The dimensional analysis (DA) setup — use this for every calculation
Answer = What you have × (Conversion factor) × (Another if needed)
Write units as fractions. Cancel the ones that appear on top and bottom. The unit left over = the unit of your answer. If the unit is wrong, you set up the fraction upside down.
1-step DA (dose to volume)
Formula: dose ordered × (volume/dose on hand)
Example: 500 mg ordered, have 250 mg/5 mL
500 mg × (5 mL / 250 mg) = 10 mL
Check: mg cancels, mL stays. ✓
Example: 500 mg ordered, have 250 mg/5 mL
500 mg × (5 mL / 250 mg) = 10 mL
Check: mg cancels, mL stays. ✓
2-step DA (weight-based)
Step 1: lb → kg (always divide by 2.2)
Step 2: kg × dose/kg → total dose
Step 3: dose × (vol/concentration) → mL
Never skip the lb→kg conversion.
Step 2: kg × dose/kg → total dose
Step 3: dose × (vol/concentration) → mL
Never skip the lb→kg conversion.
3-step DA (weight + divided dose)
Step 1: lb → kg
Step 2: kg × mg/kg/day = daily dose
Step 3: daily dose ÷ doses per day = per dose
Step 4: per-dose mg → mL using concentration
Used for TID/BID/q8h pediatric sigs.
Step 2: kg × mg/kg/day = daily dose
Step 3: daily dose ÷ doses per day = per dose
Step 4: per-dose mg → mL using concentration
Used for TID/BID/q8h pediatric sigs.
Rate conversions (IV drips)
mcg/kg/min → mL/hr:
1. mcg/kg/min × weight = mcg/min
2. mcg/min × 60 = mcg/hr
3. mcg/hr ÷ (mcg per mL concentration) = mL/hr
Watch units: mcg vs mg matters.
1. mcg/kg/min × weight = mcg/min
2. mcg/min × 60 = mcg/hr
3. mcg/hr ÷ (mcg per mL concentration) = mL/hr
Watch units: mcg vs mg matters.
★ PTCB tip: DA problems on the exam always have a weight in the scenario. Write your fractions out fully — it prevents errors. The PTCB won't ask you to do DA explicitly, but every multi-step dosage problem requires it. Expect 3–5 problems in Order Entry & Processing that need DA.
Top DA mistakes: (1) Forgetting to convert lb to kg before multiplying by mg/kg. (2) Flipping the fraction — putting mL on the bottom instead of top means you get mg²/mL, not mL. (3) Skipping the daily dose ÷ frequency step for divided doses. (4) Converting mcg to mg or vice versa mid-calculation without tracking the decimal.
Six worked examples with full DA setups showing unit cancellation at every step. Write out your fractions — this is how you catch errors.
EasyRetail
Rx: amoxicillin 500 mg. Available: 250 mg/5 mL suspension.
How many mL per dose? (1-step DA)
Set up the fraction so mg cancels:500 mg × (5 mL / 250 mg) = 500 × 5 / 250 = 10 mL
✓ 10 mL per dose
MediumHospital
Patient: 154 lb. Gentamicin 5 mg/kg IV. Available: 40 mg/mL.
How many mL to draw up? (2-step DA)
Step 1 — lb to kg:154 lb × (1 kg / 2.2 lb) = 70 kg
Step 2 — kg to dose:70 kg × (5 mg / 1 kg) = 350 mg
Step 3 — mg to mL:350 mg × (1 mL / 40 mg) = 8.75 mL
✓ Draw up 8.75 mL
MediumPatient scenario
Child: 44 lb. Amoxicillin 40 mg/kg/day in 3 divided doses. Available: 250 mg/5 mL.
How many mL per individual dose? (3-step DA)
Step 1 — weight:44 ÷ 2.2 = 20 kg
Step 2 — daily dose:20 kg × 40 mg/kg = 800 mg/day
Step 3 — per dose:800 ÷ 3 = 266.7 mg/dose
Step 4 — convert to mL:266.7 × (5/250) = 5.33 → 5.3 mL
✓ 5.3 mL per dose, three times daily
HardHospital
Nitroglycerin: 50 mg in 250 mL D5W. Order: 20 mcg/min.
What is the pump rate in mL/hr? (Rate conversion)
Step 1 — find concentration in mcg/mL:50 mg × 1,000 = 50,000 mcg / 250 mL = 200 mcg/mL
Step 2 — convert rate to per hour:20 mcg/min × 60 = 1,200 mcg/hr
Step 3 — divide by concentration:1,200 mcg/hr ÷ 200 mcg/mL = 6 mL/hr
✓ Set pump to 6 mL/hr
HardHospital
Norepinephrine: 8 mg in 250 mL D5W. Order: 0.1 mcg/kg/min for 70 kg patient.
Pump rate in mL/hr? (Full rate DA chain)
Step 1 — weight-based rate:0.1 mcg/kg/min × 70 kg = 7 mcg/min
Step 2 — per hour:7 × 60 = 420 mcg/hr
Step 3 — to mg/hr:420 ÷ 1,000 = 0.42 mg/hr
Step 4 — concentration:8 mg / 250 mL = 0.032 mg/mL
Step 5 — pump rate:0.42 ÷ 0.032 = 13.1 mL/hr
✓ Set pump to 13.1 mL/hr
HardPatient scenario
Child in status epilepticus: 55 lb. Lorazepam 0.1 mg/kg IV. Available: 2 mg/mL.
How many mL IV — quickly and accurately?
Step 1:55 ÷ 2.2 = 25 kg
Step 2:25 × 0.1 = 2.5 mg
Step 3:2.5 ÷ 2 = 1.25 mL
✓ Draw up 1.25 mL — give slowly IV over 2 minutes
Emergency speed: In a seizure emergency you still do all 3 steps. A 10x error here (drawing 12.5 mL) causes respiratory arrest. Practice until the chain is automatic.
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ⓘ This lesson has 36 questions in the bank. A 10-question quiz draws a random subset. Run multiple sets to cycle through all questions.
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Lesson 2 · Dimensional Analysis · AlabamaPharmTech.com
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