peptide reconstitution math worked through properly (where the 10x mistakes come from)
This is the calculation everything else depends on so here it is in full, because the failure mode is a 10x error not a small one.
Three numbers and you need all three: the mass in the vial (on the label, say 10mg), the volume of water you add (your choice, and people forget it's a choice), and the volume you draw.
Concentration = mass / volume. 10mg into 2ml is 5mg/ml. Same 10mg into 1ml is 10mg/ml. Same vial, double the concentration, purely because of step 2.
Converting to syringe units: on a U-100 insulin syringe 100 units = 1ml, so 1 unit = 0.01ml. At 5mg/ml one unit holds 5 x 0.01 = 0.05mg = 50mcg. So the 20 mark is 1mg and the 10 mark is 500mcg. At 10mg/ml those same marks mean double. The marks didn't change, the meaning did.
Where it goes wrong: - mg/mcg slips. Factor of 1000. - Treating units as a mass. They're a volume. Factor of anything. - Copying someone else's unit count without matching their reconstitution. The most common one because it looks like following advice. - Forgetting the powder has a little volume of its own (usually negligible, not always zero).
The reason the calculator on here exists isn't that this is hard. It's that the error is silent. Nothing about the solution looks different when you've got it wrong.