Pharmacy Calculations Deep Dive
Pharmacy calculations are one of the most heavily tested areas on the CPHT exam. This guide covers every major calculation type you may encounter, with detailed explanations and examples. Mastery of these concepts requires both understanding the underlying math and consistent practice.
Fundamental Approaches to Pharmacy Math
There are two main approaches to solving pharmacy math problems. Either method works for most problems - use whichever is most comfortable for you.
1. Ratio-Proportion
Set up two equivalent ratios and solve for the unknown value. Cross-multiply to solve.
Example: If 5 mL of a suspension contains 250 mg of amoxicillin, how many mg are in 15 mL?
250 mg / 5 mL = X mg / 15 mL
Cross multiply: 250 x 15 = 5 x X
3750 = 5X
X = 750 mg
2. Dimensional Analysis
Chain conversion factors together so that unwanted units cancel out and you are left with the desired unit.
Example: Convert 2.5 L to mL.
2.5 L x (1000 mL / 1 L) = 2500 mL
More complex example: A patient weighs 154 lb. The dose is 10 mg/kg/day divided TID. How many mg per dose?
154 lb x (1 kg / 2.2 lb) x (10 mg / 1 kg / day) x (1 day / 3 doses) = (154 x 10) / (2.2 x 3) = 1540 / 6.6 = 233.3 mg per dose
Essential Unit Conversions
| Conversion | Equivalence |
|---|---|
| Weight: metric | 1 kg = 1000 g; 1 g = 1000 mg; 1 mg = 1000 mcg |
| Weight: metric to avoirdupois | 1 kg = 2.2 lb; 1 lb = 454 g |
| Weight: apothecary | 1 grain (gr) = approximately 65 mg |
| Volume: metric | 1 L = 1000 mL |
| Volume: household | 1 tsp = 5 mL; 1 tbsp = 15 mL; 1 fl oz = 30 mL (approx.) |
| Volume: larger | 1 cup = 240 mL; 1 pint = 473 mL; 1 quart = 946 mL; 1 gallon = 3785 mL |
| Temperature | C = (F - 32) x 5/9; F = (C x 9/5) + 32 |
Percent Strength
Percent strength tells you how much active ingredient is in a given amount of product. There are three types:
- % w/v (weight in volume): grams of solute per 100 mL of solution. This is the most common type in pharmacy.
- % w/w (weight in weight): grams of solute per 100 g of preparation. Common for creams and ointments.
- % v/v (volume in volume): mL of solute per 100 mL of solution. Common for alcohol solutions.
Example: How many grams of NaCl are in 500 mL of NS (0.9% NaCl)?
0.9% w/v = 0.9 g per 100 mL
0.9 g / 100 mL = X g / 500 mL
X = (0.9 x 500) / 100 = 4.5 g
Example: Prepare 60 g of 0.5% triamcinolone cream. How much triamcinolone is needed?
0.5% w/w = 0.5 g per 100 g
0.5 g / 100 g = X / 60 g
X = 0.3 g = 300 mg
Ratio Strength
Ratio strength expresses concentration as 1 part in X parts total. For solutions, it means 1 g per X mL. For solid preparations, it means 1 g per X g.
Example: Express 1:10,000 as a percentage.
1:10,000 = 1 g / 10,000 mL = 0.01 g / 100 mL = 0.01%
Example: How many mg of epinephrine are in 3 mL of a 1:1000 solution?
1:1000 = 1 g / 1000 mL = 1 mg/mL
3 mL x 1 mg/mL = 3 mg
Dilution Calculations
Formula: C1 x V1 = C2 x V2
This works for any dilution where you know three of the four variables.
Example: You have a 10% povidone-iodine solution. How much do you need to make 1 L of 2% solution?
10% x V1 = 2% x 1000 mL
V1 = (2 x 1000) / 10 = 200 mL
Add purified water to bring the total volume to 1000 mL.
Alligation
Alligation alternate is used when you need to mix two different strengths to get a desired intermediate strength.
Step-by-step method:
- Write the higher concentration in the upper-left corner.
- Write the lower concentration (can be zero for diluent) in the lower-left corner.
- Write the desired concentration in the center.
- Subtract diagonally: desired minus lower = parts of higher; higher minus desired = parts of lower.
- Use the parts as a ratio to determine how much of each to use.
Example: Prepare 200 g of 5% ointment from 10% and 2% ointments.
- Higher: 10, Lower: 2, Desired: 5
- Parts of 10% = 5 - 2 = 3
- Parts of 2% = 10 - 5 = 5
- Total parts = 3 + 5 = 8
- Amount of 10% = (3/8) x 200 g = 75 g
- Amount of 2% = (5/8) x 200 g = 125 g
Days Supply Calculations
Days supply = Quantity dispensed / Daily usage
Common scenarios and their calculations:
| Dosage Form | Key Considerations |
|---|---|
| Tablets/capsules | Divide total quantity by number taken per day |
| Liquids | Divide total volume by daily volume used |
| Inhalers | Divide total actuations by max daily puffs |
| Eye drops | Use 20 drops/mL estimate; calculate total drops, divide by daily drops (count both eyes if OU) |
| Topical creams | Based on the prescribed amount per application and frequency |
| Insulin | Divide total units in the vial or pen by daily units |
Insulin example: A patient uses 30 units of insulin glargine daily. A vial contains 1000 units (10 mL x 100 units/mL). Days supply = 1000 / 30 = 33 days.
Body Surface Area (BSA)
BSA is sometimes used for dosing, particularly in oncology.
Mosteller formula: BSA (m2) = square root of [(height in cm x weight in kg) / 3600]
If BSA-based dosing appears on the exam, you will typically be given the BSA value and asked to calculate the dose from it.
Example: A drug is dosed at 150 mg/m2. Patient BSA = 1.8 m2.
Dose = 150 mg/m2 x 1.8 m2 = 270 mg
IV Flow Rate Calculations
Flow rate (mL/hr): Volume (mL) / Time (hr)
Drip rate (gtt/min): [Volume (mL) x Drop factor (gtt/mL)] / Time (min)
Example: Infuse 1 L of NS over 12 hours using 15 gtt/mL tubing.
Flow rate = 1000 mL / 12 hr = 83.3 mL/hr
Drip rate = (1000 x 15) / (12 x 60) = 15000 / 720 = 20.8 gtt/min (round to 21)
Exam Strategy
- Read the problem twice before starting calculations.
- Write down what you know and what you need to find.
- Check that your units cancel correctly.
- Estimate the answer before calculating - if your answer is wildly different from your estimate, re-check.
- Practice with a basic calculator (the kind allowed on the exam) before test day.
- For days supply: if the sig says PRN, always use the maximum daily dose.