Dosage Calculation · Topic 2 of 10
Ratio, Proportion & Dimensional Analysis
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Dosage calculation · methods
Ratio, Proportion & Dimensional Analysis
Two ways to solve the same dose problem: ratio-proportion for one step, dimensional analysis for multi-step chains. Both give the same answer — when the units cancel correctly.
01 · The units checkLeftover unit must be the one asked for
02 · Ratio-proportionHave/quantity = desired/x, cross-multiply
03 · Dimensional analysisChain factors so unwanted units cancel
01
Ratio-proportion or dimensional analysis?
Both give the same answer
| Ratio-proportion | Dimensional analysis | |
|---|---|---|
| Best for | A one-step dose — compact | Multi-step problems — weight-based doses, mcg/kg/min drips |
| Set up | Have over quantity = desired over x | Start with the order, then chain conversion factors |
| Solve | Cross-multiply, divide by the number beside x | Multiply the tops, multiply the bottoms, divide |
| Example | 250 mg/5 mL = 750 mg/x mL → 15 mL | 0.6 g × 1,000 mg/1 g × 4 mL/200 mg = 12 mL |
02
Ratio-proportion, step by step
Supply 250 mg/5 mL · order 750 mgWrite have over quantity: 250 mg / 5 mL
Set it equal to desired over x: 750 mg / x mL
Cross-multiply: 250 × x = 750 × 5, so 250x = 3,750
Divide by the number beside x: 3,750 ÷ 250 = 15 mL
Check: 3 times the labeled strength needs 3 × 5 mL = 15 mL
03
Dimensional analysis, step by step
Order 0.6 g · supply 200 mg/4 mLStart with the order: 0.6 g
× 1,000 mg / 1 g — grams cancel
× 4 mL / 200 mg — milligrams cancel
Multiply the tops: 0.6 × 1,000 × 4 = 2,400
Multiply the bottoms: 1 × 200 = 200
Divide: 2,400 ÷ 200 = 12 mL — mL is the only unit left
04
The rules
Let the units guide the setup
Convert to the same unit before solving
Keep like units in the same positions: mg over mL = mg over mL
A conversion factor works either way: 1,000 mg/1 g or 1 g/1,000 mg
Pick the direction that cancels the unwanted unit
Each unwanted unit appears once on top, once on the bottom
Round only at the end
05
Common errors
A wrong leftover unit means a wrong setup
Wrong leftover unit → a factor is upside down or missing
Units not converted to match (g vs mg) before solving
Like units in different positions on the two sides
Rounding mid-chain instead of only at the end
06
Before you give it
Check the answer against the supply before giving
Twice the labeled strength needs twice the labeled volume
Set it up so every unwanted unit cancels and only the asked-for unit is left. Ratio-proportion and dimensional analysis give the same answer — check it against the supply.
Sources · Clinical Nursing Skills 11.2 Dosing (OpenStax) · Pharmacology for Nurses 2.4 Dosage Calculations (OpenStax) · Follow your facility's protocol for rounding doses.
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