Excellent content from both Katzung and Lippincott. Now I have everything needed for a thorough, practical guide.
Drug Calculations & Dosing for Clinical Practice
Based on Katzung's Basic & Clinical Pharmacology 16e and Lippincott Illustrated Reviews: Pharmacology
Part 1 - The Master Formula (The Foundation of All Drug Calculations)
The single most important formula in nursing practice:
$$\text{Volume to give} = \frac{\text{Desired Dose}}{\text{Available Dose}} \times \text{Available Volume}$$
Example:
- Doctor orders: 250 mg of amoxicillin
- On hand: amoxicillin 500 mg / 5 mL suspension
$$\text{Volume} = \frac{250\text{ mg}}{500\text{ mg}} \times 5\text{ mL} = \mathbf{2.5 mL}$$
Part 2 - Weight-Based Dosing (mg/kg)
Used for most paediatric drugs, heparin, antibiotics, chemotherapy, and many critical care drugs.
$$\text{Total Dose} = \text{Weight (kg)} \times \text{Dose (mg/kg)}$$
Example:
- Child weighs 20 kg, doctor orders amoxicillin 25 mg/kg/day in 2 divided doses
- Total daily dose = 20 × 25 = 500 mg/day
- Each dose = 500 ÷ 2 = 250 mg twice daily
Then apply the master formula to calculate the volume to draw up.
Part 3 - IV Infusion Rate Calculations
3a. mL per Hour
Used when a pump is available (most modern wards):
$$\text{Rate (mL/hr)} = \frac{\text{Volume to infuse (mL)}}{\text{Time (hours)}}$$
Example: Infuse 1000 mL of normal saline over 8 hours
$$\text{Rate} = \frac{1000}{8} = \mathbf{125 \text{ mL/hr}}$$
3b. Drops per Minute (Manual Drip - no pump)
Used in settings without infusion pumps. You need to know the drop factor of the IV giving set:
- Standard giving set: 20 drops/mL
- Blood/high-viscosity giving set: 15 drops/mL
- Micro-drip/paediatric giving set: 60 drops/mL
$$\text{Drops/min} = \frac{\text{Volume (mL)} \times \text{Drop factor}}{\text{Time (minutes)}}$$
Example: 500 mL over 4 hours using a standard set (20 drops/mL)
$$\text{Drops/min} = \frac{500 \times 20}{4 \times 60} = \frac{10000}{240} \approx \mathbf{42 \text{ drops/min}}$$
3c. Drug Infusion Rate (mcg/kg/min)
Common in ICU - for vasopressors (dopamine, noradrenaline), heparin, insulin infusions:
$$\text{Infusion rate (mL/hr)} = \frac{\text{Dose (mcg/kg/min)} \times \text{Weight (kg)} \times 60}{\text{Concentration (mcg/mL)}}$$
Example: Dopamine ordered at 5 mcg/kg/min for a 70 kg patient. Bag = dopamine 400 mg in 250 mL (concentration = 400,000 mcg ÷ 250 mL = 1600 mcg/mL)
$$\text{Rate} = \frac{5 \times 70 \times 60}{1600} = \frac{21000}{1600} \approx \mathbf{13.1 \text{ mL/hr}}$$
Part 4 - Loading Dose vs Maintenance Dose
This is a key clinical concept. According to Katzung:
"In most clinical situations, drugs are administered so as to maintain a steady state of drug in the body, where the amount given with each dose replaces the drug eliminated since the preceding dose."
Maintenance Dose
Keeps the drug at a stable therapeutic level (steady-state concentration, or Css).
- It takes 4-5 half-lives to reach steady state from zero
- Formula: Dosing Rate = Clearance (CL) × Target Concentration (TC)
Loading Dose
Given when you need to reach therapeutic levels quickly - particularly for drugs with long half-lives (e.g. digoxin, amiodarone, phenytoin).
$$\text{Loading Dose} = V_d \times \text{Target Concentration (TC)}$$
Example from Katzung (theophylline):
- Target plasma level = 10 mg/L
- Volume of distribution (Vd) = 35 L (for a 70 kg person)
- Loading dose = 35 × 10 = 350 mg (given as a single dose to rapidly reach target)
- Maintenance dose = 350 mg every 12 hrs orally to keep that level
With a loading dose (red line), therapeutic levels are reached immediately. Without it (blue line), it takes 4-5 half-lives to reach steady state.
