Mathematics for the Anesthesia Provider

Comprehensive vocabulary and formulas covering medical mathematics, unit conversions, clinical calculations, and physiological indices for anesthesia providers.

Scientific Notation

A method of expressing very large or very small numbers where values are written as a decimal and multiplied by a factor of $10$.

PEMDAS

An acronym used to denote the correct order of operation: Parenthesis, Exponents, Multiplication, Division, Addition, and Subtraction.

1 Liter

Equivalent to $1000$ milliliters or $1000$ ccs.

1 Kilogram (in grams)

Equivalent to $1000$ grams.

1 Gram (in milligrams)

Equivalent to $1000$ milligrams.

1 Milligram (in micrograms)

Equivalent to $1000$ micrograms.

1 Microgram (in nanograms)

Equivalent to $1000$ nanograms.

1 Nanogram (in picograms)

Equivalent to $1000$ picograms.

1 Meter (in decimeters)

Equivalent to $10$ decimeters.

1 Decimeter (in centimeters)

Equivalent to $10$ centimeters.

1 Centimeter (in millimeters)

Equivalent to $10$ millimeters.

1 Atmosphere

Equivalent to $14.7\,lbs/inch^2$ or $760\,mmHg$.

1 Inch

Equivalent to $2.54$ centimeters.

1 Pound

Equivalent to $0.454$ kilograms.

1 Kilogram (in pounds)

Equivalent to $2.2$ pounds.

Drug Concentration Formula

$$\text{Concentration} = \frac{\text{Amount of Drug Added}}{\text{Volume of Solution}}$$

Infusion Rate Formula

$$\text{Rate} = \frac{\text{mcg/Kg/min} \times \text{weight(Kg)}}{\text{concentration}}$$

Percentage Concentration (e.g., 1% Lidocaine)

Means $1\,gram$ of drug has been added to sufficient diluent to make $100\,gm$ or $100\,mL$ of solution.

Percentage to Concentration Calculation

To calculate the concentration from a percentage, multiply the percentage by $1000$ (e.g., $1\% = 10\,mg/mL$).

Ratio Concentration (e.g., Epinephrine 1:1000)

Means $1\,gram$ of drug has been added to sufficient diluent to make $1000\,gm$ or $1000\,mL$ of solution ($1\,mg/mL$).

Standard Temperature reported in the OR

Temperature is always reported in centigrade ($^{\circ}C$).

Normal Body Temperature

$37^{\circ}$ centigrade.

Centigrade to Fahrenheit Formula

$$F = \frac{9}{5}C + 32$$

Fahrenheit to Centigrade Formula

$$C = \frac{5}{9}(F - 32)$$

Kelvin (K) Conversion

$K = C + 273$; always used for Ideal Gas Law calculations.

Body Mass Index (BMI) Formula

$\text{BMI} = \frac{Kg}{M^2}$ (Weight in kilograms divided by height in meters squared).

Underweight BMI Classification

$$< 18$$

Normal BMI Classification

$18$ to $< 24$

Overweight BMI Classification

$24$ to $< 30$

Obese BMI Classification

$30$ to $< 40$

Extreme Obesity BMI Classification

$40$ to $< 50$

Super Obesity BMI Classification

$50$ to $< 60$

Super-Super Obesity BMI Classification

$60$ and greater.

Mosteller Formula

A formula used to calculate Body Surface Area ($BSA$): $\text{BSA} = (\frac{\text{Height(cm)} \times \text{Weight(kg)}}{3600})^{0.5}$

Partial Pressure Formula

$$\text{Partial Pressure} = \text{Percent Concentration} \times 760\,mmHg$$

Gas Percentage Formula

$$\text{Percentage} = (\frac{\text{Partial Pressure}}{760\,mmHg}) \times 100$$

Mean Arterial Pressure (MAP) Formula

$$\text{MAP} = \frac{\text{Systolic BP} + 2(\text{Diastolic BP})}{3}$$

Systemic Perfusion Pressure

$\text{MAP} - \text{CVP}$ (Mean Arterial Pressure minus Central Venous Pressure).

Cerebral Perfusion Pressure (CPP)

$\text{MAP} - \text{ICP}$ (Mean Arterial Pressure minus Intracranial Pressure).

Coronary Perfusion Pressure (Left Ventricle)

$\text{Diastolic Pressure} - \text{LVEDP}$ (Left Ventricular End-Diastolic Pressure).

Systemic Vascular Resistance (SVR)

The resistance to blood flow in the peripheral vascular system, primarily determined by arteriolar tone.

Systemic Vascular Resistance (SVR) Formula

$$\text{SVR} = (\frac{\text{MAP} - \text{CVP}}{\text{CO}}) \times 80$$

Normal SVR Range

$700$ – $1600\,dyne\,sec/cm^{-5}$

pH Definition

The negative decimal logarithm of the hydrogen ion concentration in a solution.

Normal Physiologic pH

$7.35$ – $7.45$

Acidotic

A patient with a pH $< 7.35$.

Alkalotic

A patient with a pH $> 7.45$.

4:2:1 Formula

Method for hourly fluid requirement: $4\,mL/Kg/hr$ for the first $10\,Kg$, $2\,mL/Kg/hr$ for the second $10\,Kg$, and $1\,mL/Kg/hr$ for each kilogram thereafter.

Fluid Deficit Calculation

Hourly fluid requirement multiplied by the number of NPO hours.

Adult Blood Volume

$$70\,mL/Kg$$

Child Blood Volume

$$80\,mL/Kg$$

Infant Blood Volume

$$85\,mL/Kg$$

Neonate Blood Volume

$$90\,mL/Kg$$

Premature Infant Blood Volume

$$100\,mL/Kg$$

Maximum Allowable Blood Loss (MABL) Formula

$$\text{MABL} = \text{Weight(Kg)} \times \text{Blood Volume} \times (\frac{Hct_0 - Hct_1}{Hct_a})$$

Pediatric ETT Size Estimation Formula

$\text{ETT Size} = \frac{\text{Age} + 16}{4}$ (Size decreased by $0.5\,mm$ if cuffed).

Pediatric ETT Depth Estimation Formula

$$\text{Depth} = \frac{\text{Age}}{2} + 12$$

Pediatric LMA Size Estimation Formula

$\text{Size} = (\frac{kg}{5})^{0.5}$ (Round fraction up to the next size).

Pediatric Weight Estimation Formula

$$Kg = (\text{age} \times 3) + 7$$