Respiratory Math Calculations and Practice Questions (2025)

Believe it or not, math plays an essential role in respiratory therapy, serving as a foundation for various diagnostic and therapeutic procedures.

In fact, respiratory therapy students are required to learn various formulas and calculations throughout their educational journey, including respiratory therapy school, and for the TMC Exam.

This guide provides a list of practice questions on the various formulas, calculations, and equations required for aspiring respiratory therapists.

Is Math Required for Respiratory Therapists?

Yes, respiratory therapists need math skills for essential calculations in patient care. They must accurately determine medication dosages, oxygen flow rates, ventilator settings, and arterial blood gas interpretations.

These calculations help ensure proper treatment, prevent complications, and optimize patient outcomes. While advanced math isn’t required, a solid understanding of basic algebra, ratios, and unit conversions is necessary.

Respiratory Therapy Math Calculation Practice Questions

1. Are math and calculations required in respiratory therapy school?
Yes, respiratory therapy students are required to learn specific calculations that are necessary for becoming a respiratory therapist. In addition, some calculations are also required for the TMC Exam.

2. What is the most important calculation for the TMC Exam?
Ideal body weight (IBW) is the most important formula for the TMC Exam because it is used to calculate a patient’s initial tidal volume setting for mechanical ventilation. This calculation is performed several times on the TMC Exam.

3. 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

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

5. After obtaining a patient’s PFT results, you find that 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 the formula for alveolar partial pressure of carbon dioxide (PACO2)?
PACO2 = VCO2 x 0.863 / VA

9. What is the formula for calculating minute ventilation (VE)?
VE = Respiratory Rate x Tidal Volume

10. What is the formula for calculating alveolar minute ventilation (VA)?
VA = Respiratory Rate x (Tidal Volume – Deadspace)

11. What is the formula for airway resistance (Raw)?
Raw = (PIP – Plateau pressure) / Flow

12. What is the formula for calculating mean airway pressure (Paw)
Paw = ((Inspiratory Time x Frequency) / 60) x (PIP – PEEP) + PEEP

13. What is the formula for work of breathing (WOB)?
WOB = Change in Pressure x Change in Volume

14. What is the formula for alveolar-arterial oxygen tension gradient (P(A-a)O2)?
P(A-a)O2 = PAO2 – PaO2

15. What is the formula for alveolar oxygen tension (PAO2)?
PAO2 = (PB – PH2O) x FiO2 – (PaCO2 / 0.8)

16. What is the formula for the arterial/alveolar oxygen tension (a/A) ratio?
(a/A) Ratio = PaO2/PAO2

17. What is the formula for arterial oxygen content (CaO2)?
CaO2 = (Hb x 1.34 x SaO2) + (PaO2 x 0.003)

18. What is the formula for end-capillary oxygen content (CcO2)?
CcO2 = (Hb x 1.34 x SaO2) + (PAO2 x 0.003)

19. What is the formula for mixed venous oxygen content (CvO2)?
CvO2 = (Hb x 1.34 x SvO2) + (PvO2 x 0.003)

20. What is the formula for the shunt equation (QS/QT)?
QS/QT = (CcO2 – CaO2) / (CcO2 – CvO2)

21. What is the formula for the modified shunt equation (QS/QT)?
QS/QT = ((PAO2 – PaO2) x 0.003) / ((CaO2 – CvO2) + (PAO2 – PaO2) x 0.003)

