Pick the water volume before you pick the syringe
Reconstitution is one division, and the whole thing goes wrong at the syringe rather than in the arithmetic. A lyophilised vial holds a stated mass. You add a chosen volume of bacteriostatic water. What you get is a concentration:
concentration (mg/mL) = vial strength (mg) / water added (mL)
Then the draw:
volume to draw (mL) = dose (mg) / concentration (mg/mL)
Worked example
A 5 mg vial with 2 mL of bacteriostatic water is 2.5 mg/mL. A 0.25 mg dose is 0.25 / 2.5 = 0.1 mL. On a U-100 insulin syringe that is the 10 unit mark.
Reading a U-100 syringe
U-100 syringes are marked in insulin units, not millilitres. The conversion never changes: 100 units = 1 mL, so 1 unit = 0.01 mL. That means 0.05 mL is 5 units, 0.10 mL is 10 units, 0.20 mL is 20 units, 0.50 mL is 50 units.
The part people skip
Choose the reconstitution volume so that your ordinary dose lands on a mark you can actually read. A dose that works out to 2.3 units is a dose you will measure badly every single time. If the division keeps producing awkward fractions of a unit, add more water and redo it. More water is not weaker medicine, it is the same mass spread over a volume your eyes can resolve. The trade-off is only how long the mixed vial lasts and whether the vial has room.
Notice that a 5 mg vial in 2 mL and a 10 mg vial in 4 mL both give 2.5 mg/mL and behave identically at the syringe. Concentration, not vial size, is what the syringe marks answer to. I run the division and the unit conversion through the Peptide Tracker & Calculator rather than doing it in my head at 7 am, because the failure mode is a silent factor-of-ten error, not an obviously wrong number.
Syringe size
A 0.3 mL syringe, marked to 30 units, spreads its graduations furthest apart and is the right default when your draws stay under 30 units. A 0.5 mL syringe is fine up to 50 units. Step up to the full 1 mL size only if you genuinely need the volume, because the graduations sit closer together and small errors get easier to make.
Handling
Add the water slowly down the inner wall of the vial. Do not jet it onto the powder and do not shake it. Swirl gently until clear. Cloudiness or visible particles after mixing means do not use it. Write the mix date and the concentration on the vial in marker, because you will not remember either one in three weeks.
Log the concentration, not just the units
A log row that says "12 units" is worthless six weeks later if you have re-mixed at a different concentration since. Record the date and time, the concentration in mg/mL, the dose in both mg and units, the vial lot, and the injection site. When you change a dose, record the date of the change and leave the old rows alone. A step change with a date next to it is the only thing that lets you read a pattern out of a log afterwards. The dose tracking tool I use keeps the mixing numbers attached to each logged dose for exactly that reason.
None of this is medical advice. It is arithmetic and record keeping.