 before step 2. Mixing up mg and mcg is one of the most common math mistakes, and it changes the answer by a factor of 1,000. Our guide to mg, mcg and IU goes deeper.

10 worked examples

Example 1: 5 mg vial + 2 mL water, 250 mcg dose

1. Concentration: 5 mg ÷ 2 mL = 2.5 mg/mL (2500 mcg/mL)
2. Dose in mg: 250 mcg ÷ 1,000 = 0.25 mg
3. Volume: 0.25 mg ÷ 2.5 mg/mL = 0.1 mL
4. Syringe units: 0.1 mL × 100 units/mL = 10 units on a U-100 syringe
5. Doses per vial: 5 mg ÷ 0.25 mg = 20

Example 2: 5 mg vial + 1 mL water, 250 mcg dose

1. Concentration: 5 mg ÷ 1 mL = 5 mg/mL (5000 mcg/mL)
2. Dose in mg: 250 mcg ÷ 1,000 = 0.25 mg
3. Volume: 0.25 mg ÷ 5 mg/mL = 0.05 mL
4. Syringe units: 0.05 mL × 100 units/mL = 5 units on a U-100 syringe
5. Doses per vial: 5 mg ÷ 0.25 mg = 20

Example 3: 10 mg vial + 2 mL water, 500 mcg dose

1. Concentration: 10 mg ÷ 2 mL = 5 mg/mL (5000 mcg/mL)
2. Dose in mg: 500 mcg ÷ 1,000 = 0.5 mg
3. Volume: 0.5 mg ÷ 5 mg/mL = 0.1 mL
4. Syringe units: 0.1 mL × 100 units/mL = 10 units on a U-100 syringe
5. Doses per vial: 10 mg ÷ 0.5 mg = 20

Example 4: 10 mg vial + 3 mL water, 2.5 mg dose

1. Concentration: 10 mg ÷ 3 mL = 3.3333 mg/mL (3333.3 mcg/mL)
2. Dose in mg: The dose is already in mg: 2.5 mg
3. Volume: 2.5 mg ÷ 3.3333 mg/mL = 0.75 mL
4. Syringe units: 0.75 mL × 100 units/mL = 75 units on a U-100 syringe
5. Doses per vial: 10 mg ÷ 2.5 mg = 4

Example 5: 2 mg vial + 1 mL water, 100 mcg dose

1. Concentration: 2 mg ÷ 1 mL = 2 mg/mL (2000 mcg/mL)
2. Dose in mg: 100 mcg ÷ 1,000 = 0.1 mg
3. Volume: 0.1 mg ÷ 2 mg/mL = 0.05 mL
4. Syringe units: 0.05 mL × 100 units/mL = 5 units on a U-100 syringe
5. Doses per vial: 2 mg ÷ 0.1 mg = 20

Example 6: 15 mg vial + 3 mL water, 1 mg dose

1. Concentration: 15 mg ÷ 3 mL = 5 mg/mL (5000 mcg/mL)
2. Dose in mg: The dose is already in mg: 1 mg
3. Volume: 1 mg ÷ 5 mg/mL = 0.2 mL
4. Syringe units: 0.2 mL × 100 units/mL = 20 units on a U-100 syringe
5. Doses per vial: 15 mg ÷ 1 mg = 15

Example 7: 5 mg vial + 2.5 mL water, 200 mcg dose

1. Concentration: 5 mg ÷ 2.5 mL = 2 mg/mL (2000 mcg/mL)
2. Dose in mg: 200 mcg ÷ 1,000 = 0.2 mg
3. Volume: 0.2 mg ÷ 2 mg/mL = 0.1 mL
4. Syringe units: 0.1 mL × 100 units/mL = 10 units on a U-100 syringe
5. Doses per vial: 5 mg ÷ 0.2 mg = 25

Example 8: 30 mg vial + 3 mL water, 2 mg dose

1. Concentration: 30 mg ÷ 3 mL = 10 mg/mL (10000 mcg/mL)
2. Dose in mg: The dose is already in mg: 2 mg
3. Volume: 2 mg ÷ 10 mg/mL = 0.2 mL
4. Syringe units: 0.2 mL × 100 units/mL = 20 units on a U-100 syringe
5. Doses per vial: 30 mg ÷ 2 mg = 15

Example 9: 5 mg vial + 2 mL water, 250 mcg dose on a U-40 syringe

1. Concentration: 5 mg ÷ 2 mL = 2.5 mg/mL (2500 mcg/mL)
2. Dose in mg: 250 mcg ÷ 1,000 = 0.25 mg
3. Volume: 0.25 mg ÷ 2.5 mg/mL = 0.1 mL
4. Syringe units: 0.1 mL × 40 units/mL = 4 units on a U-40 syringe
5. Doses per vial: 5 mg ÷ 0.25 mg = 20

Example 10: Working backward from the syringe

Suppose a 5 mg vial was mixed with 2 mL of water and you see 20 units drawn on a U-100 syringe. What dose is that?

1. Concentration: 5 mg ÷ 2 mL = 2.5 mg/mL
2. Volume: 20 units ÷ 100 units/mL = 0.2 mL
3. Dose: 0.2 mL × 2.5 mg/mL = 0.5 mg (500 mcg)

Working backward is a good way to double-check a number before you inject.

All 10 at a glance

Why example 9 matters

Examples 1 and 9 use the exact same vial and the same dose. On a U-100 syringe the answer is 10 units. On a U-40 syringe it is 4 units. The volume is the same 0.1 mL either way, but the markings are different. If someone calculates for a U-100 syringe and then draws to the 10 mark on a U-40 syringe, they get 2.5 times the intended volume. That is why you should never switch syringe types without redoing the math. Read more in U-100 vs. U-40 syringes.

Common mistakes to avoid

• Forgetting to convert mcg to mg. 250 mcg is 0.25 mg, not 250 mg.
• Using the wrong water amount. If you add 2 mL to one vial and 3 mL to the next, the concentration changes and so does the number of units.
• Rounding too early. Keep at least three decimal places until the last step.
• Not checking the syringe size. A 0.3 mL syringe holds 30 units, a 0.5 mL syringe holds 50, and a 1 mL syringe holds 100. If your answer is bigger than the syringe, stop and ask your pharmacist.

Let the calculator do it

The free PepSteady calculator runs these same steps and shows every line of the math, so you can compare it to your own work. You can also save the result to a protocol in the tracker so it reminds you and logs each dose.

The bottom line

Reconstitution math is the same three steps every time: concentration, volume, units. Write the steps down, check them by working backward, and confirm with your pharmacist before your first dose.

Sources

• Insulin Syringes, U.S. Food and Drug Administration
• Medication errors related to U-100 and U-500 insulin, Institute for Safe Medication Practices

Frequently asked questions