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Dead Space Fraction (Bohr) Calculator

Enter arterial and mixed-expired CO₂ to get the Bohr dead space fraction.

How it is calculated

The tool applies the Bohr equation: Vd/Vt = (PaCO₂ − PeCO₂) ÷ PaCO₂ × 100. PaCO₂ is the partial pressure of CO₂ in arterial blood and PeCO₂ is the CO₂ partial pressure in mixed expired gas; enter both in the same pressure unit, usually mmHg (kPa gives the same ratio). The result is displayed as a percentage with two decimals, so 30.00% corresponds to a ratio of 0.30. PaCO₂ must be above zero, PeCO₂ cannot be negative, and PeCO₂ larger than PaCO₂ returns no result because the fraction would be negative. The formula gives the physiological dead space as a fraction of tidal volume; it is an educational calculation, not a clinical decision tool.

Worked example

A ventilated patient has an arterial CO₂ of 40 mmHg and a mixed expired CO₂ of 28 mmHg. Step 1: PaCO₂ − PeCO₂ = 40 − 28 = 12 mmHg. Step 2: divide by PaCO₂, 12 ÷ 40 = 0.30. Step 3: as a percentage that is 30.00%. About 30% of each breath ventilates dead space, which falls inside the 0.2–0.4 range given for a normal ratio. Lower mixed expired CO₂ at the same PaCO₂ would push the value up.

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Common mistakes

  • Using end-tidal CO₂ in place of mixed expired CO₂; end-tidal is higher than the mixed value, so the result looks too low.
  • Taking the arterial sample at a different time from the expired gas collection, which makes the two pressures not comparable.
  • Mixing units, such as PaCO₂ in mmHg and PeCO₂ in kPa.
  • Reading 30.00% as 30 mL of dead space: the result is a fraction of tidal volume, so multiply by the tidal volume to get a volume.
  • Swapping the two inputs, which makes PeCO₂ larger than PaCO₂ and returns no result.

Sources

About this calculator

This calculator applies the Bohr equation, the classic respiratory physiology formula for physiological dead space: Vd/Vt = (PaCO₂ − PeCO₂) ÷ PaCO₂, where PaCO₂ is arterial CO₂ tension and PeCO₂ is the mixed expired CO₂. It measures the fraction of each breath that ventilates the airways and alveoli without ever taking part in actual gas exchange.

Anesthesiologists and intensive-care clinicians use the Vd/Vt ratio to assess ventilation efficiency in mechanically ventilated patients — a normal ratio is roughly 0.2–0.4, and an elevated value points to conditions like pulmonary embolism or severe lung disease that waste ventilation.

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