Key Takeaways
- Day supply calculation: (Quantity dispensed / Daily dose) = Days supply.
- Dosage calculations require matching units and using dimensional analysis.
- Concentration conversions: 1% = 1g/100mL = 10mg/mL.
- Ratio strength: 1:1000 means 1g of drug per 1000mL of solution.
- Common conversions: 1 tsp = 5mL, 1 tbsp = 15mL, 1 oz = 30mL, 1 kg = 2.2 lb.
Pharmacy Calculations
Quick Answer: Pharmacy calculations include day supply (quantity divided by daily dose), dosage calculations (using dimensional analysis), and concentration conversions (1% = 10mg/mL). These calculations are heavily tested on the PTCE and are essential for daily pharmacy work.
Pharmacy calculations are among the most practical skills tested on the PTCE. This section covers day supply, dosage calculations, concentration conversions, and the essential conversion factors you must know.
Essential Conversion Factors
Volume Conversions
| Conversion | Value |
|---|---|
| 1 teaspoon (tsp) | 5 mL |
| 1 tablespoon (tbsp) | 15 mL (3 tsp) |
| 1 fluid ounce (fl oz) | 30 mL (2 tbsp) |
| 1 cup | 240 mL (8 fl oz) |
| 1 pint | 480 mL (16 fl oz) |
| 1 quart | 960 mL (32 fl oz) |
| 1 gallon | 3,840 mL (128 fl oz) |
| 1 liter (L) | 1,000 mL |
Weight Conversions
| Conversion | Value |
|---|---|
| 1 kilogram (kg) | 1,000 grams (g) |
| 1 gram (g) | 1,000 milligrams (mg) |
| 1 milligram (mg) | 1,000 micrograms (mcg) |
| 1 pound (lb) | 454 grams |
| 1 kilogram (kg) | 2.2 pounds |
| 1 ounce (oz) | 28.4 grams |
| 1 grain (gr) | 65 mg (approximately) |
Day Supply Calculations
Day supply tells insurance companies and patients how long a prescription will last.
Basic Formula
Day Supply = Quantity Dispensed / (Dose per administration × Administrations per day)
Or simply:
Day Supply = Quantity Dispensed / Daily Dose
Example 1: Tablets
Rx: Lisinopril 10mg #90, Sig: 1 tab PO QD
Calculation:
- Quantity = 90 tablets
- Daily dose = 1 tablet/day
- Day supply = 90 ÷ 1 = 90 days
Example 2: Multiple Daily Doses
Rx: Metformin 500mg #180, Sig: 1 tab PO BID
Calculation:
- Quantity = 180 tablets
- Daily dose = 2 tablets/day (BID = twice daily)
- Day supply = 180 ÷ 2 = 90 days
Example 3: Liquid Medications
Rx: Amoxicillin 250mg/5mL, Disp: 150mL, Sig: 1 tsp TID
Calculation:
- Quantity = 150 mL
- Each dose = 1 tsp = 5 mL
- Doses per day = 3 (TID)
- Daily usage = 5 mL × 3 = 15 mL/day
- Day supply = 150 ÷ 15 = 10 days
Example 4: Eye/Ear Drops
Rx: Latanoprost 0.005% ophthalmic solution, 2.5mL, Sig: 1 gtt OU QHS
Standard Estimate: 20 drops per mL (industry standard for most ophthalmic solutions)
Calculation:
- Total drops = 2.5 mL × 20 drops/mL = 50 drops
- Drops per day = 1 drop × 2 eyes = 2 drops/day
- Day supply = 50 ÷ 2 = 25 days
Example 5: Inhalers
Rx: Albuterol HFA 90mcg inhaler, 200 actuations, Sig: 2 puffs Q4-6H PRN
PRN Calculation (Maximum Daily Use):
- Maximum frequency: every 4 hours = 6 times/day
- Puffs per use: 2
- Maximum daily puffs = 2 × 6 = 12 puffs/day
- Day supply = 200 ÷ 12 = 16.7 = 16 days (round down for PRN)
Note: For PRN medications, calculate based on maximum frequency to determine minimum day supply.
Dosage Calculations
Weight-Based Dosing
Many pediatric and some adult medications are dosed based on weight.
Formula:
Dose = Weight (kg) × Dose per kg
Example: A child weighs 44 lbs. The prescribed dose is 25 mg/kg/day in divided doses TID. What is each dose?
Step 1: Convert weight to kg
- 44 lbs ÷ 2.2 = 20 kg
Step 2: Calculate total daily dose
- 20 kg × 25 mg/kg = 500 mg/day
Step 3: Divide into three doses (TID)
- 500 mg ÷ 3 = 166.7 mg per dose (round to 167 mg)
BSA-Based Dosing (Body Surface Area)
Some medications (often chemotherapy) are dosed based on BSA.
Mosteller Formula:
BSA (m²) = √[(Height (cm) × Weight (kg)) / 3600]
Concentration Calculations
Percentage Strength
| Expression | Meaning |
|---|---|
| % w/v (weight/volume) | Grams per 100 mL |
| % v/v (volume/volume) | mL per 100 mL |
| % w/w (weight/weight) | Grams per 100 grams |
Key Conversion: 1% = 1g/100mL = 10mg/mL
Example: How many mg of hydrocortisone are in 30g of 2.5% hydrocortisone cream?
Calculation:
- 2.5% = 2.5g per 100g
- 30g of cream × (2.5g/100g) = 0.75g = 750 mg
Ratio Strength
Ratio strength expresses concentration as a ratio.
| Ratio | Meaning |
|---|---|
| 1:100 | 1g in 100mL (or 1g per 100g) |
| 1:1000 | 1g in 1000mL |
| 1:10,000 | 1g in 10,000mL |
Example: How many mg of epinephrine are in 5mL of a 1:1000 solution?
Calculation:
- 1:1000 = 1g per 1000mL = 1mg/mL
- 5mL × 1mg/mL = 5 mg
Converting Between Ratio and Percentage
Percentage = (1 / Ratio denominator) × 100
Example: Convert 1:10,000 to a percentage
- (1/10,000) × 100 = 0.01%
Dilution Calculations
Basic Dilution Formula (C1V1 = C2V2)
Initial Concentration × Initial Volume = Final Concentration × Final Volume
Example: How much stock 70% isopropyl alcohol is needed to make 500mL of 30% solution?
Calculation:
- C1 = 70%, V1 = ?
- C2 = 30%, V2 = 500mL
- 70% × V1 = 30% × 500mL
- V1 = (30 × 500) / 70 = 214.3 mL
Mix 214.3 mL of 70% alcohol with 285.7 mL of water (500 - 214.3) to make 500mL of 30% solution.
Alligation Method
Used when mixing two different strengths to achieve a desired concentration.
Example: Mix 20% and 5% solutions to make 100mL of 12% solution. How much of each is needed?
Alligation Grid:
20% | 7 parts (20-12=8... wait)
X
12% (desired)
X
5% | 8 parts (12-5=7... wait)
Correct Method:
- Parts of 20% needed: |12 - 5| = 7 parts
- Parts of 5% needed: |20 - 12| = 8 parts
- Total parts = 7 + 8 = 15 parts
For 100mL:
- Volume of 20%: (7/15) × 100 = 46.7 mL
- Volume of 5%: (8/15) × 100 = 53.3 mL
A prescription reads: Metoprolol 50mg #60, Sig: 1 tab PO BID. What is the day supply?
How many milligrams of active ingredient are in 50mL of a 2% solution (w/v)?
A child weighs 66 pounds. A medication is dosed at 10 mg/kg/day in two divided doses. What is each dose?