The reconstitution arithmetic, worked through properly — where the ten-fold errors come from
This is the calculation everything else depends on, and it's worth writing out in full because the failure mode is a factor-of-ten error rather than a small one.
**Three quantities, and you need all three.**
1. Mass in the vial. Printed on the label. Say 10 mg. 2. Diluent volume you add. Your choice, and this is the variable people forget is a choice. 3. The volume you subsequently draw.
**Concentration = mass ÷ volume.**
10 mg into 2 mL gives 5 mg/mL. The same 10 mg into 1 mL gives 10 mg/mL. Same vial, double the concentration, purely because of step 2.
**Converting to syringe units.** On a U-100 insulin syringe, 100 units = 1 mL, so 1 unit = 0.01 mL.
At 5 mg/mL, one unit contains 5 mg/mL × 0.01 mL = 0.05 mg = 50 mcg. So the 20 mark corresponds to 1 mg. The 10 mark to 500 mcg.
At 10 mg/mL those same marks mean double. **The marks did not change. The meaning did.**
**Where it goes wrong:**
- **mg/mcg slips.** Factor of 1000. - **Assuming units are a mass.** They're a volume. Factor of anything. - **Copying someone else's unit count** without matching their reconstitution. This is the most common one, because it looks like following advice. - **Not accounting for the powder's own volume**, which is usually negligible for these masses but not always zero.
The reason the calculator exists is not that this arithmetic is hard. It's that the error is silent — nothing about the solution looks different when you've got it wrong.
Evidence tier: arithmetic. No research claim here at all.