Are you ready to learn about the Respiratory Therapy Formulas, Calculations, and Equations? I sure hope so because that is what this study guide is all about.

Here on this page, we’ve created an all-in-one stop that you can use as a reference for each and every formula that you’ll see as a Respiratory Therapy Student.

Some are hard. Some are easy.

But the good news is, I have faith that you can master them all if you set your mind to it. Practice (and lots of repetitions) makes perfect. So the more time you spend going through these formulas, the more likely it is that you’ll actually learn and memorize this information.

And, if you keep scrolling, we’ve even included some practice questions that can help you out as well. So if you’re ready, let’s go ahead and dive right in. 

? In general, these Formulas and Equations may vary from one publication to another. With that said, we have attempted to provide the ones that will be most helpful for the Respiratory Therapy Board Exams.

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Respiratory Therapy Formulas and Equations:

Minute Ventilation (VE)
VE = Respiratory Rate x Tidal Volume

Alveolar Minute Ventilation (VA)
VA = Respiratory Rate x (Tidal Volume – Deadspace)

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)
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)

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)

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 = (Body Weight in lbs / 150) x Adult Dose

Infant and Children Dosage Estimation (Fried’s Rule)
Infant or Child 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

Boyle’s Law
P1 x V1 = P2 x V2

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 to 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)
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

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In the next section, we’ve provided some additional practice questions so that you can practice and test your knowledge.

Going through practice questions is a technique that you can use to truly learn and memorize all of the equations.

Respiratory Therapy Calculations Practice Questions:

1. What is the most important calculation for the TMC Exam?
Ideal Body Weight (IBW) because it is needed to determine the patient’s initial tidal volume setting for mechanical ventilation. You will need to calculate a patient’s IBW multiple times on the TMC Exam.

We break this down even further inside of our Hacking the TMC Exam video course.

Inside the course, we share our best tips, tricks, and insights to boost your chances of passing the exam.

2. A patient receiving mechanical ventilation has a PIP of 60 cmH2O and a plateau pressure of 45 cmH2O. The ventilator flow rate is set at 60 L/min. What is the patient’s airway resistance?
15 cm H2O/L/sec

3. What is the A-a gradient and why is its significant?
The A-a gradient is the alveolar arterial oxygen gradient and represents the driving force of oxygen from the alveolar sac into the artery.

4. What is the normal value of the A-a gradient?
The A-a gradient is normally around 10 mmHg.

5. After obtaining a patient’s PFT results, they have a VC of 3.4, FRC of 5.8, and an ERV of 1.2. What is the patient’s TLC?
8.0

6. The physician has requested the dynamic compliance measurement for an adult patient who is receiving mechanical ventilation. This value can be obtained by dividing the patient’s tidal volume by what?
(PIP – PEEP)

7. The doctor has requested the static compliance measurement for an adult patient who is receiving mechanical ventilation. This value can be obtained by dividing the patient’s tidal volume by what?
(Pplat – PEEP)

8. What is a normal carbon dioxide production?
200 mL/min

9. What is the formula for alveolar partial pressure of carbon dioxide (PACO2)?
PACO2 = VCO2 X 0.863 / VA

10. What is the formula for Deadspace/Tidal Volume Ratio?
VD/VT = (PaCO2 – PeCO2) / PaCO2

11. What is the patient’s VD/VT if their PaCO2 is 40 mmHg with a mixed expired CO2 of 28 mm Hg?
0.3

12. What is the patient’s VD/VT if their PaCO2 is 58 mmHg with a mixed expired CO2 of 32 mmHg?
0.45

13. What is the formula for Boyle’s Law?
P1 x V1 = P2 x V2

14. What is the formula for Charles law?
V1 / T1 = V2 / T2

15. What is the formula for Combined Gas law?
(P1 x V1 ) / T1 = (P2 x V2 ) / T2

16. An H cylinder is half full (full = 2200) and the patient is receiving oxygen via nasal cannula at 3 L/min. How long will the cylinder last in minutes and in hours?
1151 minutes and 19.18 hours

17. An E cylinder is at 1400 psi and the flow rate is 2.5 L/minute. How many minutes will the tank last?
156.8 minutes

18. If a patient has smoked 2 packs of cigarettes daily for the past 35 years, what would their pack year history be?
70 pack years

19. What is the formula for Minute Ventilation?
MV = Respiratory Rate x Tidal Volume

20. A 36-year-old female patient has a respiratory rate of 12 and tidal volume of 500 mL. What is the minute ventilation?
6 L/min

21. A 78-year-old male patient with a history of COPD has a respiratory rate of 20 and tidal volume of 650 mL. What would his minute volume be in Liters?
13 L/min

22. What is the formula for partial pressure?
Partial Pressure = Barometric Pressure x Fractional concentration of Gas

23. What is the PO2 in dry air at a barometric pressure of 760 mmHg?
760 x 0.21 = 159.6

24. How do you calculate the PO2 of humidified air?
Partial Pressure = (Barometric Pressure – Water Vapor Pressure) x Fractional concentration of gas

25. What is the PO2 of humidified tracheal air?
(760 – 47) x 0.21 = 149.7

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26. If the alveolar gas has a PO2 of 100 mmHg, what is the PO2 of the pulmonary capillary blood?
100 mmHg

27. In air, what is the mol percentage of Nitrogen?
78%

28. In air, what is the mol percentage of oxygen?
21%

29. In air, what is the mol percentage of Argon?
1%

30. At a normal body temperature, what is the partial pressure of water vapor?
47 mmHg

31. PA and Pa in the alveolar gas equation represents the gas pressures in what locations?
PA represents the gas pressure in the alveoli. Pa represents the gas pressure in the artery.

