Dosage Calculations Made Simple (2025): Dimensional Analysis + 25 Practice Problems

If you can read a label and set up unit-canceling fractions, you can master every common nursing math task - IV drip rates, mL/hr pumps, mcg/kg/min titrations, pediatric mg/kg dosing, and insulin. This guide gives you a repeatable method, safety checks, and 25 practice problems with answers so you’re ready for clinicals and NGN items.

For skill-building with clinical judgment, pair this with NGN Med-Surg / Physiological Adaptation Case Studies (2025). If you’d like AI help scaffolding calculations step-by-step, see AI in Nursing Education (2025): Complete Guide and our AI Prompt Library for Nursing Students (2025).

Table of Contents

• Core Method: Dimensional Analysis that Always Works
• Safety & Accuracy: Rounding, High-Alert Meds, and Double-Checks
• Quick Formulas: gtt/min, mL/hr, mcg/kg/min, mg/kg
• Practice Problems (25) with Answers
  • A. Dose ↔ Volume & Tablets (5)
  • B. IV Drip Rate: gtt/min (5)
  • C. IV Pump: mL/hr (5)
  • D. Weight-Based Titrations: mcg/kg/min (5)
  • E. Pediatrics: mg/kg/dose (5)
  • F. Insulin: Carb Ratio + Correction (2)
• FAQs: Common Pitfalls in Nursing Math
• Key Takeaways
• Further Reading

Core Method: Dimensional Analysis that Always Works

1. Write the order and the available concentration.
2. Build a fraction string so unwanted units cancel and the answer’s unit remains (e.g., mL, gtt/min, mL/hr).
3. Multiply across, divide, then apply rounding rules (facility-specific).
4. Sanity check: Does the answer make clinical sense for this med and route?

Bolded concepts to notice: order, supply concentration, unit cancellation, desired unit, rounding, sanity check.

Safety & Accuracy: Rounding, High-Alert Meds, and Double-Checks

• High-alert meds (e.g., insulin, heparin, vasoactives) often require a second RN check—follow policy.
• Rounding: Pumps typically accept whole mL/hr; gtt/min must be whole drops; insulin units per facility rule (whole or 0.5).
• Document the label, lot, and calculation when required.
• When in doubt, use GoodNurse to generate a step-by-step setup for your calculation flow (AI Prompt Library).

Quick Formulas: gtt/min, mL/hr, mcg/kg/min, mg/kg

• gtt/min = (\frac{\text{mL} \times \text{drop factor (gtt/mL)}}{\text{minutes}}) → round to whole gtt.
• mL/hr = (\frac{\text{mL}}{\text{hours}}) (or (\frac{\text{mL}}{\text{minutes}} \times 60)).
• mcg/kg/min infusions →
  [ \text{mL/hr} = \frac{\text{ordered mcg/kg/min} \times \text{kg} \times 60}{\text{solution mcg/mL}} ] (Convert mg → mcg and know your bag’s mcg/mL.)
• mg/kg (pediatrics) → (\text{Dose mg} = \text{mg/kg} \times \text{kg}), then convert to mL with the supply concentration.

Practice Problems (25) with Answers

Tip: Work them with dimensional analysis and check against the key. Where rounding differs by policy, we show a common choice.

A. Dose ↔ Volume & Tablets (5)

1. Acetaminophen 650 mg PO. Supply: 325 mg tablet.
   Answer: 2 tablets.
   Why: 650 ÷ 325 = 2.

2. Morphine 2 mg IV. Supply: 4 mg/mL.
   Answer: 0.5 mL.
   Why: (2,\text{mg} \times \frac{1,\text{mL}}{4,\text{mg}} = 0.5,\text{mL}).

3. Cefazolin 1 g IV. Supply: 2 g/100 mL premix.
   Answer: 50 mL.
   Why: (1,\text{g} \times \frac{100,\text{mL}}{2,\text{g}} = 50,\text{mL}).

4. Furosemide 40 mg IV. Supply: 10 mg/mL.
   Answer: 4 mL.

5. Amoxicillin 500 mg PO. Supply: 250 mg capsule.
   Answer: 2 capsules.

B. IV Drip Rate: gtt/min (5)

1. 1,000 mL NS over 8 hr, drop factor 15 gtt/mL.
   Answer: 31 gtt/min.
   Math: (\frac{1000 \times 15}{480} = 31.25 \rightarrow 31).

2. 500 mL over 4 hr, 10 gtt/mL.
   Answer: 21 gtt/min.
   Math: (\frac{500 \times 10}{240} = 20.8 \rightarrow 21).

3. 250 mL over 2 hr, 20 gtt/mL.
   Answer: 42 gtt/min.
   Math: (\frac{250 \times 20}{120} = 41.7 \rightarrow 42).

4. 125 mL over 1 hr, 15 gtt/mL.
   Answer: 31 gtt/min.
   Math: (\frac{125 \times 15}{60} = 31.25 \rightarrow 31).

5. 75 mL over 30 min, 60 gtt/mL (microdrip).
   Answer: 150 gtt/min.
   Math: (\frac{75 \times 60}{30} = 150).