Nursing caution: Loading doses carry increased toxicity risk. IV loading doses must be given slowly (e.g. over an hour, NOT by rapid bolus) to prevent dangerously high initial concentrations - especially for phenytoin, digoxin, and amiodarone.
Part 5 - Therapeutic Drug Monitoring (TDM)
Some drugs have a narrow therapeutic index - the gap between the effective dose and the toxic dose is small. These drugs must be monitored with blood levels.
| Drug | Therapeutic Range | Toxic Signs to Watch For |
|---|
| Digoxin | 0.5-2 ng/mL | Nausea, bradycardia, visual changes |
| Lithium | 0.6-1.2 mEq/L | Tremor, confusion, arrhythmia |
| Warfarin | INR 2-3 (most indications) | Bleeding |
| Phenytoin | 10-20 mcg/mL | Nystagmus, ataxia, confusion |
| Gentamicin | Peak 5-10 mcg/mL | Nephrotoxicity, ototoxicity |
| Theophylline | 10-20 mcg/mL | Nausea, seizures, arrhythmia |
From Lippincott Illustrated Reviews: Pharmacology - "If the therapeutic window of the drug is small (for example, digoxin or lithium), extra caution should be taken in selecting a dosage regimen, and drug levels should be monitored."
Part 6 - Dose Adjustments in Special Populations
Renal Impairment
- Kidneys are the primary route of excretion for most drugs
- Reduced clearance → drug accumulates → toxicity risk
- Key dose reduction formula using creatinine clearance (CrCl) - calculated by the Cockcroft-Gault equation:
$$\text{CrCl (mL/min)} = \frac{(140 - \text{age}) \times \text{weight (kg)}}{72 \times \text{serum creatinine (mg/dL)}} \times (0.85 \text{ if female})$$
- If CrCl is reduced, the dose is reduced or the interval is extended
- Drugs needing renal dose adjustment include: gentamicin, metformin, digoxin, many antibiotics
Hepatic Impairment
- Liver metabolises most drugs via CYP enzymes
- Reduced metabolism → higher drug levels → toxicity
- Particularly relevant for: morphine, warfarin, statins, antifungals
Elderly Patients
- Reduced renal AND hepatic function
- Lower body weight and higher fat/muscle ratio changes Vd
- Principle: "Start low, go slow"
Paediatric Patients
- Immature liver enzymes (especially in neonates)
- Always dose by weight (mg/kg) - never extrapolate adult doses
- Dose adjustment reference: Harriet Lane Handbook
Part 7 - The 5 Rights of Medication Administration (Never Skip These)
Before giving any drug, verify:
| Right | What to Check |
|---|
| Right Patient | Two identifiers (name + DOB or ID) |
| Right Drug | Correct medication name (generic vs brand confusion is common) |
| Right Dose | Recalculate - never assume someone else's calculation |
| Right Route | Oral, IV, IM, sublingual, topical, etc. |
| Right Time | Correct frequency and timing relative to meals/other drugs |
Some institutions add: Right Documentation, Right Reason, Right Response.
Part 8 - Quick Reference: Unit Conversions for Drug Calculations
| From | To | Multiply by |
|---|
| grams (g) | milligrams (mg) | × 1,000 |
| milligrams (mg) | micrograms (mcg / μg) | × 1,000 |
| micrograms (mcg) | nanograms (ng) | × 1,000 |
| kilograms (kg) | pounds (lb) | × 2.2 |
| litres (L) | millilitres (mL) | × 1,000 |
Common trap: Orders may be written in mcg but your drug vial may be labelled in mg. Always convert to the same unit before calculating.
Practice Questions
Try these to test yourself:
Q1. A doctor orders gentamicin 80 mg IV. On hand: gentamicin 40 mg/mL. How many mL do you draw up?
Q2. Infuse 500 mL of D5W over 6 hours. What is the rate in mL/hr?
Q3. A child weighs 15 kg. The order is paracetamol 15 mg/kg. The suspension is 250 mg/5 mL. What volume do you give?
Q4. Heparin infusion running at 25,000 units in 500 mL. Patient needs 1,000 units/hr. What is the pump rate in mL/hr?
(Answers: Q1 = 2 mL, Q2 = 83.3 mL/hr, Q3 = 4.5 mL, Q4 = 20 mL/hr)
Would you like me to go deeper on any of these areas - for example, heparin/insulin infusion calculations, paediatric dosing, or practice a set of worked examples together?