Pharmacy Calculations
Pharmacy calculations are the mathematical operations pharmacy technicians must perform to accurately process prescriptions, including dosage conversions, day supply calculations, concentration and dilution problems, and percentage calculations.
Exam Tip
Use consistent units. Days supply = quantity / units used per day; C1V1 = C2V2 applies to a suitable dilution. Distinguish fluid ounces (volume) from ounces (mass), and label customary approximations. Recheck the dose, decimal, units, and final volume.
What Are Pharmacy Calculations?
Pharmacy math is a core competency for pharmacy technicians. The ExCPT Dispensing Process domain contains 43 of 100 scored items; its Calculations subdomain contains 7 items. Mastering these formulas and conversions is essential for safe and accurate medication dispensing.
Metric and Common U.S. Pharmacy Conversions
Use the conversion specified by the problem. Customary volume approximations below are not exact SI equalities. Use calibrated metric dosing devices rather than household spoons.
| Conversion | Equivalent |
|---|---|
| 1 kg | Approximately 2.2 lb |
| 1 U.S. fluid ounce (volume) | Approximately 29.57 mL; often rounded to 30 mL in pharmacy problems |
| 1 avoirdupois ounce (mass) | Approximately 28.35 g; not a volume conversion |
| 1 teaspoon | Common medication approximation: 5 mL |
| 1 tablespoon | Common medication approximation: 15 mL (3 teaspoons) |
| 1 U.S. cup | Approximately 236.6 mL; often rounded to 240 mL (8 U.S. fluid ounces) |
| 1 U.S. liquid pint | Approximately 473 mL (16 U.S. fluid ounces) |
| 1 U.S. liquid gallon | Approximately 3,785 mL (128 U.S. fluid ounces) |
| 1 grain | Approximately 64.8 mg; use 65 mg only when the problem specifies that convention |
| 1 L | 1,000 mL |
| 1 g | 1,000 mg |
| 1 mg | 1,000 mcg |
Day Supply Calculation
Day Supply = Total Quantity Dispensed / Daily Dose
Example: Amoxicillin 500 mg #30, Sig: 1 cap TID
- Daily dose = 3 capsules/day
- Day supply = 30 / 3 = 10 days
Concentration and Dilution (C1V1 = C2V2)
C1 x V1 = C2 x V2
Arithmetic example: Prepare 500 mL of a 30% v/v solution from a 70% v/v stock, assuming no solute loss. This is a dilution exercise, not a recommended disinfectant formulation.
- 70% x V1 = 30% x 500 mL
- V1 = (30 x 500) / 70 = 214.3 mL of stock; add diluent to a final volume of 500 mL (QS), rather than assuming volumes are additive
Percentage Calculations
| Type | Formula | Example |
|---|---|---|
| % w/v | grams per 100 mL | 0.9% NS = 0.9 g NaCl per 100 mL |
| % w/w | grams per 100 g | 2% hydrocortisone = 2 g per 100 g |
| % v/v | mL per 100 mL | 70% alcohol = 70 mL per 100 mL |
Ratio and Proportion
Known ratio = Unknown ratio
mg/mL = mg/mL
Example: A solution is 250 mg/5 mL. How many mL for a 400 mg dose?
- 250 mg / 5 mL = 400 mg / X mL
- X = 8 mL
Alligation Method
Used to mix two compatible preparations of the same ingredient using consistent concentration units:
Higher % ---- Desired - Lower = Parts of higher
X
Lower % ---- Higher - Desired = Parts of lower
Exam Alert
Pharmacy calculations are heavily tested on the ExCPT. Practice day supply, concentration/dilution (C1V1 = C2V2), metric conversions, and percentage calculations. An on-screen calculator is provided, but you must know which formulas to apply.
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Sig Codes (Prescription Abbreviations)
Sig codes are conventional abbreviations derived primarily from Latin used on prescriptions to communicate directions for medication use, including frequency, route, timing, and special instructions.
Compounding Pharmacy
A compounding pharmacy prepares customized medications by mixing, combining, or altering ingredients to create preparations not commercially available, following USP 795 (non-sterile) and USP 797 (sterile) standards.
NDC Number (National Drug Code)
The NDC (National Drug Code) is a unique 10-digit, 3-segment numeric identifier assigned to each medication product in the United States, identifying the labeler, product, and package size.
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