C. IV Pump: mL/hr (5)

1. 100 mL over 30 min → 200 mL/hr.
2. 1,000 mL over 10 hr → 100 mL/hr.
3. 250 mL over 2.5 hr → 100 mL/hr.
4. 400 mL over 3 hr → 133 mL/hr (pump whole number).
5. 75 mL over 45 min (0.75 hr) → 100 mL/hr.

D. Weight-Based Titrations: mcg/kg/min (5)

Use mL/hr formula: (\frac{\text{mcg/kg/min} \times \text{kg} \times 60}{\text{mcg/mL}})

1. Dobutamine 5 mcg/kg/min for 80 kg. Bag: 400 mg/250 mL = 1600 mcg/mL.
   Answer: 15 mL/hr.
   Math: (\frac{5 \times 80 \times 60}{1600} = 15).

2. Dopamine 7.5 mcg/kg/min for 60 kg. Same bag 1600 mcg/mL.
   Answer: 17 mL/hr (16.9→17).

3. Norepinephrine 0.05 mcg/kg/min for 70 kg. Bag: 4 mg/250 mL = 16 mcg/mL.
   Answer: 13.1 mL/hr (≈ 13 mL/hr per policy).
   Math: (\frac{0.05 \times 70 \times 60}{16} = 13.125).

4. Epinephrine 0.02 mcg/kg/min for 50 kg. Bag: 1 mg/250 mL = 4 mcg/mL.
   Answer: 15 mL/hr.
   Math: (\frac{0.02 \times 50 \times 60}{4} = 15).

5. Milrinone 0.375 mcg/kg/min for 80 kg. Bag: 20 mg/100 mL = 200 mcg/mL.
   Answer: 9 mL/hr.
   Math: (\frac{0.375 \times 80 \times 60}{200} = 9).

Cross-link for pharmacology context and monitoring: Therapeutic Drug Levels (2025).

E. Pediatrics: mg/kg/dose (5)

Convert mg/kg to total mg, then to mL using the supply strength.

1. Amoxicillin 25 mg/kg/dose for 18 kg. Liquid 250 mg/5 mL (50 mg/mL).
   Answer: 9 mL.
   Math: (25 \times 18=450,\text{mg};\ 450/50=9,\text{mL}).

2. Acetaminophen 15 mg/kg/dose for 22 kg. Liquid 160 mg/5 mL (32 mg/mL).
   Answer: 10.3 mL (per policy).
   Math: (15 \times 22=330,\text{mg};\ 330/32=10.31,\text{mL}).

3. Ibuprofen 10 mg/kg/dose for 30 kg. Suspension 100 mg/5 mL (20 mg/mL).
   Answer: 15 mL.
   Math: (10 \times 30=300,\text{mg};\ 300/20=15,\text{mL}).

4. Cefdinir 14 mg/kg/day divided q12h for 20 kg → 7 mg/kg/dose. Suspension 250 mg/5 mL (50 mg/mL).
   Answer: 2.8 mL per dose.
   Math: (7 \times 20=140,\text{mg};\ 140/50=2.8,\text{mL}).

5. Azithromycin 10 mg/kg (Day 1) for 25 kg. Suspension 200 mg/5 mL (40 mg/mL).
   Answer: 6.25 mL.
   Math: (10 \times 25=250,\text{mg};\ 250/40=6.25,\text{mL}).

F. Insulin: Carb Ratio + Correction (2)

1. Carb ratio 1:15; 60 g carbs eaten. Correction factor 1:50; BG 210 mg/dL, target 120.
   Answer: 6 units total (4 meal + 2 correction*).
   Math: Meal (60/15=4); Correction ((210-120)/50=1.8 \rightarrow 2) per policy.
   *Follow your facility’s rounding rule for insulin.

2. Correction only: Factor 1:40; BG 275, target 120.
   Answer: 4 units.
   Math: ((275-120)/40=3.875 \rightarrow 4).

For safe titration thinking and lab tie-ins, review Electrolytes (2025): Patterns & Nurse Actions.

FAQs: Common Pitfalls in Nursing Math

How do I avoid errors with mcg/kg/min infusions?
Convert the bag to mcg/mL first, then plug into the mL/hr formula. Write every unit and cancel visibly.

When do I round up vs down on gtt/min?
Drops must be whole numbers. Follow your hospital policy—many round to the nearest whole drop.

What should I document for high-alert meds?
Typically: calculation steps, second RN verification, label details, and parameters you’ll monitor (MAP, SpO₂, rhythm, UOP).

Is there a “best” method for all math?
Yes—dimensional analysis. It’s consistent, transparent, and reduces mistakes under stress.

Key Takeaways

• Use dimensional analysis to cancel units and land on mL, gtt/min, mL/hr, or mcg/kg/min reliably.
• Memorize just a few formulas and know your bag concentration (mcg/mL).
• Follow rounding rules: whole gtt/min, pump mL/hr to whole, insulin per policy.
• Treat insulin, heparin, vasoactives as high-alert—get the required double-check.
• Prove safety with parameters: SpO₂, MAP, rhythm, UOP, mentation—then adjust.

Further Reading