Dead Space Fraction Calculator (Bohr and Enghoff)

Bohr’s equation uses MEAN ALVEOLAR CO₂; Enghoff substituted arterial CO₂ and thereby folded shunt and V/Q mismatch into the answer. The Enghoff value is systematically larger, and most bedside calculations labelled Bohr are Enghoff.

Last updated 8 Oct 2026

Dead space fraction, Bohr and Enghoff

Vd/Vt by both equations

Arterial PaCO₂From an arterial blood gas. Use ONE unit consistently for all three inputs — mmHg throughout or kPa throughout. The ratio is dimensionless so the unit cancels, but mixing mmHg and kPa gives a meaningless number. The pCO₂ unit converter converts.

Mean alveolar PACO₂Mean alveolar CO₂ from VOLUMETRIC CAPNOGRAPHY — the only input here that a blood gas and a ventilator cannot give. It is not the end-tidal value and not the mixed expired value; substituting end-tidal understates the Bohr fraction.

Mixed expired PĒCO₂CO₂ averaged over the WHOLE expirate, same unit as above — volumetric capnography or a Douglas bag, and again not end-tidal, which is always higher.

0.50Vd/Vt by EnghoffExample

PaCO₂ 48 mmHg, mean alveolar PACO₂ 40 mmHg, mixed expired PĒCO₂ 24 mmHg

Formula

Bohr: V_D/V_T = (P_ACO₂ − P̄_ECO₂) ÷ P_ACO₂
Enghoff: V_D/V_T = (PaCO₂ − P̄_ECO₂) ÷ PaCO₂

PACO2 against PaCO2: Bohr uses MEAN ALVEOLAR CO₂, averaged over the alveolar phase of a volumetric capnogram, and that version is the only one that measures dead space as such. Enghoff substituted ARTERIAL CO₂ to make the calculation possible from a blood gas; the substitution is what made it usable and what changed what it measures
PEbarCO2: mixed expired CO₂, averaged over the whole expirate — not the end-tidal value, which is always higher, so substituting it understates both fractions
why Enghoff is larger: PaCO₂ almost invariably exceeds mean alveolar PCO₂, because blood shunted past ventilated alveoli delivers its CO₂ unchanged to the arterial side. Both equations are 1 minus (mixed expired ÷ reference), so the larger reference gives the larger fraction. The Enghoff value therefore includes dead space AND venous admixture, and is a global index of V/Q mismatch. In 50 ventilated ICU patients the gap was 0.091 in near-normal lungs and 0.156 in diseased lungs
units: none. Each equation is a difference of two CO₂ tensions divided by one of them, so the unit cancels. Any consistent unit works — mmHg, kPa or a CO₂ fraction — and mixing two of them in one calculation does not

Worked example

PaCO₂ 48 mmHg, mean alveolar PACO₂ 40 mmHg, mixed expired PĒCO₂ 24 mmHg
Enghoff: (48 − 24) ÷ 48 = 0.50
Bohr: (40 − 24) ÷ 40 = 0.40
Enghoff exceeds Bohr by 0.10, which is the venous admixture contribution — the 8 mmHg by which arterial exceeds mean alveolar CO₂, divided through
The same three tensions in kPa — 6.40, 5.33 and 3.20 — return the same 0.50 and 0.40, because the ratio is dimensionless
Let the shunt worsen so PaCO₂ rises to 56 while the other two hold: Enghoff becomes 0.57 and Bohr stays at 0.40. The apparent dead space grew by a sixth and the dead space did not change
Set the mean alveolar value equal to the arterial 48 and both equations collapse to 0.50 — the degenerate case, which is why the test of a correct implementation is that Enghoff EXCEEDS Bohr whenever arterial exceeds mean alveolar, not that the two agree when they are equal
Substitute an end-tidal CO₂ of 44 for the mean alveolar value and Bohr reads 0.45 instead of 0.40 — a plausible number from the wrong input

Bohr and Enghoff are not the same dead space

The distinction decides what the number means. A rising Enghoff fraction in a patient whose lungs are collapsing may reflect no change in dead space at all, only a growing shunt — and recruitment will lower it for the same reason.
	Bohr	Enghoff
Reference CO₂	Mean alveolar, from volumetric capnography	Arterial, from a blood gas
What it measures	Dead space: the fraction of each breath not taking part in gas exchange	Dead space PLUS venous admixture and V/Q mismatch
Size	The smaller of the two	Larger by 0.09 in near-normal and 0.16 in diseased lungs in one series
Behaviour with a large shunt	Unaffected by shunt	Rises with the shunt; at high shunt better read as a severity index
What bedside calculations report	Rarely this one	This one, including the large ARDS outcome studies, which name the Enghoff modification explicitly

