What it does
The Fick principle says that the oxygen the body takes up each minute must be carried away from the lungs by the blood. Each 100 mL of blood leaving the lungs holds more O₂ (arterial content, CaO₂) than the blood coming back (mixed venous content, CvO₂). So:
cardiac output = V̇O₂ ÷ (CaO₂ − CvO₂)
with V̇O₂ in mL/min and the contents in mL O₂ per litre of blood (the calculator multiplies mL/dL by 10). It is the classic way physiology students meet cardiac output, and the same idea underlies indicator-dilution methods.
The page also has two short calculators that go with it in a physiology course: Fick’s law of diffusion (how fast a gas or solute crosses a membrane) and Poiseuille’s law (how pressure, radius, length and viscosity set the flow through a tube).
For study and teaching, not for clinical use.
How to use it
- Type the O₂ uptake, for example from a spirometer or the respirometry calculator.
- Type haemoglobin, the arterial and mixed venous saturations and the two PO₂ values. Choose mmHg or kPa; switching converts the numbers you typed.
- Hüfner factor: the mL of O₂ one gram of fully saturated haemoglobin binds. 1.34 is the usual textbook value, 1.39 the theoretical maximum, 1.36 a common compromise.
- Heart rate and body surface area are optional and add stroke volume and cardiac index.
The diffusion and Poiseuille calculators work on their own. Each result explains in one line what it means.
Worked example
The illustrative example is a resting adult: V̇O₂ 250 mL/min, Hb 15 g/dL, SaO₂ 98 % at PO₂ 95 mmHg, SvO₂ 75 % at PO₂ 40 mmHg, heart rate 70.
- CaO₂ = 1.34 × 15 × 0.98 + 0.0031 × 95 = 19.99 mL/dL; CvO₂ = 15.20 mL/dL.
- The a–v difference is 4.79 mL/dL, so cardiac output = 5.22 L/min and stroke volume 74.5 mL.
- O₂ delivery is 1043 mL/min and extraction 24 %.
Diffusion: with D = 2 × 10⁻⁵ cm²/s across 1 cm² of a 1 µm sheet and a 0.1 mmol/L difference, the rate is 20 nmol/s, and the time scale to cross is 0.250 ms.
Poiseuille: a 10 mmHg drop along 10 cm of a 1.5 mm radius tube with a viscosity of 3.5 mPa·s gives 7.573 mL/s (454.4 mL/min), a mean velocity of 107.1 cm/s and a Reynolds number of 973.4 (laminar).
Tips
- The dissolved O₂ is small at normal PO₂ (about 0.3 mL/dL), which is why saturation matters far more than PO₂.
- Radius enters Poiseuille’s law to the fourth power: a vessel 19 % wider carries twice the flow.
- Blood is not a simple liquid: its viscosity falls in small vessels and at high shear, so Poiseuille is a teaching model.
FAQ
Why mixed venous blood? The Fick principle needs the average of all blood returning to the lungs, which is only found in the pulmonary artery.
Does anything leave my device? No. Everything is worked out in your browser.
Where the numbers come from
- Fick principle: A. Fick (1870). O₂ content = 1.34 × Hb × SaO₂ + 0.0031 × PO₂ is the standard textbook form (Hüfner factor 1.34 to 1.39 mL O₂/g Hb; O₂ solubility 0.003 mL/dL/mmHg); see any physiology text, e.g. West's Respiratory Physiology. Formulas only.
- Fick's first law of diffusion: A. Fick (1855). Poiseuille's law: J. L. M. Poiseuille (1840s) and G. Hagen (1839). Pressure units: 1 mmHg = 133.322 Pa (NIST).
- Checked in the tests against a Python rewrite of the formulas, and Poiseuille flow against SciPy numerical integration of the parabolic velocity profile. The example values are illustrative textbook-style numbers, made up and rounded.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.