22. What is the formula for arterial-mixed venous oxygen content difference (C(a-v)O2)?
C(a-v)O2 = CaO2 – CvO2

23. What is the formula for the oxygen-to-air entrainment ratio (O2:Air)?
O2:Air = 1 : (100 – FiO2) / (FiO2 – 2)

24. What is the formula for arterial oxygen saturation estimation (SaO2)?
SaO2 = PaO2 + 30

25. What is the formula for the PaO2/FiO2 ratio?
P/F Ratio = PaO2 / FiO2

26. What is the formula for the deadspace/tidal volume ratio?
VD/VT = (PaCO2 – PeCO2) / PaCO2

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

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

29. What is the formula for the oxygenation index (OI)
OI = ((Paw x FiO2) / PaO2) x 100

30. What is the formula for oxygen consumption (VO2)?
VO2 = Cardiac Output x C(a-v)O2

31. What is the formula for the oxygen extraction ratio (O2ER)?
O2ER = (CaO2 – CvO2) / CaO2

32. What is the formula for the FiO2 estimation when a patient is wearing a nasal cannula?
FiO2 = 20 + (4 x Liter Flow)

33. What is the formula for calculating oxygen cylinder duration?
Duration = (Gauge Pressure x Tank Factor) / Liter Flow

34. What is the formula for calculating the duration of a liquid oxygen system?
Duration = (344 x Liquid Weight) / Flow

35. What is the formula for cardiac output (QT)?
QT = Heart Rate x Stroke Volume

36. What is the formula for calculating cardiac output using Fick’s method?
CO = (O2 Consumption / CaO2 – CvO2)

37. What is the formula for cerebral perfusion pressure (CPP)?
CPP = Mean Arterial Pressure – Intracranial Pressure

38. What is the formula for mean arterial pressure (MAP)?
MAP = (Systolic BP + (2 x Diastolic BP)) / 3

39. What is the formula for stroke volume (SV)?
SV = Cardiac Output / Heart Rate

40. What is the formula for calculating a patient’s maximum heart rate (HRmax)?
HRmax = 220 – Age

41. What is the formula for determining heart rate by looking at an EKG strip?
HR = 300 / # of large boxes between R waves

42. What is the formula for combined gas law?
(P1 x V1 ) / T1 = (P2 x V2 ) / T2

43. An H cylinder is half full (full = 2,200), and the patient is receiving oxygen via nasal cannula at 3 L/min. How long will the cylinder last in minutes and in hours?
1,151 minutes and 19.18 hours

44. An E cylinder is at 1,400 psi, and the flow rate is 2.5 L/min. How many minutes will the tank last?
156.8 minutes

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

46. What is the formula for minute ventilation?
MV = Respiratory Rate x Tidal Volume

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

48. A 78-year-old male patient with a history of COPD has a respiratory rate of 20 and a tidal volume of 650 mL. What is the minute volume?
13 L/min

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

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

51. How do you calculate the PO2 of humidified air?
Partial Pressure = (Barometric Pressure – Water Vapor Pressure) x Fractional Concentration of Gas

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

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

54. What is the formula for respiratory quotient (RQ)?
RQ = VCO2 / VO2

55. What is the formula for systemic vascular resistance (SVR)?
SVR = (MAP – CVP) x (80 / Cardiac Output)

56. What is the formula for pulmonary vascular resistance (PVR)?
PVR = (MPAP – PCWP) x (80 / Cardiac Output)

57. What is the formula for static compliance (Cst)?
Cst = Tidal Volume / (Plateau Pressure – PEEP)

58. What is the formula for dynamic compliance (Cdyn)?
Cdyn = Tidal Volume / (Peak Pressure – PEEP)

59. What is the formula for the deadspace to tidal volume ratio (VD/VT)?
(VD/VT) = (PaCO2 – PECO2) / PaCO2

60. What is the formula for estimating the appropriate medication dosage for children?
Child Dose = (Age / Age + 12) x Adult Dose

61. What is the formula for estimating the appropriate medication dosage for infants?
Infant Dose = (Body Weight in lbs / 150) x Adult Dose

62. What is the formula for estimating the appropriate medication dosage for infants and children using Fried’s rule?
Infant or Child Dose = (Age in Months / 150) x Adult Dose

63. What is the formula for calculating the anion gap?
Anion Gap = Na+ – (Cl- + HCO3-)

64. What is the formula for calculating body surface area (BSA)?
BSA = ((4 x Body Weight) + 7) / (Body Weight + 90)

65. What is the formula for elastance?
Elastance = Change in Pressure / Change in Volume

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

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

68. What two factors determine cardiac output?
Heart rate (HR) and stroke volume (SV)

69. What is the formula for cardiac index (CI)?
CI= Cardiac Output / BSA

70. A cardiac index below what value can be life-threatening?
Less than 2.2

71. What is the formula for stroke index?
SI = Stroke Volume / BSA

72. What is the Fick equation?
CO = VO2 / CaO2 – CvO2

73. What does the deadspace-to-tidal volume ratio measure?
It measures the percentage of deadspace in the tidal volume that does not participate in gas exchange.

