Dosage Calculations
Dimensional analysis method, IV drip rate calculations, weight-based dosing, and worked examples for nursing math.
Dimensional Analysis Method
Dimensional analysis (factor-label method) is the most versatile approach for dosage calculations. It uses conversion factors to cancel unwanted units until you arrive at the desired unit.
The Formula
Desired Dose × Conversion Factors = Amount to Give
Set up so that unwanted units cancel diagonally (numerator to denominator).
Basic Oral/Injection Calculation
Formula: (Desired / Have) × Vehicle = Amount to administer
Example 1: Oral Medication
Order: Amoxicillin 500 mg PO. Available: 250 mg/5 mL
| Step | Calculation |
|---|---|
| Set up | 500 mg × (5 mL / 250 mg) |
| Cancel units | mg cancels, leaving mL |
| Calculate | 500 × 5 / 250 = 10 mL |
Example 2: Injection
Order: Morphine 4 mg IM. Available: 10 mg/mL
| Step | Calculation |
|---|---|
| Set up | 4 mg × (1 mL / 10 mg) |
| Cancel units | mg cancels, leaving mL |
| Calculate | 4 / 10 = 0.4 mL |
IV Flow Rate Calculations
mL/hr (Pump Rate)
Formula: Total Volume (mL) / Total Time (hr) = mL/hr
Example: Infuse 1000 mL NS over 8 hours
1000 mL / 8 hr = 125 mL/hr
Drops per Minute (gtt/min)
Formula: (Volume in mL × Drop Factor) / (Time in minutes) = gtt/min
Common Drop Factors
| Tubing Type | Drop Factor (gtt/mL) |
|---|---|
| Macrodrip | 10, 15, or 20 gtt/mL |
| Microdrip | 60 gtt/mL |
Example 3: Drip Rate
Order: 500 mL D5W over 4 hours. Tubing: 15 gtt/mL
| Step | Calculation |
|---|---|
| Convert hours to minutes | 4 hr × 60 = 240 minutes |
| Apply formula | (500 mL × 15 gtt/mL) / 240 min |
| Calculate | 7500 / 240 = 31 gtt/min (round to nearest whole drop) |
Microdrip Shortcut
When using 60 gtt/mL tubing: gtt/min = mL/hr (the numbers are the same!)
Weight-Based Dosing
Conversion
1 kg = 2.2 lbs
To convert lbs to kg: Weight in lbs / 2.2 = Weight in kg
Example 4: Weight-Based Dose
Order: Gentamicin 2 mg/kg IV q8h. Patient weighs 176 lbs.
| Step | Calculation |
|---|---|
| Convert weight | 176 lbs / 2.2 = 80 kg |
| Calculate dose | 2 mg/kg × 80 kg = 160 mg per dose |
Example 5: Pediatric Safe Dose Range
Order: Amoxicillin for a child weighing 22 lbs. Safe range: 25–50 mg/kg/day divided q8h.
| Step | Calculation |
|---|---|
| Convert weight | 22 lbs / 2.2 = 10 kg |
| Daily range | 25 × 10 = 250 mg/day to 50 × 10 = 500 mg/day |
| Per dose (q8h = 3 doses/day) | 250/3 = 83 mg to 500/3 = 167 mg per dose |
| Verify | If ordered dose falls within 83–167 mg, it is safe |
IV Medication Infusion Rates
Example 6: mcg/min to mL/hr
Order: Dopamine 5 mcg/kg/min. Patient: 70 kg. Available: 400 mg in 250 mL D5W.
| Step | Calculation |
|---|---|
| Desired dose/min | 5 mcg/kg/min × 70 kg = 350 mcg/min |
| Convert to mg/min | 350 mcg / 1000 = 0.35 mg/min |
| Concentration | 400 mg / 250 mL = 1.6 mg/mL |
| mL/min | 0.35 mg/min / 1.6 mg/mL = 0.219 mL/min |
| mL/hr | 0.219 × 60 = 13.1 mL/hr |
Units/hr Calculations
Example 7: Heparin Drip
Order: Heparin 1000 units/hr. Available: 25,000 units in 500 mL NS.
| Step | Calculation |
|---|---|
| Concentration | 25,000 units / 500 mL = 50 units/mL |
| mL/hr | 1000 units/hr / 50 units/mL = 20 mL/hr |
Key Reminders
- Always double-check calculations with a second nurse for high-alert medications
- Label all syringes and IV bags
- Question any dose that requires more than 2–3 tablets or more than 2–3 mL by injection
- Round to the nearest tenth for oral liquids, hundredth for injections
- If a calculated dose seems unusual, verify the order before administering