What is an Equation?

An equation says that two things are equal. It will have an equals sign "=" like this:

x

+

2

=

6

That equations says: what is on the left (x + 2) is equal to what is on the right (6)

So an equation is like a statement "this equals that"

(Note: this equation has the solution x=4, read how to solve equations.

What is a Formula?

A formula is a fact or rule that uses mathematical symbols.

It will usually have:

• an equals sign (=)
• two or more variables (x, y, etc) that stand in for values we don't know yet

It shows us how things are related to each other.

Example:

V stands for volume, l for length, w for width, and h for height.

 

When l=10, w=4, and h=5, then:

V = 10 × 4 × 5 = 200

These are all equations, but only some are formulas:

x = 2y - 7	Formula (relating x and y)
a2 + b2 = c2	Formula (relating a, b and c)
x/2 + 7 = 0	Not a Formula (just an equation)

Without the Equals

Sometimes a formula is written without the "=":

Example: The formula for the volume of a box is:

lwh

But in a way the "=" is still there, because we can write V = lwh if we want to.

Subject of a Formula

The "subject" of a formula is the single variable (usually on the left of the "=") that everything else is equal to.

Example: in the formula

s = ut + ½ at2

"s" is the subject of the formula

Changing the Subject

A very powerful thing that Algebra can do is to "rearrange" a formula so that another variable is the subject.

Respiratory Formulas:

Minute Ventilation (VE)
VE = Respiratory Rate x Tidal Volume
Alveolar Minute Ventilation (VA)
VA = (Tidal Volume – Deadspace) x Respiratory Rate
Airway Resistance (Raw)
Raw = (PIP – Plateau pressure) / Flow
Mean Airway Pressure (Paw)
Paw = ((Inspiratory Time x Frequency) / 60) x (PIP – PEEP) +PEEP
Work of Breathing (WOB)
WOB = Change in Pressure x Change in Volume
Alveolar-Arterial Oxygen Tension Gradient (P(A-a)O2) P(A-a)O2 = PAO2 – PaO2
Alveolar Oxygen Tension (PAO2)
PAO2 = (PB – PH2O) x FiO2 – (PaCO2 / 0.8)
Arterial/Alveolar Oxygen Tension (a/A) Ratio (a/A) Ratio = PaO2/PAO2
Arterial Oxygen Content (CaO2)
CaO2 = (Hb x 1.34 x SaO2) + (PaO2 x 0.003)
End-Capillary Oxygen Content (CcO2)
 5

CcO2 = (Hb x 1.34 x SaO2) + (PAO2 x 0.003)
Mixed Venous Oxygen Content (CvO2) CvO2 = (Hb x 1.34 x SvO2) + (PvO2 x 0.003)
Shunt Equation (QS/QT)
QS/QT = (CcO2 – CaO2) / (CcO2 – CvO2)
Modified Shunt Equation (QS/QT)
QS/QT = ((PAO2 – PaO2) x 0.003) / ((CaO2 – CvO2) + (PAO2 – PaO2) x 0.003)
Arterial-Mixed Venous Oxygen Content Difference (C(a-v)O2) C(a-v)O2 = CaO2 – CvO2
Oxygen-to-Air Entrainment Ratio (O2:Air) O2:Air=1:(100–FiO2)/(FiO2 –2)
Arterial Oxygen Saturation Estimation (SaO2) SaO2 = PaO2 + 30
PaO2/FiO2 Ratio (P/F Ratio) P/F Ratio = PaO2 / FiO2
Oxygenation Index (OI)
OI = ((Paw x FiO2) / PaO2) x 100
Oxygen Consumption (VO2) VO2 = Cardiac Output x C(a-v)O2
Oxygen Extraction Ratio (O2ER) O2ER = (CaO2 – CvO2) / CaO2
FiO2 Estimation for Nasal Cannula FiO2 = 20 + (4 x Liter Flow)
6

