Dead Space Calculator (Bohr–Enghoff Vd/Vt from PaCO₂ and expired CO₂)

Understanding the dead space calculator — concept and principle

This calculator estimates physiological dead space, the part of each breath that does not take part in gas exchange, with the Bohr equation as modified by Enghoff. From arterial and mixed expired carbon dioxide and the tidal volume, it shows the dead space fraction, the dead space volume and the part of each breath that reaches working alveoli. Respiratory therapists, intensive care staff and physiology students use it.

Air that never reaches blood — with the default inputs: Vd/Vt 0.3.

How it is calculated

Vd/Vt = (PaCO₂ − PECO₂) ÷ PaCO₂
Both pressures in the same unit (mmHg or kPa)
Dead space volume = Vd/Vt × tidal volume
Alveolar part = (1 − Vd/Vt) × tidal volume

The principle

Only air that reaches perfused alveoli picks up carbon dioxide. Gas from the airways and from alveoli without blood flow leaves with almost no CO₂ and dilutes the exhaled mixture. Bohr compared alveolar and expired CO₂ to find the diluted share; Enghoff replaced alveolar CO₂ with arterial CO₂, which is easier to measure and also captures alveoli with poor blood flow. PECO₂ must be the average CO₂ of all exhaled gas, collected in a bag or measured by volumetric capnography, not end-tidal CO₂.

Worked example

Defaults: PaCO₂ 40 mmHg, PECO₂ 28 mmHg, tidal volume 500 mL.

Vd/Vt = (40 − 28) ÷ 40 = 0.3, or 30%.
Dead space volume = 0.3 × 500 = 150 mL.
Alveolar part = 500 − 150 = 350 mL.

How to read the result

Where does your result fall?

In healthy adults breathing at rest, Vd/Vt is about 0.2–0.35, roughly 150 mL of a 500 mL breath. Higher values mean more wasted ventilation, as in pulmonary embolism, COPD or ARDS, and in ventilated patients with extra tubing. To keep the same CO₂ removal, a person with more dead space must breathe more.

Common mistakes

Using end-tidal CO₂ instead of mixed expired CO₂.
Mixing mmHg and kPa.
Forgetting the dead space added by ventilator tubing and filters.
Reading a single value without the clinical context.

Keep in mind: Not a diagnosis. Blood gas results are interpreted by the treating clinical team.

Frequently asked questions

What is a normal dead space fraction?

About 0.2–0.35 in healthy adults at rest.

Why use arterial CO₂?

It is easy to measure and also reflects alveoli with poor blood flow.

Can I use end-tidal CO₂?

It gives a different, smaller quantity; the Enghoff formula needs mixed expired CO₂.

Sources: Bohr equation with Enghoff modification, Vd/Vt = (PaCO₂ − PECO₂) ÷ PaCO₂, and the normal range of about 0.2–0.35 (standard respiratory physiology)

Checked 9 Nov 2026. Bohr equation with Enghoff modification, Vd/Vt = (PaCO₂ − PECO₂)/PaCO₂, and the normal range of about 0.2–0.35 — standard respiratory physiology values.

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