1. Concentration
Concentration is mass per unit volume. If a vial contains M mg of dry powder and you add V mL of bacteriostatic water, the resulting concentration is:
concentration (mg/mL) = M / V
Worked example. 10 mg of powder reconstituted into 2 mL of water = 5 mg/mL. The choice of V is conventionally made to give a workable per-injection volume; that choice is published in the research protocol, not derived from the patient.
2. Injection volume per intended dose
To translate a dose D (mg) into a withdrawal volume V_inj (mL):
V_inj (mL) = D / concentration
= D / (M / V)
= D × V / MWith insulin syringes (U-100 scale, 1 mL = 100 units) the same quantity expressed in units is:
V_inj (units) = V_inj (mL) × 100
In licensed pharmaceutical products (e.g. semaglutide pens) the user does not perform this calculation — the device delivers a pre-set metered dose. The arithmetic above describes the maths researchers use when reading protocols that report doses in mg.
3. Doses per vial
doses_per_vial = M / D
A 10 mg vial dosed at 0.5 mg per injection yields 20 doses. This number determines how long a single reconstituted vial would last in a research protocol, which is relevant for stability calculations (most reconstituted peptides are stable in the fridge for 4–6 weeks, though specific stability is compound-dependent and published in the product literature).
4. What this arithmetic does NOT tell you
- Whether the substance is safe or appropriate at any dose for any individual.
- Whether the product in the vial is what the label says it is (without third-party analytical certificates of analysis).
- Whether sterile technique, injection site choice, or rotation is being followed.
- What pharmacokinetic exposure that dose produces in any given person — that requires clinical context, comorbidities, concomitant medication, and supervision.
For licensed weight-management GLP-1 medicines (Wegovy, Mounjaro, Saxenda) in the UK, the prescriber sets the dose and titration schedule following NICE guidance. The maths above is not a substitute for that clinical decision.