Oxygen Cylinder Duration
Duration = (Gauge Pressure x Tank Factor) / Liter Flow
Liquid Oxygen System Duration Duration = (344 x Liquid Weight) / Flow
Cardiac Index (CI)
CI = Cardiac Output / Body Surface Area
Cardiac Output (QT)
QT = Heart Rate x Stroke Volume
Cardiac Output (CO) Fick’s Method CO = (O2 Consumption / CaO2 – CvO2)
Cerebral Perfusion Pressure (CPP)
CPP = Mean Arterial Pressure – Intracranial Pressure
Mean Arterial Pressure (MAP)
MAP = (Systolic BP + (2 x Diastolic BP)) / 3
Stroke Volume (SV)
SV = Cardiac Output / Heart Rate
Maximum Heart Rate (HRmax) HRmax = 220 – Age
Heart Rate on an EKG Strip (HR)
HR = 300 / # of large boxes between R waves
Respiratory Quotient (RQ) RQ = VCO2 / VO2
Systemic Vascular Resistance (SVR)
SVR = (MAP – CVP) x (80 / Cardiac Output)
7

Pulmonary Vascular Resistance (PVR)
PVR = (MPAP – PCWP) x (80 / Cardiac Output)
Static Compliance (Cst)
Cst = Tidal Volume / (Plateau Pressure – PEEP)
Dynamic Compliance (Cdyn)
Cdyn = Tidal Volume / (Peak Pressure – PEEP)
Deadspace to Tidal Volume Ratio (VD/VT) (VD/VT) = (PaCO2 – PECO2) / PaCO2
Children Dosage Estimation
Child Dose = (Age / Age + 12) x Adult Dose
Infant Dosage Estimation
Infant Dose = (Age in Months / 150) x Adult Dose
Anion Gap
Anion gap = Na+ – (Cl- + HCO3-)
Body Surface Area (BSA)
BSA = ((4 x Body Weight) + 7) / (Body Weight + 90)
Elastance
Elastance = Change in Pressure / Change in Volume
Smoking Use Calculation (Pack Years)
Pack Years = (Packs Smoked per Day) x (Number of Years Smoked)
Suction Catheter Size Estimation Catheter Size = (Internal Diameter / 2) x 3
Endotracheal Tube Size Estimation in Children Tube Size = (Age + 16) / 4
8

Boyle’s Law
P1 xV1 =P2 xV2
Charles’ Law V1 /T1 =V2 /T2
Gay-Lussac’s Law P1/T1 = P2/T2
LaPlace’s Law
P = (2 x Surface Tension) / Radius
Celsius to Fahrenheit Temperature Conversion  ̊F = ( ̊C x 1.8) + 32
Fahrenheit Celsius Temperature Conversion  ̊C = ( ̊F – 32) x 1.8
Celsius to Kelvins Temperature Conversion K =  ̊C + 273
Helium/Oxygen Conversion (He/O2) Actual Flow = Given Flow Rate x Factor
Total Lung Capacity (TLC) TLC=IRV+VT +ERV+RV TLC = VC + RV
TLC = IC + FRC
Vital Capacity (VC) VC=IRV+VT +ERV VC = IC + ERV
VC = TLC – RV
Inspiratory Capacity (IC)
9

IC = IRV + VT IC = TLC – FRC IC = VC – ERV
Functional Residual Capacity (FRC) FRC = ERV + RV
FRC = TLC – IC
Time Constant (t)
t = Compliance x Resistance
Ideal Body Weight (IBW)
IBW = 50 kg + (2 x Number of Inches over 5 feet)
Tidal Volume (VT)
VT = Flow Rate x Inspiratory Time
Exhaled Tidal Volume (VT)
VT = Minute Ventilation / Frequency
Corrected Tidal Volume (VT)
VT = Expired Tidal Volume – Tube Volume
Pressure Support Ventilator Setting (PSV)
PSV = ((Peak Pressure – Plateau Pressure) / Set Flow) x Peak Flow
Rapid Shallow Breathing Index (RSBI) RSBI = Rate / Tidal Volume
Endotracheal Tube Size Estimation in Children Tube Size = (Age + 16) / 4
Minimum Flow Rate in Mechanical Ventilation
Flow Rate = Minute Ventilation x I:E Ratio Sum of Parts