How dimensional analysis works
Dimensional analysis writes the problem as one line of fractions. You start with the unit you want in the answer, add each conversion as a fraction, and arrange the fractions so every unwanted unit appears once on top and once on the bottom. Those units cancel, and only the answer's unit is left.
Because it uses the same steps for every kind of problem, many nursing programs teach it as the main method. It also catches mistakes: if the units do not cancel, the setup is wrong.
The steps
- Write the unit you want on the left (for example mL, tablets or mL/hr).
- Put the fraction from the label or the drug on hand next to it, with the wanted unit on top (for example 5 mL / 250 mg).
- Add conversion fractions so the units cancel (for example 1 g / 1,000 mg).
- End with the order (what the prescriber wants, for example 0.5 g).
- Cancel the units, multiply across the top, multiply across the bottom, and divide.
Example 1: tablets with a unit conversion
Order: levothyroxine 0.1 mg PO. Available: 50 mcg tablets. How many tablets?
- tablets = (1 tablet / 50 mcg) × (1,000 mcg / 1 mg) × (0.1 mg / 1)
- mcg and mg cancel: (1 × 1,000 × 0.1) ÷ 50 = 100 ÷ 50
- = 2 tablets
Example 2: liquid medication
Order: amoxicillin 0.5 g PO. Available: 250 mg per 5 mL. How many mL?
- mL = (5 mL / 250 mg) × (1,000 mg / 1 g) × (0.5 g / 1)
- = (5 × 1,000 × 0.5) ÷ 250 = 2,500 ÷ 250
- = 10 mL
Example 3: IV drip rate
Infuse 1,000 mL over 8 hours with 15 gtt/mL tubing. How many gtt/min?
- gtt/min = (15 gtt / 1 mL) × (1,000 mL / 8 hr) × (1 hr / 60 min)
- = (15 × 1,000) ÷ (8 × 60) = 15,000 ÷ 480 = 31.25
- = 31 gtt/min
Example 4: weight-based critical care drip
Order: dopamine 5 mcg/kg/min. Weight 80 kg. Available: 400 mg in 250 mL. How many mL/hr?
- mL/hr = (250 mL / 400 mg) × (1 mg / 1,000 mcg) × (5 mcg / kg·min) × (80 kg) × (60 min / 1 hr)
- = (250 × 5 × 80 × 60) ÷ (400 × 1,000) = 6,000,000 ÷ 400,000
- = 15 mL/hr
Frequently asked questions
Is dimensional analysis better than desired over have?
Both give the same answer. Dimensional analysis handles conversions and multi-step problems (IV drips, mcg/kg/min) in a single setup, so many students find it safer for complex problems.
What if the units do not cancel?
The setup is wrong: flip the fraction whose unit is in the wrong place, or add the missing conversion factor.