Oxygen therapy & respiratory calculations: practice problems with step-by-step solutions
Also called: oxygen tank duration · P/F ratio · oxygen delivery
Free Oxygen therapy & respiratory calculations practice problems with diagrams, hints and full worked solutions. New values every time, at three levels: FiO₂, cylinder contents and minute ventilation, cylinder duration, P/F ratio and oxygen content, oxygen delivery, ventilation targets and ARDS severity.
Free practice problemEasy
Practice exercise (made-up values, not clinical guidance). The gauge on a size E oxygen cylinder reads 2050 psi. Its cylinder factor is 0.28 L/psi. How many litres V can be used before the safe residual of 200 psi is reached?
Oxygen is prescribed like a drug: a device, a flow or a concentration, and a target saturation. Nurses check that a portable cylinder will last a transfer, estimate the oxygen a patient breathes, and follow how well the lungs work.
This topic covers:
Delivery: FiO₂ from a nasal cannula, cylinder contents and duration.
Ventilation: minute and alveolar ventilation and lung-protective tidal volumes.
Oxygenation: the P/F ratio with the Berlin ARDS grades, oxygen content and oxygen delivery, and the ROX index.
2FiO₂ and cylinder duration
Room air is 21% oxygen. A nasal cannula adds roughly 4% per L/min, used from 1 to 6 L/min, so FiO₂ ≈ 21% + 4% × flow. The real value depends on how the patient breathes. In formulas, FiO₂ is a fraction: 40% = 0.40.
A cylinder’s usable gas is the pressure above a safe reserve times its cylinder factor (litres per psi): D 0.16, E 0.28, H 3.14. The usual safe residual is 200 psi.
Minute ventilation in a resting adult is about 5–8 L/min. The air left in the airways, the dead space of about 150 mL, never reaches the alveoli, so fast shallow breathing wastes a larger share of every breath.
Lung-protective ventilation sets about 6 mL per kg of predicted body weight (PBW), which depends only on sex and height:
PBW men = 50 + 0.91 × (cm − 152.4) PBW women = 45.5 + 0.91 × (cm − 152.4)
Self-check A patient breathes 20 times a minute with a tidal volume of 350 mL and a dead space of 150 mL. What is the alveolar ventilation?
4 L/min
4000 L/min
6.85 L/min
7 L/min
Answer: 4 L/min. (350 − 150) × 20 = 4000 mL/min = 4 L/min. 7 L/min is the minute ventilation, which includes the dead space.
4P/F ratio and ARDS
The P/F ratio is PaO₂ in mmHg divided by FiO₂ as a fraction. With PaO₂ in kPa, multiply by 7.5 first.
The Berlin definition grades ARDS only when the PEEP or CPAP is at least 5 cmH₂O and the other criteria are met (onset within a week, bilateral opacities, not fully explained by heart failure):
mild: 200 < P/F ≤ 300 mmHg;
moderate: 100 < P/F ≤ 200 mmHg;
severe: P/F ≤ 100 mmHg.
Self-check PaO₂ 78 mmHg on FiO₂ 0.6 with a PEEP of 10 cmH₂O. Which Berlin grade fits?
Mild
Moderate
Not ARDS range
Severe
Answer: Moderate. 78/0.6 = 130 mmHg, which lies above 100 and up to 200: moderate.
5Oxygen content and delivery
CaO₂ = 1.34 × Hb × SaO₂ + 0.003 × PaO₂
Hb is in g/dL (divide g/L by 10), SaO₂ is a fraction and PaO₂ is in mmHg. The answer is in mL of oxygen per dL of blood, normally about 18–20. Almost all of it is bound to haemoglobin.
DO₂ = CaO₂ × cardiac output × 10
The factor 10 turns dL into L, giving mL/min; about 1000 mL/min is normal at rest. A low haemoglobin lowers the delivery as much as a low saturation does.
The ROX index, (SpO₂/FiO₂)/respiratory rate, follows patients on high-flow nasal oxygen; in studies, values of 4.88 or more were linked with success.
6Common mistakes
Forgetting the safe residual, or rounding a cylinder time up.
Using the factor of another cylinder size.
Putting FiO₂ in as a percentage, or SaO₂ as 97 instead of 0.97.
Using the actual body weight for a lung-protective tidal volume.
Grading ARDS without checking that the PEEP is at least 5 cmH₂O.
Forgetting the × 10 in oxygen delivery.
7How exam questions look
Easy: FiO₂, cylinder contents and minute ventilation. Estimate the FiO₂ of a nasal cannula or the flow for a target, the usable litres in a cylinder and the minute ventilation.
Medium: cylinder duration, P/F ratio and oxygen content. Work out how long a cylinder lasts, grade ARDS by the P/F ratio, and calculate CaO₂ and alveolar ventilation.
Hard: oxygen delivery, ventilation targets and ARDS severity. Calculate DO₂, the highest flow for a transfer, a tidal volume from predicted body weight, the ROX index, and grade ARDS with kPa values or a low PEEP.
