Concentration calculations in pharmacy: the core principles
Solution concentration is the amount of solute dissolved in a given volume of solvent. Getting this calculation right matters enormously, the difference between 1mg/mL and 10mg/mL is a 10-fold dose error. USP General Chapter 795 sets the compounding standards that exist specifically to prevent errors of this kind.
Percent concentration (% w/v)
Percent weight-per-volume (% w/v) means grams of solute per 100mL of solution. 1% w/v = 1g/100mL = 10mg/mL. Normal saline is 0.9% NaCl = 9mg/mL = 154 mmol/L. Glucose 5% = 50mg/mL. This relationship (1% = 10mg/mL) is one of the most useful conversions to memorise, and it carries over directly into extemporaneous work: creams, suspensions and other compounded preparations are usually labelled the same way, which is where our Compounding Calculator picks up, scaling a formula's percentages to a full batch size.
Dilution: C1V1 = C2V2
The dilution equation states that the amount of solute is conserved when you dilute a solution: concentration times volume before = concentration times volume after. To make 100mL of a 1mg/mL solution from a 10mg/mL stock: V1 = (1 × 100) / 10 = 10mL of stock, made up to 100mL with diluent. The remaining 90mL is diluent. When the stock solution is a cytotoxic or otherwise hazardous drug, the dilution step itself carries handling requirements beyond the arithmetic; check whether the drug appears on the NIOSH List of Hazardous Drugs in Healthcare Settings before preparing it on an open bench.
IV bag concentrations
When adding a drug to an IV bag, the final concentration = drug added (mg) / total final volume (mL). 500mg vancomycin added to 250mL = 2mg/mL. At 100mL/hr infusion rate: 2mg/mL × 100mL/hr = 200mg/hr. For weight-based rates, divide by patient weight in kg and convert to mcg/kg/min if needed. Pair this tool with our IV Drip Rate Calculator for the full calculation workflow. For unit conversions between mg, mcg, mL and percent, use the Pharmacy Unit Converter.