How to double-check a calculator result by hand
A calculator repeats whatever you type, including mistakes. Checking the result by a second route takes under a minute and catches wrong units, wrong water volume and slipped decimal points.
The example below uses round numbers chosen for easy arithmetic: a 10 mg vial, 2 mL of water, and a prescription figure of 1 mg. They are not a suggestion of what anyone should use.
Check 1: the three lines, written out
- Concentration: 10 mg ÷ 2 mL = 5 mg/mL.
- Volume: 1 mg ÷ 5 mg/mL = 0.2 mL.
- Units: 0.2 mL × 100 = 20 units.
Write the unit after every number. If the units do not cancel properly, for example mcg divided by mg/mL, the mistake shows up on paper before it reaches the syringe.
Check 2: fraction of the vial
This route does not use concentration at all, which makes it a true second opinion.
- 2 mL of water is 200 units of liquid in total.
- 1 mg out of 10 mg is one tenth of the vial.
- One tenth of 200 units is 20 units.
The answer matches Check 1.
Check 3: work backwards
Start from the answer and see whether it returns the number on the prescription.
- 20 units ÷ 100 = 0.2 mL.
- 0.2 mL × 5 mg/mL = 1 mg.
The calculator has a "Units → mg" mode that does this, and the 20 units to mg page shows the same thing as a table. If the backwards result is not the figure you started with, one of the inputs is wrong.
Sanity checks that need no arithmetic
- The result must be smaller than the vial. One draw cannot exceed the total units of liquid (water × 100).
- The result must fit the syringe. No more than 30, 50 or 100 units depending on the barrel.
- The result must be readable. A figure such as 0.4 units is below one tick. That usually means a unit mix-up, not a real answer.
- Direction check. More water should always give more units for the same amount. If your numbers moved the other way, the division was upside down.
Errors and what catches them
| Mistake | Effect on the result | Caught by |
|---|---|---|
| mcg entered as mg, or mg as mcg | Off by 1,000× | Result larger than the vial, or smaller than one tick |
| Water volume wrong (planned amount, not actual) | Off in proportion, for example 2× if 1 mL was entered for 2 mL | Re-reading the instructions; Check 2 |
| Division upside down (concentration ÷ amount) | Nonsense figure | Units not cancelling; direction check |
| Decimal slipped (0.2 mL read as 2 units) | Off by 10× | Check 3 |
| Syringe is U-40, not U-100 | Draw is 2.5× the intended volume | Reading the syringe label |
| Vial in IU, prescription in mg | Unrelated numbers combined | Units written beside every figure |
More detail on three of these: mcg vs mg, U-100 vs U-40 and IU vs mg.
A one-line version
Combining the three lines gives a single formula for U-100 syringes:
If the checks disagree
Do not average them or pick the one that looks right. Go back to the three source numbers, the vial label, the water volume and the prescription, and read each one again with its unit. If they are all correct and the result still looks odd, or if it does not match what the pharmacy label says to draw, call the pharmacist before using it. The pharmacy's written instruction takes priority over any calculator, including this one.
Questions
How do I check a peptide calculation by hand?
Divide the mg in the vial by the mL of water to get mg/mL. Divide the prescribed mg by that to get mL. Multiply by 100 for units on a U-100 syringe. Then confirm it a second way: prescribed mg ÷ vial mg × water mL × 100 should give the same units.
What is the formula for syringe units?
Units = prescribed amount (mg) ÷ amount in vial (mg) × water added (mL) × 100, for a U-100 syringe. For a 10 mg vial with 2 mL and a figure of 1 mg: 1 ÷ 10 × 2 × 100 = 20 units.
How do I know if a calculator result is wrong?
It is wrong if it is larger than the total liquid in the vial (water in mL × 100 units), larger than the syringe holds, or far smaller than one tick mark. Working backwards from units to mg should also return the figure on your prescription.
My result does not match my pharmacy label. Which is right?
Follow the pharmacy label and call the pharmacist to resolve the difference. A calculator only reflects the numbers typed into it.