Published Vd/Vt values, all by the Enghoff modification

Every figure is an Enghoff value measured with volumetric capnography in ARDS, and the Kallet analysis found it predicted mortality in moderate and severe ARDS by the Berlin definition but not in mild. A threshold derived in ARDS does not transfer to a post-operative or an obstructive patient.
Population	Vd/Vt	Source
ARDS survivors	0.54 (SD 0.09)	Nuckton and colleagues, NEJM 2002
ARDS non-survivors	0.63 (SD 0.10)	Nuckton and colleagues, NEJM 2002
ARDS across aetiologies, 685 patients	About 0.50 to 0.60	Kallet and colleagues, Respir Care 2017
Odds of death per 0.05 rise in Vd/Vt	1.45 (1.15 to 1.83); and 1.22 (1.11 to 1.35) in 685 patients	Nuckton 2002; Kallet 2017

The substitution that changed what the equation measures

Christian Bohr’s equation asks a simple question: what fraction of each breath never reached a gas-exchanging alveolus? The answer is the mean alveolar carbon dioxide minus the carbon dioxide averaged over the whole expirate, divided by the mean alveolar value. Both numbers come from volumetric capnography, and the result is a dead space — anatomical plus alveolar, the wasted part of the tidal volume.

Enghoff replaced the mean alveolar value with the arterial PaCO₂, which turned an equation needing a capnogram into one needing a blood gas, and that is why nearly every bedside dead-space fraction in use is an Enghoff value, including those in the large ARDS outcome studies. But the substitution is not innocent. Blood shunted past ventilated alveoli never unloads its carbon dioxide, so it arrives on the arterial side carrying it, and arterial PaCO₂ almost invariably exceeds mean alveolar PCO₂. Both equations have the shape of one minus the mixed expired value divided by a reference, so the larger reference gives the larger fraction. The Enghoff value is therefore systematically bigger than Bohr’s — by about 0.09 in near-normal lungs and 0.16 in diseased lungs in one series of 50 ventilated patients — and the excess is shunt and V/Q mismatch, not dead space.

That has a practical consequence. The Enghoff fraction is a strong mortality marker in ARDS: 0.63 against 0.54 in the non-survivors and survivors of Nuckton’s cohort, and a 22% rise in the risk of death per 0.05 in 685 patients measured by capnography. It earns that by being a global index of gas-exchange inefficiency rather than a measurement of wasted ventilation. So a falling Enghoff fraction after recruitment may mean nothing about dead space at all, and a page that calls the Enghoff number a Bohr dead space is reporting the right arithmetic under the wrong name. The ventilatory ratio exists because neither equation can be computed without a mixed expired carbon dioxide, and most beds do not have one.

This supports a clinician’s judgement rather than replacing it.

Frequently asked questions

What is the difference between the Bohr and Enghoff dead space?

The reference carbon dioxide. Bohr’s equation uses mean alveolar PACO₂ from volumetric capnography and measures dead space. Enghoff substituted arterial PaCO₂, which is almost always higher because shunted blood carries its carbon dioxide to the arterial side, so the Enghoff value is systematically larger and includes shunt and V/Q mismatch as well as dead space.

Which equation does a bedside monitor report?

Almost always Enghoff, often labelled as a Bohr dead-space fraction. Kallet and colleagues name the Enghoff modification explicitly, and so is every calculation that takes an arterial PaCO₂ as an input, this page included.

Can I use end-tidal CO₂ in these equations?

No, in either slot. End-tidal CO₂ is the value at the very end of expiration and is higher than the mixed expired value averaged over the whole breath, and it is not mean alveolar CO₂ either. Substituting it produces a plausible-looking fraction from the wrong input, and the error moves in the reassuring direction.

What is a high dead space fraction?

In ARDS, Enghoff values of roughly 0.50 to 0.60 are usual, and the figures associated with mortality sit above that: 0.63 in the non-survivors of Nuckton’s cohort against 0.54 in survivors, with the odds of death rising 45% per 0.05. Those are population associations in ARDS measured by volumetric capnography, not thresholds for an individual patient.

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References

Mosing M, Böhm SH, Rasis A, et al. Physiologic factors influencing the arterial-to-end-tidal CO₂ difference and the alveolar dead space fraction in spontaneously breathing anaesthetised horses. Front Vet Sci. 2018;5:58.
Cipulli F, et al. Dead space in critical care: a practical approach with clinical scenarios. J Anesth Analg Crit Care. 2026;6:20.
Kallet RH, Zhuo H, Ho K, Lipnick MS, Gomez A, Matthay MA. Lung injury etiology and other factors influencing the relationship between dead-space fraction and mortality in ARDS. Respir Care. 2017;62(10):1241–8.
Nuckton TJ, Alonso JA, Kallet RH, Daniel BM, Pittet JF, Eisner MD, Matthay MA. Pulmonary dead-space fraction as a risk factor for death in the acute respiratory distress syndrome. N Engl J Med. 2002.
Kunal K, Gupta T, Rout A, Sarath Chandran CR, Gajbhiye DJ, Singhmar N. Comparison of Bohr and Enghoff methods for assessing ventilatory inefficiency in mechanically ventilated intensive care unit patients. APIK J Intern Med. 2026;223–8. doi:10.4103/ajim.ajim_13_26

Not medical advice. For healthcare professionals and education. Reference intervals vary by laboratory and assay — always use your own laboratory's. Never base a dose or a treatment decision on this page alone. Full disclaimer at calcengines.com/disclaimer/