Dead Space Calculator

Calculate physiologic dead space with the Bohr equation from tidal volume, arterial PaCO2, and mixed expired CO2, plus an anatomic dead space estimate from body weight.

Quick Facts

Bohr equation
VD/VT = (PaCO2 - PECO2) / PaCO2
CO2-free dead-space gas dilutes exhaled CO2; the dilution reveals the wasted fraction of each breath.
Anatomic dead space rule of thumb
≈ 2.2 mL per kg body weight
Roughly 1 mL per lb of body weight — about 150 mL in an average adult.
Normal VD/VT
0.2 - 0.4 (20% - 40%)
Rises with pulmonary embolism, COPD, ARDS, low cardiac output, or positive-pressure ventilation.

Your Results

Calculated
Physiologic Dead Space (VD)
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Bohr equation: VT × (PaCO2 - PECO2) / PaCO2
Dead Space Fraction (VD/VT)
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Wasted ventilation per breath
Alveolar Tidal Volume (VA)
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VT - VD, the gas-exchanging portion
Anatomic Dead Space Estimate
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≈ 2.2 mL/kg body weight, for comparison

Ready

Enter tidal volume, PaCO2, PECO2, and body weight, then press Calculate.

Understanding Dead Space and the Bohr Equation

In respiratory physiology, "dead space" is the portion of each breath that does not participate in gas exchange. Anatomic dead space is the volume of the conducting airways — the trachea, bronchi, and bronchioles — that carry air but have no alveoli to exchange gas across; it is roughly 2.2 mL per kg of body weight, or about 150 mL in an average adult. Physiologic (total) dead space adds alveolar dead space — alveoli that are ventilated but poorly or not perfused with blood — to the anatomic dead space, and is calculated from measured gas values with the Bohr equation: VD/VT = (PaCO2 - PECO2) / PaCO2, where PaCO2 is arterial carbon dioxide tension, PECO2 is the CO2 tension of mixed expired gas, and VT is tidal volume. This calculator uses the Bohr equation to estimate physiologic dead space and compares it with the simple anatomic estimate from body weight. It is an educational and reference tool, not a substitute for arterial blood gas interpretation or clinical judgment by a qualified provider.

How the calculation works

Because exhaled gas from well-perfused alveoli carries CO2 while dead-space gas carries essentially none, mixing the two together dilutes the measured expired CO2 below the true alveolar/arterial value. The size of that dilution — (PaCO2 - PECO2) divided by PaCO2 — is the fraction of each breath that is "wasted," VD/VT. Multiplying that fraction by tidal volume gives the dead space volume itself, VD = VT x (PaCO2 - PECO2) / PaCO2, and subtracting VD from VT gives the alveolar tidal volume (VA), the portion of the breath that actually reaches gas-exchanging alveoli. Many bedside monitors substitute end-tidal CO2 (PetCO2) from capnography for mixed expired CO2 — this variant is called the Enghoff modification and tends to run slightly higher than the classic Bohr value.

Why dead space matters clinically

An elevated VD/VT means a patient must breathe more total volume per minute to achieve the same effective (alveolar) ventilation, which increases the work of breathing and can signal an underlying problem. Common causes of increased physiologic dead space include pulmonary embolism (perfusion loss to ventilated alveoli), COPD and emphysema (destroyed alveolar-capillary surface), ARDS, hypovolemia or low cardiac output (reduced pulmonary blood flow), and mechanical ventilation with large tidal volumes or high PEEP (overdistended, under-perfused alveoli). Anatomic dead space, by contrast, changes mainly with airway size — it increases somewhat with larger body size and with conditions like bronchodilation, and decreases slightly with tracheostomy (which bypasses the upper airway).

Frequently Asked Questions

What is the Bohr equation for dead space?
The Bohr equation is VD/VT = (PaCO2 - PECO2) / PaCO2, where PaCO2 is arterial carbon dioxide tension, PECO2 is the mixed expired CO2 tension, and VT is tidal volume. It works because CO2-free dead-space gas dilutes the CO2 exhaled from perfused alveoli, so the size of that dilution reveals the wasted fraction of each breath.
What is the difference between anatomic and physiologic dead space?
Anatomic dead space is the volume of the conducting airways (trachea, bronchi) that never reach gas-exchanging alveoli, roughly 2.2 mL per kg of body weight (about 150 mL in an average adult). Physiologic dead space, calculated with the Bohr equation, also includes alveolar dead space — alveoli that are ventilated but poorly perfused — so it can be elevated in lung disease even when the airway anatomy is unchanged.
What is a normal VD/VT ratio?
A healthy adult breathing spontaneously at rest typically has a VD/VT of about 0.2-0.4 (20%-40%). Values above this range suggest increased wasted ventilation and are seen in conditions such as pulmonary embolism, COPD, ARDS, low cardiac output, or high levels of positive-pressure ventilation.
Can I use end-tidal CO2 (PetCO2) instead of mixed expired CO2?
Yes — substituting end-tidal CO2 for mixed expired CO2 in the same equation is called the Enghoff modification, VD/VT = (PaCO2 - PetCO2) / PaCO2. It is widely used at the bedside with capnography but tends to slightly overestimate dead space compared with true mixed expired sampling.

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