🧬 Dead Space Calculator

Every breath has a wasted fraction: air that fills airways and unperfused alveoli without exchanging gas. The Bohr equation quantifies it from two CO2 numbers, arterial and mixed expired, as the dead space fraction Vd/Vt. Normal is 0.2 to 0.4; ARDS and pulmonary embolism push it far higher. Enter both values for the fraction and its meaning.

How to Use This Calculator

Enter PaCO2 from arterial blood gas and PeCO2 (mixed expired CO2) from volumetric capnography.

The Bohr Equation

Christian Bohr published it in 1891 from mass balance: all exhaled CO2 comes from alveolar gas, so diluting alveolar CO2 (approximated by arterial) down to the mixed expired value reveals the diluting dead-space volume. The Enghoff modification substitutes arterial for alveolar CO2, which folds shunt and low V/Q regions into the "dead space" number; physiologists call the result physiologic dead space to distinguish it from true anatomic dead space. In practice, the Enghoff version is what ICUs compute, and its elevation reflects the sum of ventilatory inefficiency.

Anatomic dead space (airways, ~150 mL) is fixed; alveolar dead space (ventilated but unperfused alveoli) is the variable part. PE creates pure alveolar dead space: clot blocks perfusion while ventilation continues. ARDS creates it through microthrombosis and overdistension. High PEEP can both recruit (reducing dead space) and overdistend (increasing it), which is why dead space helps titrate ventilation.

Worked Example

PaCO2 40, PeCO2 28: Vd/Vt = (40-28)/40 = 0.30, normal. Only 70 percent of each breath participates in gas exchange. Now ARDS: PaCO2 55, PeCO2 22: Vd/Vt = (55-22)/55 = 0.60, very high; just 40 percent of ventilation is effective, explaining why the PaCO2 stays high despite large minute ventilation. The number quantifies what the blood gas suggests: this patient is ventilating a lot of dead space, and proning or PEEP adjustment targets exactly that.

Clinical Uses

ARDS prognosis: high dead space fraction predicts mortality in ARDS cohorts, and it falls with effective interventions like proning. PE diagnosis: a sudden rise in dead space with hypotension and clear lungs points at embolism. Ventilator management: rising Vd/Vt suggests overdistension (consider less PEEP or smaller tidal volumes) or worsening perfusion; falling suggests recruitment. Weaning: high dead space predicts extubation failure in some studies. It is a bedside number with real decision weight, not a physiology curiosity.

Measurement caveats: PeCO2 needs proper mixed expired gas collection, tricky with leaks or variable ventilation. The Enghoff version overestimates true dead space when shunt is large, since shunted blood raises PaCO2 without dead space. End-tidal CO2 alone cannot substitute: the arterial-to-end-tidal gradient is related but not identical. Get the two right numbers and the equation does the rest; it has been doing it since 1891.

Dead Space vs Shunt: The Mirror Images

Dead space is ventilation without perfusion (wasted air); shunt is perfusion without ventilation (wasted blood). PE causes dead space; pneumonia and atelectasis cause shunt. Both widen the arterial-alveolar gradients and both cause hypoxemia, but they respond oppositely: dead space improves with perfusion and careful PEEP, shunt improves with recruitment and FiO2. The Bohr equation measures one mirror half; the shunt equation measures the other. Together they describe V/Q mismatch completely, which is why respiratory physiology keeps returning to this pair.

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For informational purposes only, not medical advice. Consult a healthcare professional.