Dimensional Analysis for Dosage Calculation, Explained
Shows the work. Every example is computed with the formula and numbered steps. For study and exam practice, not for patient care.
Dimensional analysis: Solving a dosage problem as one chain of fractions (conversion factors), arranged so every unit cancels except the unit of the answer.
Dimensional analysis writes the whole problem as one line. Start with the ordered amount, then multiply by fractions (conversion factors and the strength on the label), arranged so that each unit you don’t want appears once on top and once on the bottom and cancels. What is left is the unit of the answer.
For an order of clonidine 100 mcg with 0.05 mg tablets on hand, the number of tablets is set up as:
100 mcg × (1 mg / 1,000 mcg) × (1 tablet / 0.05 mg)
The mcg cancel, then the mg, leaving tablets. Its strength is that the conversion is built into the setup, so it can’t be forgotten. It suits multi-step problems such as mcg/kg/min infusions.
The worked example below solves the same problem step by step. Your answer by dimensional analysis should match it.
Order: clonidine 100 mcg PO twice daily. Available: clonidine 0.05 mg tablets.
- Desired dose
- 0.1 mg
- Have
- 0.05 mg
- Give as
- Tablets
- Scored tablet
- Yes
Formula Amount = desired ÷ have × vehicle.
- Tablets = desired dose ÷ tablet strength.
- 0.1 mg ÷ 0.05 mg = 2 tablets.
- The answer is a whole number of tablets: 2 tablets.
Answer 2 tablets
Sources
- Clinical Calculations: With Applications to General and Specialty Areas — Elsevier (Kee, Marshall, et al.)
- Calculate with Confidence — Elsevier (Morris)