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

75. What is the formula for estimating the proper suction catheter size?
Catheter Size = (Internal Diameter / 2) x 3

76. What is the formula for estimating the proper endotracheal tube size for children?
Tube Size = (Age + 16) / 4

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

78. What is the formula for Charles’s law?
V1 / T1 = V2 / T2

79. What is the formula for Gay-Lussac’s law?
P1 / T1 = P2 / T2

80. What is the formula for LaPlace’s law?
P = (2 x Surface Tension) / Radius

81. What is the formula for converting Celsius to Fahrenheit?
˚F = (˚C x 1.8) + 32

82. What is the formula for converting Fahrenheit to Celsius?
˚C = (˚F – 32) / 1.8

83. What is the formula for converting Celsius to Kelvin?
K = ˚C + 273

84. What is the formula for calculating the actual flow for heliox (He/O2)?
Actual Flow = Given Flow Rate x Factor

85. What are the formulas for total lung capacity (TLC)?
TLC = IRV + VT + ERV + RV
TLC = VC + RV
TLC = IC + FRC

86. What are the formulas for vital capacity (VC)?
VC = IRV + VT + ERV
VC = IC + ERV
VC = TLC – RV

87. What are the formulas for inspiratory capacity (IC)?
IC = IRV + VT
IC = TLC – FRC
IC = VC – ERV

88. What are the formulas for functional residual capacity (FRC)?
FRC = ERV + RV
FRC = TLC – IC

89. What is the formula for the time constant (t)?
t = Compliance x Resistance

90. What is the formula for ideal body weight (IBW)?
IBW = 50 kg + (2 x Number of Inches over 5 feet)

91. What is the formula for calculating tidal volume (VT)?
VT = Flow rate x Inspiratory Time

92. What is the formula for calculating exhaled tidal volume (VT)?
VT = Minute Ventilation / Frequency

93. What is the formula for the corrected tidal volume (VT)?
VT = Expired Tidal Volume – Tube Volume

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

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

96. What is the tubing compliance when the measured volume is 100 mL and the static pressure is 65 cmH2O?
1.5 mL/cm H2O

97. While setting up a new patient on the ventilator, the plateau pressure is 47 cmH2O, and the tidal volume is set at 100 mL. The average PIP reached during a breath delivery is 28 cmH2O. What amount of volume was lost in the ventilator tubing?
60 mL

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

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

100. 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

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

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

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

104. What is the formula for determining the level of pressure support ventilation (PSV)?
PSV = ((Peak Pressure – Plateau Pressure) / Set Flow) x Peak Flow

105. What is the formula for the rapid shallow breathing index (RSBI)?
RSBI = Rate / Tidal Volume

106. What is the formula for calculating the minimum flow rate during mechanical ventilation?
Minimum Flow Rate = Minute Ventilation x I:E Ratio Sum of Parts

107. What is Winters’ formula for calculating the expected PaCO2 range?
Expected PaCO2 = (1.5 x HCO3-) + 8 ± 2

108. How should the initial minute ventilation setting be adjusted for an adult patient with 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.

109. A 52-year-old female patient has been smoking 1.5 packs of cigarettes per day for 30 years. What is her smoking history in pack year?
45 pack years

110. A patient is receiving 3 L/min of oxygen from an E-cylinder at 1,200 psi. What is the approximate duration of flow?
112 minutes

111. A female patient who is 5’6″ and weighs 130 lbs has normal lungs, 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

112. A 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

113. A patient has a respiratory rate of 12, tidal volume of 450 mL, deadspace of 147 mL, and a vital capacity of 1.2 L. What is the alveolar minute ventilation?
3.6 L/min

114. A patient is receiving 2 L/min of oxygen from an H-cylinder at 1,500 psi. What is the approximate duration of flow?
39 hours, 15 minutes

115. What size suction catheter is most appropriate for an infant who is intubated with a size 3.0 mm endotracheal tube?
5 Fr

116. What is the formula for calculating inspiratory time (Ti) during volume-controlled ventilation?
Ti = Tidal Volume / Flow Rate

117. What is the formula for calculating expiratory time (Te)?
Te = Total Cycle Time – Inspiratory Time

118. What is the formula for calculating total cycle time?
Total Cycle Time = 60 / Respiratory Rate

119. A patient has a respiratory rate of 16 breaths per minute. What is their total cycle time?
Total Cycle Time = 60 / 16 = 3.75 seconds

120. What is the formula for determining the compliance of a ventilator circuit?
Circuit Compliance = Volume / Pressure

121. A ventilator circuit delivers 50 mL of volume for every 2 cmH2O of pressure. What is the circuit compliance?
Circuit Compliance = 50 / 2 = 25 mL/cmH2O

122. What is the formula for estimating a patient’s anatomic deadspace (VDanat)?
VDanat ≈ 1 mL per pound of ideal body weight (IBW)

123. A 70 kg patient is estimated to have how much anatomic deadspace?
VDanat ≈ 1 mL per pound of IBW → 70 kg ≈ 154 lbs → 154 mL

124. What is the formula for calculating time constant (τ) in mechanical ventilation?
Time Constant (τ) = Compliance x Resistance

125. A patient has a compliance of 30 mL/cmH2O and an airway resistance of 5 cmH2O/L/sec. What is their time constant?
τ = 30 x 5 = 150 msec (0.15 sec)

