Anesthesia Review

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Anesthesia calculations and formulas

Anesthesia Calculations and Formulas for AA Boards

Turn common anesthesia formulas into fast board-day decisions by pairing the equation with its units, assumptions, and the clinical clue that tells you when to use it.

For AA students reviewing an anesthesia formula sheet, calculation practice, or a fast review of board-relevant math.

What you will practice

  • Hemodynamics and perfusion
  • Oxygen content and delivery
  • Ventilation and gas equations
  • Fluid and blood-loss estimates
  • Drug concentrations and ratios
  • Weight-based dosing and unit conversion

What this resource helps you do

  • Recognize which formula a stem is testing
  • Keep units aligned before doing the arithmetic
  • Practice calculations with real question-bank examples

Anesthesia equations with unit-conversion checks called out

Learn the relationship first, then calculate. Check decimals and percentages, liters and deciliters, kilograms and pounds, and micrograms and milligrams before finalizing an answer.

Hemodynamics

  • MAP ≈ (SBP + 2 × DBP) ÷ 3 for a normal heart rate and waveform.
  • Cardiac output = heart rate × stroke volume; cardiac index = cardiac output ÷ body surface area.
  • Systemic vascular resistance = 80 × (MAP − CVP) ÷ cardiac output. The factor 80 converts to dyn·s·cm⁻⁵.

Oxygen content and delivery

  • CaO₂ = (1.34 × hemoglobin × SaO₂) + (0.003 × PaO₂). Enter saturation as a decimal, not a whole percentage.
  • DO₂ = cardiac output × CaO₂ × 10. The ×10 reconciles L/min with oxygen content reported per dL.
  • Oxygen extraction ratio = VO₂ ÷ DO₂. Interpret the number with the patient’s perfusion context.

Ventilation and gas equations

  • Minute ventilation = tidal volume × respiratory rate.
  • Alveolar ventilation = (tidal volume − dead-space volume) × respiratory rate.
  • Alveolar gas equation: PAO₂ = FiO₂ × (atmospheric pressure − water-vapor pressure) − PaCO₂ ÷ respiratory quotient. State the assumptions before calculating.

Fluids and blood loss

  • Pediatric 4-2-1 rule: 4 mL/kg/hr for the first 10 kg, 2 mL/kg/hr for the next 10 kg, then 1 mL/kg/hr above 20 kg.
  • Estimated blood volume = weight × age-appropriate blood-volume estimate.
  • Maximum allowable blood loss = estimated blood volume × (starting hematocrit − target hematocrit) ÷ starting hematocrit. Targets and replacement decisions remain clinical.

Concentrations and ratios

  • A 1% solution contains 1 g per 100 mL, which equals 10 mg/mL.
  • For a 1:X ratio, concentration in mg/mL = 1,000 ÷ X; concentration in mcg/mL = 1,000,000 ÷ X.
  • Convert the final answer back to the unit requested in the stem before selecting an option.

Weight-based dosing

  • Dose = ordered amount per kg × weight in kg.
  • Infusion delivery in mcg/min = mcg/kg/min × weight in kg; divide or multiply by 60 only when converting minutes and hours.
  • Use the body-weight convention specified by the question or protocol; total, ideal, lean, and adjusted body weight are not interchangeable.

This formula sheet is educational. Confirm constants, body-weight conventions, transfusion thresholds, and medication dosing against current references, institutional policy, and supervising anesthesiologist guidance.

Practice questions from this topic

An adult has just received 5,000 units of IV unfractionated heparin, and immediate complete reversal is required. Assuming negligible heparin elimination and using 1 mg protamine per 100 units heparin, what is the calculated protamine dose?

  1. 25 mg
  2. 50 mg
  3. 75 mg
  4. 100 mg

Correct answer: B

The calculation is 5,000 units ÷ 100 units/mg = 50 mg protamine. Administer slowly according to labeling, over a 10-minute period, with close monitoring for hypotension and hypersensitivity reactions. If time has elapsed since heparin administration, less protamine may be needed because heparin is cleared. Actual reversal should be guided by the clinical setting and coagulation assessment; an ACT value alone does not establish the residual heparin dose.

Source: Protamine Sulfate Injection prescribing information, Dosage and Administration. https://www.dailymed.nlm.nih.gov/dailymed/fda/fdaDrugXsl.cfm?setid=e1964129-33f4-4e4e-86e3-8e6a4e65bd83&type=display

An epinephrine-containing local anesthetic is labeled 1:200,000 epinephrine. What is the equivalent epinephrine concentration?

  1. 2.5 micrograms/mL
  2. 5 micrograms/mL
  3. 10 micrograms/mL
  4. 20 micrograms/mL

Correct answer: B

The ratio denotes 1 g in 200,000 mL: 1,000,000 micrograms / 200,000 mL = 5 micrograms/mL, equivalent to 0.005 mg/mL. This is the epinephrine concentration, separate from the local anesthetic concentration. Converting the ratio to an explicit mass per volume helps avoid confusion when checking a preparation.

Source: Lidocaine hydrochloride and epinephrine prescribing information, concentration table. https://dailymed.nlm.nih.gov/dailymed/drugInfo.cfm?setid=61d39a4f-f65d-4ded-8c2d-972d56c1f35a

Using the hourly 4-2-1 rule, what is the calculated full maintenance fluid rate for a 10-kg child?

  1. 20 mL/hr
  2. 40 mL/hr
  3. 50 mL/hr
  4. 60 mL/hr

Correct answer: B

The hourly 4-2-1 rule assigns 4 mL/kg/hr to the first 10 kg: 10 × 4 = 40 mL/hr. The daily Holliday-Segar formula gives 100 mL/kg/day for the first 10 kg, or 1000 mL/day; division by 24 gives about 41.7 mL/hr. The hourly rule is an approximation of that daily calculation. Calculated full maintenance is a starting estimate, not an automatic intraoperative prescription; adjust for clinical condition, other fluid inputs, losses and monitoring.

Source: Royal Children's Hospital, Intravenous Fluids. https://www.rch.org.au/clinicalguide/guideline_index/Intravenous_fluids/ RCH Paediatric IV Fluid Chart. https://www.rch.org.au/uploadedFiles/Main/Content/educationhub/180270-ViCTOR-Fluid-Chart-Paeds-web-WM.pdf

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Turn this review into practice

Apply dose and unit-conversion checks to worked questions in the 100-question NCCAA-style PDF.

Connect perfusion concepts to clinical reasoning with neuroanesthesia practice questions.

Schedule another review of missed calculations with the 30-day NCCAA study plan.

Frequently asked questions

Which anesthesia formulas are most useful for AA boards?

Start with MAP, cardiac output and index, SVR, oxygen content and delivery, minute and alveolar ventilation, pediatric maintenance fluids, maximum allowable blood loss, concentration ratios, and weight-based dosing.

Should I memorize every anesthesia formula?

Memorize the common relationships and units, but focus on recognizing which clinical clue calls for each formula. Understanding the variables is more durable than memorizing isolated symbols.

Are the calculation examples from the AA Review question bank?

Yes. The three previews use real AA Review question-bank records with their answer choices, explanations, and references.