32. In the alveolar gas equation, what does R represent?
R represents the V:Q ratio of carbon dioxide and is dependent upon the type of metabolism that a person is undergoing.

33. What two factors determine cardiac output?
Heart Rate and Stroke volume

34. What is the formula for Cardiac Index?
CI= Cardiac Output / BSA

35. A Cardiac Index below what value can be life-threatening?
< 2.2

36. What is the formula for Stroke Index?
SI = Stroke Volume / BSA

37. What is the Fick Equation?
CO = VO2 / CaO2 – CvO2

38. What does the Deadspace-to-Tidal Volume Ratio measure?
It measures the percentage of the tidal volume that is dead space which does not participate in gas exchange.

39. What is the normal value for (Vd/Vt)?
20 to 40% (or up to 60% for patients on the ventilator)

40. What is the formula to Vd/Vt?
Vd/Vt = (PaCO2 – PeCO2 / PaCO2) x 100

41. What is the average PCO2 of the exhaled air that can be measured by a capnograph?
PeCO2

42. If you know the patient’s tidal volume but the deadspace must be calculated, what formula should be used?
Vd/Vt x Vt

43. What is the tubing compliance when the measured volume is 100 mL and the static pressure is 65 cm H2O?
1.5 mL/cm H2O

44. While setting up a new patient on the ventilator the plateau pressure is 47 cm H2O and the tidal volume is set at 100 mL. The average PIP reached during the delivery of a breath is 28 cm H2O. What is the amount of volume that was lost in the ventilator tubing?
60 mL

45. What is the average tidal volume for a patient who has a minute ventilation of 10 L/min and rate 12/min?
833 mL

46. What is inspiratory time when the tidal volume is set at 800 mL and a flow rate of 40 L/min?
1.2 seconds

47. What is the I:E ratio for a ventilator that is set to deliver a tidal volume of 850 mL at a frequency of 15/min with a flow rate of 45 L/min?
1:2.5

48. What is the expiratory time when the rate is set to 25/min and the inspiratory time is 0.75 seconds?
1.65 seconds

49. What flow rate would be necessary in order to deliver a tidal volume of 600 mL with a constant waveform at a respiratory rate of 15/min with an I:E of 1:4?
45 L/min

50. What tidal volume setting for mechanical ventilation would be appropriate for a 5’2″ female patient with normal lungs?
400 mL

51. How should the initial minute ventilation setting be adjusted for an adult patient who has a body temperature of 40 °C?
Increase it by 30% because the minute ventilation would have to be increased by 10% for each degree above 37° C.

52. A 52-year-old female patient has been smoking 1.5 packs of cigarettes per day for 30 years. Her smoking history would be recorded as:
45 pack-years

53. A patient is receiving 3 L/min of oxygen from an E-cylinder at 1200 psi. What is the approximate duration of flow?
112 minutes

54. A 5-foot, 6-inch-tall 130-lb. female patient with normal lungs has a tidal volume of 480 mL and is breathing at a rate of 12 breaths/min. What is her alveolar ventilation?
4.20 L/min

55. A patient 43-year-old male patient is receiving volume controlled ventilation at a rate of 12/min. The expiratory time is 3.30 seconds. What is the inspiratory time?
1.70 seconds

Example TMC Practice Question:

A 61-year-old male patient who weighs 165 lbs is receiving volume control A/C ventilation with a tidal volume of 500 mL. He has the following data:

PEEP 5
PIP 35
Pplat 30

What is the patient’s static compliance?

A. 16.7 mL/cm H2O
B. 20.0 mL/cm H2O
C. 25.7 mL/cm H2O
D. 30.0 mL/cm H2O

For the TMC Exam, you need to know how to calculate both static and dynamic compliance. That means you should know the formulas for both.

  • Static Compliance = Exhaled VT / (Pplat – PEEP)
  • Dynamic Compliance = Exhaled VT / (PIP – PEEP)

So for this one, the question asks for the patient’s static compliance. To get the answer, all you have to do is plug the numbers in the formula.

Static Compliance = 500 / (30 – 5)
Static Compliance = 20

The correct answer is: B. 20.0 mL/cm H2O

This practice question was actually taken from our TMC Test Bank, which is a massive bank of premium practice questions that cover every topic that students must know in order to pass the TMC Exam.

As you can see, each question comes with a detailed rationale that explains exactly why the answer is correct. This is critical when it comes to actually learning the information.

If you’re interested in getting access to more practice questions like this one, definitely consider checking it out.

Final Thoughts

So there you have it. You now have access to all of the most important Respiratory Therapy Formulas, Calculations, and Equations. You will probably be required to learn most of these in Respiratory Therapy School. Not to mention, some of them will be on the TMC Exam as well.

You know what that means, right?

It means that now it’s up to you to learn and master this information. I definitely recommend going through each formula several times until the information sticks. Your future self will be glad that you did.

No worries, I have faith in you.

Keep working and studying hard and you will be just fine. Thank you so much for reading all the way to the end. I wish you the best of luck on your journey, and as always, breathe easy my friend.

Don’t forget to grab your FREE digital copy of this study guide now — no strings attached.

References

The following are the sources that were used while doing research for this article:

  • Maury, Bertrand. The Respiratory System in Equations (MS&A). 2013th ed., Springer, 2013. [Link]
  • Chang, David. Respiratory Care Calculations. 4th ed., rtexam, 2018. [Link]
  • Chang, David. Clinical Application of Mechanical Ventilation. 4th ed., Cengage Learning, 2013. [Link]
  • Faarc, Kacmarek Robert PhD Rrt, et al. Egan’s Fundamentals of Respiratory Care. 11th ed., Mosby, 2016. [Link]

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