Practice exercise (made-up values, not clinical guidance). A patient receives oxygen by nasal cannula at 2 L/min. Using FiO₂ ≈ 21% + 4% per L/min, estimate the inspired oxygen FiO₂ in percent.
2 L/min
Find FiO₂(%)
Show hints
Room air already contains 21% oxygen.
Each L/min adds about 4%.
4·2 = 8%.
Show the answer and the step-by-step solution
Estimating FiO₂: room air is 21% oxygen. A nasal cannula adds roughly 4% for every L/min, used from 1 to 6 L/min, so FiO₂ ≈ 21% + 4% × flow (about 25–45%). The real value depends on the breathing pattern. For calculations FiO₂ is used as a fraction: 40% = 0.40.
Estimate
FiO₂ ≈ 21 + 4·2 = 29 %
= 0.29 as a fraction
Answer
FiO₂ = 29 %
Example 2Medium
Practice exercise (made-up values, not clinical guidance). A patient breathes 22 times a minute with a tidal volume of 390 mL. The anatomical dead space is 160 mL. Find the alveolar ventilation V̇A in L/min.
VT 390 mL22/minVD 160 mL
Find V̇A(L/min)
Show hints
Only the air beyond the dead space reaches the alveoli.
390 − 160 = 230 mL per breath.
Multiply by the rate and convert to L/min.
Show the answer and the step-by-step solution
Ventilation: minute ventilation V̇E = tidal volume × respiratory rate (normal adult about 5–8 L/min). Alveolar ventilation V̇A = (tidal volume − dead space) × rate, because the air in the airways (about 150 mL in an adult) takes no part in gas exchange. Lung-protective ventilation uses about 6 mL per kg of predicted body weight (PBW): men 50 + 0.91 × (height in cm − 152.4) kg, women 45.5 + 0.91 × (height in cm − 152.4) kg (with inches: 2.3 per inch above 60 in).
Alveolar part of a breath
390 − 160 = 230 mL
Alveolar ventilation
V̇A = 230·22 = 5060 mL/min = 5.06 L/min
Answer
V̇A = 5.06 L/min
Example 3Hard
Practice exercise (made-up values, not clinical guidance). A cylinder with a water capacity of 2 L is filled to 99 bar and runs at 5 L/min. The gas volume is about the water capacity × the pressure. In this exercise the cylinder is changed at 20 bar. How many minutes t until it must be changed? Round down to a whole minute.
2 L99 bar5 L/min20 bar
Find t(min)
Show hints
Usable pressure = 99 − 20 = 79 bar.
Usable gas = 2 L × 79 bar = 158 L.
Divide by the flow and round down.
Show the answer and the step-by-step solution
Cylinder duration: usable litres = (gauge pressure − safe residual) × cylinder factor, with the safe residual usually 200 psi. Cylinder factors in L/psi: D 0.16, E 0.28, H (and K) 3.14. Duration (min) = usable litres/flow (L/min). Round a duration down, never up, so the cylinder is changed in time. In bar-based systems, the gas volume is the water capacity (L) × the pressure (bar).
Usable gas
2·(99 − 20) = 158 L
Duration
158/5 = 31.6 min → t = 31 min
Answer
t = 31 min
Questions and answers
What is Oxygen therapy & respiratory calculations?
Oxygen is prescribed like a drug: a device, a flow or a concentration, and a target saturation. Nurses check that a portable cylinder will last a transfer, estimate the oxygen a patient breathes, and follow how well the lungs work.
This topic covers:
How do I solve Oxygen therapy & respiratory calculations problems step by step?
Put every value in the units of the formula: FiO₂ and SaO₂ as fractions, PaO₂ in mmHg, Hb in g/dL.
For a cylinder, subtract the safe residual, multiply by the cylinder factor and divide by the flow.
Round cylinder times and flows down, never up.
For the P/F ratio, check the PEEP first, then divide PaO₂ by FiO₂ and compare with 300, 200 and 100 mmHg.
For ventilation, subtract the dead space for alveolar ventilation and use the predicted body weight for tidal volumes.
What are common mistakes in Oxygen therapy & respiratory calculations?
Forgetting the 200 psi safe residual.
Using the factor of the wrong cylinder size.
Using FiO₂ or SaO₂ as a percentage.
Using the actual weight instead of the predicted body weight.
Forgetting the × 10 when turning CaO₂ into oxygen delivery.
Grading ARDS when the PEEP is below 5 cmH₂O.
What do the Oxygen therapy & respiratory calculations exercises cover?
Easy: FiO₂, cylinder contents and minute ventilation
Medium: cylinder duration, P/F ratio and oxygen content
Hard: oxygen delivery, ventilation targets and ARDS severity
Every problem has new values, so you learn the method instead of an answer. Stuck? Open a small hint first, and the full explanation only when you need it.
How practising works
Every problem has new values, so you learn the method instead of an answer.
Stuck? Open a small hint first, and the full explanation only when you need it.
Your progress, mistakes and saved problems are kept, so you can review before the exam.