18 Chapter 18: Pharmaceutical Calculations

Pharmaceutical calculations can be complicated in compounding.  It is absolutely imperative to be able to perform these calculations accurately.  Below are the math skills you should have and the types of calculations you may see in non-sterile compounding.

1. Foundational Math Skills

• Units of measurement:

  • Metric system (g, mg, mcg, mL, L)

  • Apothecary and household units (for interpretation only)

  • Conversion tables between systems

• Rounding rules (for solids, liquids, percentages)

• Significant figures and decimal places

 2. Weight and Volume Calculations

• Calculating required weight/volume from prescription orders

• Use of balances and volumetric devices

• Density and specific gravity:

  • Converting between volume and weight

  • Using SG to convert mL ↔ g

 3. Percentage Strengths and Concentrations

• Weight/weight (w/w) – grams per 100 grams (solid in solid)

• Weight/volume (w/v) – grams per 100 mL (solid in liquid)

• Volume/volume (v/v) – mL per 100 mL (liquid in liquid)

• Expressing and converting concentrations (e.g., 1:1000 ↔ %)

 4. Dilution and Concentration

• Dilution equations:

  • Alligation method (used for mixing different strengths)

  • C₁V₁ = C₂V₂ (used for single-step dilution)

• Serial dilution

• Use of diluents or vehicles

5. Aliquots and Minimum Weighable Quantity

• Use of aliquots to measure below a balance’s minimum sensitivity

• Calculating dilutions to create a measurable quantity

6. Density, Specific Gravity, and Displacement Volume

• Calculating displacement volume for suppositories

• Converting drug amounts when compounding using density or SG

Strategies to Ensure Accuracy in Pharmacy Calculations

1. Use a Standardized Process

• Follow a consistent, step-by-step calculation method for every type of formula (e.g., C₁V₁ = C₂V₂ for dilutions).
• Double-check all inputs (strengths, units, volume, weights).

2. Check Units Carefully

• Always convert to metric units (g, mg, mcg, mL) before beginning.
• Ensure unit consistency throughout the calculation.
• Watch for percent strength misunderstandings (e.g., 1% = 1 g per 100 mL, not 1 mg/mL).

3. Use Dimensional Analysis

• A systematic way to organize and convert units correctly.
• Helps reduce errors from skipping conversion steps or misapplying formulas.

4. Perform Independent Double-Checks

• A second person should independently verify all calculations, especially for:
  • Potent or low-dose medications
  • Pediatric or geriatric formulations
  • High-alert medications (e.g., hormones, narcotics)

5. Label Calculations Clearly

• Use labeled equations with all units written out.
• Avoid mental math—write out intermediate steps to show how each value was derived.

6. Use Verified References

• Base calculations on reliable, evidence-based references such as:
• NAPRA Compounding Guidelines
• USP <795>
• Compounding reference texts (e.g., Trissel’s Stability of Compounded Formulations)
• Product Monographs for commercial product equivalents
• Canadian monographs and formularies (e.g., CPS, Lexicomp, eCPS)

7. Apply Appropriate Significant Figures and Rounding

• Don’t round until the final step unless specified.
• Round to the number of decimal places appropriate for the measuring equipment (e.g., 0.01 g for Class A balance).

8. Use Validated Equipment

• Make sure measuring devices (balances, syringes, cylinders) are:
  • Calibrated
  • Appropriately sized for the quantity
  • Clean and in working condition

9. Document and Review All Work

• Keep written calculation records as part of the compounding record (per NAPRA).
• Ensure all figures, units, and sources are documented and verifiable.

10. Train and Practice Regularly

• Provide regular calculation exercises and assessments.
• Use simulated compounding scenarios to practice applying math to clinical contexts.