Physiological Dead Space Calculator (Bohr–Enghoff VD/VT)
Calculate the physiological dead space fraction VD/VT with the Bohr–Enghoff equation from arterial and mixed expired CO₂, plus dead space volume, minute ventilation and alveolar ventilation.
How it works
VD/VT = (PaCO₂ − PĒCO₂) ÷ PaCO₂ (Bohr equation with Enghoff’s substitution of arterial for alveolar CO₂) · VD = VD/VT × VT · alveolar ventilation = (VT − VD) × respiratory rate.
Physiological dead space is the part of each breath that does not take part in gas exchange: the anatomical dead space of the airways plus alveolar dead space from lung units that are ventilated but poorly perfused. Bohr’s equation compares alveolar and mixed expired CO₂; Enghoff replaced alveolar with arterial CO₂, so the result also captures shunt and ventilation–perfusion mismatch. In healthy adults breathing spontaneously VD/VT is about 0.2–0.35. In acute respiratory distress syndrome, Nuckton and colleagues (NEJM 2002) found a mean dead space fraction of 0.58 early in the disease, and each 0.05 rise was associated with 45% higher odds of death. Pulmonary embolism, low cardiac output and over-distension from high PEEP also raise dead space.
Worked example
A patient has a PaCO₂ of 40 mmHg and a mixed expired CO₂ of 28 mmHg, with a tidal volume of 500 mL at 14 breaths per minute. VD/VT = (40 − 28) ÷ 40 = 0.30 (30%), so dead space = 150 mL and alveolar tidal volume = 350 mL. Minute ventilation is 7.0 L/min and alveolar ventilation 4.9 L/min — a dead space fraction in the usual range.
Sources: Nuckton TJ et al. Pulmonary dead-space fraction as a risk factor for death in the acute respiratory distress syndrome. N Engl J Med 2002;346:1281–1286 · Robertson HT. Dead space: the physiology of wasted ventilation. Eur Respir J 2015;45:1704–1716
Frequently asked questions
What is a normal dead space fraction?
About 0.2–0.35 (20–35% of each breath) in healthy adults breathing spontaneously. Mechanical ventilation and lung disease increase it.
What is the difference between Bohr and Enghoff dead space?
Bohr’s original equation uses alveolar CO₂ and measures true dead space. Enghoff used arterial CO₂, which is easier to obtain; the result (physiological dead space) also includes the effect of shunt and V/Q mismatch, so it is somewhat higher.
Where do I get mixed expired CO₂?
From volumetric capnography on the ventilator, which reports mean expired CO₂, or by collecting expired gas in a Douglas bag. End-tidal CO₂ is not the same — it is higher than the mixed expired value.
Why does dead space matter in ARDS?
A high dead space fraction reflects microvascular injury and is an independent predictor of death in ARDS. It also means higher minute ventilation is needed to clear CO₂.
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Clinical decision tool for education and for use by trained clinicians alongside clinical judgement — not a diagnosis and not a substitute for medical assessment. Scores and cut-offs come from the cited validation studies and may not apply to every patient; follow local protocols.