Pharmacy calculations are a fundamental component of the PEBC Qualifying Examination Part 1 (MCQ). While therapeutic knowledge is essential, the ability to accurately perform calculations is critical for safe and effective pharmacy practice. This comprehensive guide covers essential calculation types, formulas, and step-by-step practice problems to help you master this crucial aspect of the exam.

Dosage Calculations

Dosage calculations are among the most frequently tested calculation types on the PEBC MCQ. These questions require you to determine the correct dose based on patient weight, body surface area, or other patient-specific factors.

Weight-Based Dosing

Many medications are dosed based on patient weight (mg/kg or mcg/kg). The formula is:

Example: A 70 kg patient requires vancomycin 15 mg/kg. Calculate the dose.

Solution: Dose = 70 kg × 15 mg/kg = 1,050 mg

Body Surface Area (BSA) Calculations

Some medications, particularly in oncology, are dosed based on BSA using the Mosteller formula:

Example: Calculate BSA for a patient who is 170 cm tall and weighs 75 kg.

Solution: BSA = √[170 × 75 / 3600] = √[12750 / 3600] = √3.54 = 1.88 m²

Dosage Adjustments for Renal Function

Many medications require dose adjustments based on creatinine clearance (CrCl). The Cockcroft-Gault equation is commonly used:

Dose adjustments are then made based on the calculated CrCl according to drug-specific guidelines.

Compounding Calculations

Compounding calculations test your ability to prepare medications, calculate quantities needed, and determine concentrations. These questions often involve alligation, percentage strength, and ratio calculations.

Percentage Strength Calculations

Percentage strength can be expressed as weight/weight (w/w), weight/volume (w/v), or volume/volume (v/v).

Example: How many grams of drug are needed to prepare 500 mL of a 2% w/v solution?

Solution: 2% = 2 g/100 mL, so for 500 mL: (2 g/100 mL) × 500 mL = 10 g

Alligation Method

The alligation method is used to calculate the proportions of two solutions of different strengths needed to prepare a solution of desired strength.

Example: How many mL of 50% solution and 10% solution are needed to prepare 200 mL of a 30% solution?

Solution: Using alligation: 30 - 10 = 20 parts of 50% solution, and 50 - 30 = 20 parts of 10% solution. Total parts = 40. For 200 mL: (20/40) × 200 = 100 mL of each solution.

Ratio Strength

Ratio strength (e.g., 1:1000) means 1 part solute in 1000 parts total solution.

Example: How many mg of epinephrine are in 1 mL of a 1:1000 solution?

Solution: 1:1000 = 1 g/1000 mL = 1000 mg/1000 mL = 1 mg/mL

Pharmacokinetics Calculations

Pharmacokinetic calculations involve drug absorption, distribution, metabolism, and excretion. Common topics include half-life, clearance, volume of distribution, and dosing adjustments.

Half-Life Calculations

Half-life (t₁/₂) is the time required for drug concentration to decrease by 50%.

Clearance Calculations

Clearance (Cl) is the volume of plasma cleared of drug per unit time.

Loading Dose

Loading dose is used to rapidly achieve therapeutic concentrations.

Maintenance Dose

Maintenance dose maintains steady-state concentrations.

IV Preparations and Flow Rates

Intravenous medication calculations are critical for hospital pharmacy practice. These include drip rates, infusion rates, and concentration calculations.

IV Flow Rate Calculations

Flow rate is typically expressed as mL/hour or drops/minute.

Example: An IV bag contains 500 mL to be infused over 4 hours. Calculate the flow rate in mL/hr and drops/min (drop factor = 15 gtt/mL).

Solution: Flow Rate = 500 mL / 4 hr = 125 mL/hr. Drops/min = (125 × 15) / 60 = 31.25 ≈ 31 drops/min

IV Drug Concentration

Calculating drug concentration in IV solutions is essential for safe administration.

Example: 500 mg of vancomycin is added to 250 mL of D5W. What is the concentration?

Solution: Concentration = 500 mg / 250 mL = 2 mg/mL

Infusion Rate for Drug Delivery

When a specific dose rate is required (e.g., mcg/kg/min), calculate the infusion rate.

Note: The 1000 converts mg to mcg, and 60 converts minutes to hours.

Practice Problems with Solutions

Problem 1: Pediatric Dosing

A 25 kg child requires amoxicillin 50 mg/kg/day divided into three doses. What is each dose?

Solution: Total daily dose = 25 kg × 50 mg/kg = 1,250 mg/day. Each dose = 1,250 mg / 3 = 416.67 mg ≈ 417 mg per dose

Problem 2: CrCl and Dose Adjustment

A 65-year-old male (75 kg) with serum creatinine 1.5 mg/dL requires a medication normally dosed at 100 mg every 8 hours. The drug requires a 50% dose reduction if CrCl < 50 mL/min. What is the adjusted dose?

Solution: CrCl = [(140 - 65) × 75] / [72 × 1.5] = [75 × 75] / 108 = 5,625 / 108 = 52.08 mL/min. Since CrCl > 50, no adjustment needed. Dose = 100 mg every 8 hours.

Problem 3: IV Infusion Rate

A 70 kg patient requires dopamine at 5 mcg/kg/min. The solution contains 400 mg dopamine in 250 mL D5W. Calculate the infusion rate in mL/hr.

Solution: Concentration = 400 mg / 250 mL = 1.6 mg/mL = 1,600 mcg/mL. Infusion Rate = (5 × 70 × 60) / (1,600 × 1) = 21,000 / 1,600 = 13.125 ≈ 13 mL/hr

Common Calculation Errors to Avoid

1. Unit Conversion Errors

Always ensure consistent units throughout your calculation. Common mistakes include:

• Mixing mg and mcg (1 mg = 1,000 mcg)
• Forgetting to convert kg to g or vice versa
• Mixing mL and L (1 L = 1,000 mL)

2. Rounding Errors

Be careful with rounding, especially in multi-step calculations. Round only at the final answer unless intermediate steps require it.

3. Formula Application Errors

Ensure you're using the correct formula for the situation. Don't confuse similar formulas (e.g., loading dose vs. maintenance dose).

4. Patient-Specific Factor Oversight

Always consider patient-specific factors such as:

• Age (pediatric vs. adult dosing)
• Renal/hepatic function (dose adjustments)
• Body weight or BSA (for weight-based dosing)

Key Takeaways

Pharmacy calculations are a critical component of the PEBC Qualifying Examination Part 1. By mastering these essential formulas and practicing regularly, you can confidently approach calculation questions on the exam. Remember, accuracy is paramount in pharmacy practice, and these skills will serve you throughout your career.