Pharmacy Calculations Quick Reference
Pharmacy calculations are a critical component of the CPHT exam. This cheat sheet covers the most commonly tested formulas with worked examples.
Days Supply Calculations
Formula: Days Supply = Total Quantity Dispensed / Total Daily Dose
Worked Examples
Example 1 - Tablets: Rx: Lisinopril 10 mg, #90, Sig: 1 tab PO daily
Days Supply = 90 tablets / 1 tablet per day = 90 days
Example 2 - Tablets (BID): Rx: Metformin 500 mg, #60, Sig: 1 tab PO BID
Days Supply = 60 tablets / 2 tablets per day = 30 days
Example 3 - Liquid: Rx: Amoxicillin 250 mg/5 mL, Disp: 150 mL, Sig: 5 mL PO TID
Daily use = 5 mL x 3 = 15 mL per day
Days Supply = 150 mL / 15 mL per day = 10 days
Example 4 - Eye drops: Rx: Latanoprost 0.005%, 2.5 mL bottle, Sig: 1 gtt OU QHS
1 drop per eye x 2 eyes = 2 drops per day. Assume approximately 20 drops per mL (standard ophthalmic estimate).
Total drops = 2.5 mL x 20 drops/mL = 50 drops
Days Supply = 50 drops / 2 drops per day = 25 days
Example 5 - Inhaler: Rx: Albuterol MDI, 200 actuations, Sig: 2 puffs Q4-6H PRN
Maximum daily use = 2 puffs x 6 times/day (every 4 hours) = 12 puffs/day
Days Supply = 200 actuations / 12 puffs per day = 16.67, round down to 16 days (when using max frequency)
Concentration and Dilution
Percent Strength Definitions:
| Type | Meaning | Example |
|---|---|---|
| % w/v (weight-in-volume) | Grams of solute per 100 mL of solution | 0.9% NaCl = 0.9 g NaCl in 100 mL |
| % w/w (weight-in-weight) | Grams of solute per 100 g of product | 1% hydrocortisone cream = 1 g HC in 100 g cream |
| % v/v (volume-in-volume) | mL of solute per 100 mL of solution | 70% isopropyl alcohol = 70 mL IPA in 100 mL |
Example - How many grams of dextrose in 1 L of D5W?
D5W = 5% dextrose in water = 5 g per 100 mL
1 L = 1000 mL
5 g / 100 mL = X g / 1000 mL
X = 50 g of dextrose
Dilution Formula
C1 x V1 = C2 x V2
Where C1 = initial concentration, V1 = initial volume, C2 = final concentration, V2 = final volume.
Example: How much 95% ethanol is needed to prepare 500 mL of 70% ethanol?
95% x V1 = 70% x 500 mL
V1 = (70 x 500) / 95 = 35000 / 95 = 368.4 mL of 95% ethanol
Add purified water to bring total volume to 500 mL (qs ad 500 mL).
Ratio Strength
Ratio strength expresses concentration as a ratio, e.g., 1:1000 means 1 g in 1000 mL (or 1 g in 1000 g for solids).
Example: How many mg of epinephrine are in 5 mL of a 1:1000 solution?
1:1000 = 1 g / 1000 mL = 1000 mg / 1000 mL = 1 mg/mL
5 mL x 1 mg/mL = 5 mg
Alligation Method
Alligation is used to determine the proportions needed when mixing two concentrations to achieve a desired intermediate concentration.
Alligation medial finds the resulting concentration when known quantities are mixed.
Alligation alternate finds the ratio of two concentrations to mix.
Alligation Alternate - Setup
Draw a tic-tac-toe grid. Place the higher concentration in the upper left, the lower concentration in the lower left, and the desired concentration in the center. Subtract diagonally (always subtract the smaller from the larger).
Example: Mix 70% alcohol and 40% alcohol to get 500 mL of 55% alcohol.
- Higher concentration: 70 (upper left)
- Lower concentration: 40 (lower left)
- Desired: 55 (center)
- Diagonal subtraction: 55 - 40 = 15 parts of 70%; 70 - 55 = 15 parts of 40%
- Total parts = 15 + 15 = 30 parts
- Volume of 70% = (15/30) x 500 mL = 250 mL
- Volume of 40% = (15/30) x 500 mL = 250 mL
Weight-Based Dosing
Formula: Dose = Patient Weight (kg) x Dose per kg
Conversion: 1 kg = 2.2 lb
Example: A patient weighs 176 lb. The ordered dose is 5 mg/kg/day in 2 divided doses. How many mg per dose?
- Convert weight: 176 lb / 2.2 = 80 kg
- Total daily dose: 80 kg x 5 mg/kg = 400 mg/day
- Per dose: 400 mg / 2 doses = 200 mg per dose
Proportion / Dimensional Analysis
Example: A prescription calls for 250 mg of amoxicillin. The available suspension is 125 mg/5 mL. How many mL should be dispensed per dose?
125 mg / 5 mL = 250 mg / X mL
X = (250 x 5) / 125 = 10 mL
Unit Conversions Reference
| From | To | Factor |
|---|---|---|
| 1 kg | 2.2 lb | Multiply kg by 2.2 |
| 1 oz | 30 mL (approx.) | Multiply oz by 30 |
| 1 tsp | 5 mL | Multiply tsp by 5 |
| 1 tbsp | 15 mL | Multiply tbsp by 15 |
| 1 cup | 240 mL | Multiply cups by 240 |
| 1 pint | 473 mL | Multiply pints by 473 |
| 1 gallon | 3785 mL | Multiply gallons by 3785 |
| 1 grain (gr) | 65 mg (approx.) | Multiply gr by 65 |
| 1 g | 1000 mg | Multiply g by 1000 |
| 1 mg | 1000 mcg | Multiply mg by 1000 |
| 1 L | 1000 mL | Multiply L by 1000 |
Exam Tips
- Always check your units before solving - convert to consistent units first.
- For days supply with PRN medications, use the maximum daily dose allowed.
- Know the standard assumption of 20 drops per mL for ophthalmic solutions.
- Double check your answer by asking: "Does this make sense?" If a calculation yields an unusually large or small number, re-check your work.
- Alligation problems appear frequently - practice the grid method until it is automatic.