Med math & clinical refresher

CRNA programs and interviews probe whether your medication math and critical-care fundamentals are sharp. This is the refresher — the calculations and concepts you'll be expected to know cold, with worked examples and practice.

Study aid, not a clinical reference. Use this to review for interviews and coursework — always follow your institution's protocols and verify every dose against an authoritative source before clinical use.

Conversions to know cold

1 kg = 1000 g · 1 g = 1000 mg · 1 mg = 1000 mcg

1 kg = 2.2 lb (lb ÷ 2.2 = kg)

1 L = 1000 mL · 1 tsp ≈ 5 mL

1% solution = 10 mg/mL

60 min = 1 hr (for mcg/min ↔ mcg/hr)

The calculations you must know

Desired over have

Volume = (desired dose ÷ available concentration) × volume per unit

Example: Order 40 mg; vial is 80 mg / 2 mL → (40 ÷ 80) × 2 = 1 mL.

Weight-based dose

Dose = ordered (mg/kg) × weight (kg)

Example: Propofol 2 mg/kg for a 70 kg patient → 2 × 70 = 140 mg.

IV drip rate (gtt/min)

gtt/min = (volume mL × drop factor gtt/mL) ÷ time in minutes

Example: 1000 mL over 8 h with a 15 gtt/mL set → (1000 × 15) ÷ 480 ≈ 31 gtt/min.

Infusion rate from a weight-based dose

mL/hr = (mcg/kg/min × weight kg × 60) ÷ concentration (mcg/mL)

Example: Norepinephrine 0.1 mcg/kg/min, 80 kg, bag 4 mg/250 mL (= 16 mcg/mL) → (0.1 × 80 × 60) ÷ 16 = 30 mL/hr.

Percent concentration

A 1% solution = 10 mg/mL (1 g per 100 mL)

Example: Lidocaine 2% = 20 mg/mL; so 5 mL holds 100 mg.

Practice problems

Work each one on paper first, then check yourself.

1. Order 25 mg; the vial is 50 mg/mL. How many mL do you draw up?

Show the work

25 ÷ 50 = 0.5 mL.

2. Succinylcholine 1.5 mg/kg for a 60 kg patient. What dose?

Show the work

1.5 × 60 = 90 mg.

3. Infuse 1000 mL over 6 h with a 10 gtt/mL set. Rate in gtt/min?

Show the work

(1000 × 10) ÷ 360 ≈ 28 gtt/min.

4. Dopamine 5 mcg/kg/min, 90 kg, bag 400 mg/250 mL (1600 mcg/mL). Rate in mL/hr?

Show the work

(5 × 90 × 60) ÷ 1600 = 27,000 ÷ 1600 ≈ 16.9 mL/hr.

5. How many mg of lidocaine are in 3 mL of a 2% solution?

Show the work

2% = 20 mg/mL → 20 × 3 = 60 mg.

6. Convert 0.5 g to mcg.

Show the work

0.5 g × 1000 = 500 mg × 1000 = 500,000 mcg.

Critical-care quick reference

Interview-ready

Hemodynamics

CO = HR × SV (normal ≈ 4–8 L/min)
MAP = DBP + ⅓ (SBP − DBP) — target ≥ 65 mmHg
SV depends on preload, afterload, and contractility

Vasoactive drugs

Pressors (raise SVR): norepinephrine, phenylephrine, vasopressin
Inotropes (raise contractility): dobutamine, milrinone, epinephrine
Dopamine is dose-dependent across receptors

ABG, four steps

1) pH — acidemia < 7.35, alkalemia > 7.45
2) PaCO₂ (respiratory) — normal 35–45 mmHg
3) HCO₃⁻ (metabolic) — normal 22–26 mEq/L
4) Compensation — which system is correcting?

Electrolytes to respect

K⁺ 3.5–5.0 — hyperkalemia → peaked T waves; hypokalemia → arrhythmias
Na⁺ 135–145 — correct slowly to avoid shifts
Mg²⁺ and Ca²⁺ matter for rhythm and contractility

Turn knowledge into answers

Clinical questions are a big part of CRNA interviews. Practice articulating your reasoning out loud — browse the clinical question bank, then get feedback from Coach or a full mock with Ana.

Clinical question bank ICU experience guide

For study and interview prep only. Doses, formulas, and reference ranges are summarized for review and may differ by source and institution — always confirm against an authoritative clinical reference and your program's protocols.