126. What is the formula for calculating alveolar gas equation (PAO2)?
PAO2 = (PB – PH2O) x FiO2 – (PaCO2 / RQ)

127. What is the oxygen content of venous blood (CvO2)?
CvO2 = (Hb x 1.34 x SvO2) + (PvO2 x 0.003)

128. What is the formula for oxygen pulse?
Oxygen Pulse = VO2 / Heart Rate

129. What is the formula for calculating alveolar ventilation (VA)?
VA = (Tidal Volume – Deadspace) x Respiratory Rate

130. A patient has a tidal volume of 500 mL, a deadspace of 150 mL, and a respiratory rate of 12. What is their alveolar ventilation?
VA = (500 – 150) x 12 = 4,200 mL/min or 4.2 L/min

131. What is the formula for oxygen delivery (DO2)?
DO2 = Cardiac Output x CaO2 x 10

132. A patient has a cardiac output of 5 L/min and an arterial oxygen content (CaO2) of 20 mL O2/dL. What is their oxygen delivery?
DO2 = 5 x 20 x 10 = 1,000 mL O2/min

133. What is the formula for determining alveolar ventilation to minute ventilation ratio?
VA / VE = (VT – VD) / VT

134. A patient has a tidal volume of 600 mL and a deadspace volume of 150 mL. What is their alveolar ventilation to minute ventilation ratio?
VA / VE = (600 – 150) / 600 = 0.75 (or 75%)

135. What is the formula for calculating static compliance (Cst)?
Cst = Tidal Volume / (Plateau Pressure – PEEP)

136. A ventilated patient has a tidal volume of 500 mL, a plateau pressure of 25 cmH2O, and a PEEP of 5 cmH2O. What is their static compliance?
Cst = 500 / (25 – 5) = 25 mL/cmH2O

137. What is the formula for dynamic compliance (Cdyn)?
Cdyn = Tidal Volume / (PIP – PEEP)

138. A patient on mechanical ventilation has a tidal volume of 450 mL, a PIP of 30 cmH2O, and a PEEP of 10 cmH2O. What is their dynamic compliance?
Cdyn = 450 / (30 – 10) = 22.5 mL/cmH2O

139. What is the formula for calculating inspiratory flow rate?
Flow Rate = (Tidal Volume / Inspiratory Time) x 60

140. A ventilator is set with a tidal volume of 600 mL and an inspiratory time of 1.2 seconds. What is the inspiratory flow rate?
Flow Rate = (600 / 1.2) x 60 = 30 L/min

141. What is the formula for the I:E ratio?
I:E Ratio = Inspiratory Time : (Total Cycle Time – Inspiratory Time)

142. A patient has a total cycle time of 4 seconds and an inspiratory time of 1 second. What is the I:E ratio?
I:E = 1 : (4 – 1) = 1:3

143. A patient has a pH of 7.30, PaCO2 of 55 mmHg, and HCO3 of 24 mEq/L. What acid-base disorder is present?
Uncompensated respiratory acidosis

144. What is the formula for the anion gap?
Anion Gap = Na+ – (Cl- + HCO3-)

145. A patient has a sodium of 140 mEq/L, chloride of 100 mEq/L, and bicarbonate of 24 mEq/L. What is their anion gap?
Anion Gap = 140 – (100 + 24) = 16

146. What is the expected PaCO2 in metabolic acidosis according to Winter’s formula?
Expected PaCO2 = (1.5 x HCO3-) + 8 ± 2

147. A patient has a bicarbonate (HCO3-) of 18 mEq/L. What is the expected PaCO2?
Expected PaCO2 = (1.5 x 18) + 8 ± 2 = 35 ± 2 mmHg

148. What is the formula for calculating oxygenation index (OI)?
OI = (Mean Airway Pressure x FiO2 x 100) / PaO2

149. A patient has a mean airway pressure of 20 cmH2O, an FiO2 of 0.50, and a PaO2 of 100 mmHg. What is their oxygenation index?
OI = (20 x 0.50 x 100) / 100 = 10

150. What is the formula for calculating shunt fraction (Qs/Qt)?
Qs/Qt = (CcO2 – CaO2) / (CcO2 – CvO2)

Final Thoughts

Mastering the mathematical aspects of respiratory therapy is a pivotal step in preparing for a successful career in the field of respiratory care.

The practice questions provided in this guide are designed to reinforce your understanding of essential formulas, calculations, and equations, ensuring you’re well-equipped for both the TMC Exam and the practical challenges of respiratory therapy school.

Embracing these mathematical principles will not only aid in your academic achievements but also enhance your ability to provide top-notch patient care in your professional journey.

For more practice problems and explanations, check out our Formulas and Calculations (Premium Course) to gain access to step-by-step breakdowns for all 65+ essential respiratory care formulas.