Find the volume of blood the heart pumps per minute — the cardiac output — using the Fick principle, which treats oxygen as a natural tracer in the body. Adjust oxygen consumption, arterial and venous oxygen content and heart rate to see cardiac output, stroke volume, cardiac index and oxygen extraction update in real time.
Parameters
Oxygen consumption V̇O₂
mL/min
Oxygen the body takes up per minute. About 250 mL/min for a resting adult
Arterial O₂ content Ca
mL/L
Oxygen in one litre of arterial blood after oxygenation in the lungs
Mixed-venous O₂ content Cv
mL/L
Oxygen in one litre of venous blood returning to the heart after the tissues
Heart rate HR
bpm
Beats per minute, used to compute the stroke volume
Results
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A-v O₂ difference (mL/L)
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Cardiac output CO (L/min)
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Stroke volume SV (mL)
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Cardiac index (L/min/m²)
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Oxygen extraction (%)
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Cardiac-output class
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Circulation loop — blood flow and oxygen exchange
Blood circulates from the heart to the lungs (picking up oxygen, becoming bright arterial blood) and around the body tissues (giving up oxygen, becoming darker venous blood). Colour shows oxygen content; arrows show flow direction.
Cardiac output CO = oxygen consumption V̇O₂ ÷ arteriovenous oxygen difference (Ca−Cv). The Fick principle applies conservation of oxygen as a tracer, and (Ca−Cv) is the oxygen each litre of blood delivers. Stroke volume SV is the cardiac output divided by the heart rate HR.
Cardiac index CI normalises cardiac output to the body surface area BSA (assumed 1.8 m² here). The oxygen extraction ratio ERO₂ is the fraction of delivered oxygen the tissues take up.
What is the Fick principle and cardiac output?
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"Cardiac output" came up in my physiology class — what quantity is it, exactly?
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Roughly, it is "the volume of blood the heart pumps per minute". The heart's central job is to pump blood, and the rate at which it does so — the cardiac output, CO — is one of the most important numbers in all of physiology and clinical medicine. About 5 L/min for a resting adult. The trouble is, you cannot just put a flow meter on the heart.
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Right... so how do you measure it? You can't exactly open the heart up.
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That is where the Fick principle comes in — proposed in 1870 by the German physiologist Adolf Fick. The idea is brilliantly simple: it is conservation of mass. Pick some tracer substance flowing through the body, count how much of it goes in and out, and you can back-calculate the flow. And the body provides a perfect natural tracer: oxygen.
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Oxygen as a tracer? How does that give you the cardiac output?
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Think of it like this. The whole body consumes oxygen at a measurable rate — the oxygen taken in by the lungs each minute, the oxygen consumption V̇O₂. Every bit of that oxygen is carried to the tissues by the blood. So the rate at which oxygen is delivered must equal the cardiac output multiplied by the amount of oxygen each litre of blood gives up. That "amount given up per litre" is the arteriovenous oxygen difference — the gap between the bright, freshly-oxygenated arterial blood and the depleted mixed-venous blood. Rearranged, CO = oxygen consumption ÷ arteriovenous difference. Move the Ca and Cv sliders on the left so they get close, and you will see the difference shrink and CO shoot up.
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I see! Once you have cardiac output, you can also get stroke volume and cardiac index?
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Exactly. Cardiac output is a "per minute" quantity, so dividing by the heart rate gives the "per beat" quantity — the stroke volume SV. Divide cardiac output by body surface area and you get the cardiac index CI, which scales out body size so a small adult and a large one compare fairly. The same conservation-of-tracer logic, with dyes or with thermal "cold" instead of oxygen, underlies the indicator-dilution and thermodilution methods used at the bedside. And do keep in mind — this is an educational engineering and physiology tool, not a medical device or medical advice.
Frequently Asked Questions
The Fick principle is conservation of mass applied to a tracer substance in the circulation. The rate at which the body takes up oxygen (the oxygen consumption VO2) must equal the cardiac output multiplied by the amount of oxygen each litre of blood gives up to the tissues — the arteriovenous oxygen difference Ca-Cv. Solving for cardiac output gives CO = VO2/(Ca-Cv), which converts a difficult flow measurement into three quantities that can be measured: the oxygen uptake, the arterial oxygen content and the mixed-venous oxygen content.
Cardiac output (CO) is the volume of blood the heart pumps per minute (L/min) and is one of the most important numbers in circulatory physiology. Stroke volume (SV) is the blood ejected by a single heartbeat (mL), related by SV = CO*1000/heart rate. Cardiac index (CI) is the cardiac output normalised to body size (the body surface area), in L/min/m2, so that people of different sizes can be compared fairly. This tool assumes a typical body surface area of 1.8 m2.
The arteriovenous oxygen difference (Ca-Cv) is the amount of oxygen each litre of blood delivers to the tissues on its trip around the body (mL/L); at rest it is roughly 40-50 mL/L. The oxygen extraction ratio is the fraction of the delivered oxygen the tissues actually take up — (Ca-Cv)/Ca*100% — and is about 25% at rest. During exercise, tissue oxygen demand rises and the extraction ratio increases together with the cardiac output.
No. This is an educational engineering and physiology simulator, not a medical device or medical advice. Real cardiac-output measurement is performed by healthcare professionals using the Fick method, dye-dilution or thermodilution. The displayed classifications and numbers are only there to help you understand the principle and must not be used for diagnosis or treatment decisions.
Real-World Applications
Teaching circulatory physiology: Cardiac output, stroke volume, cardiac index and the arteriovenous oxygen difference are core quantities taught in the circulatory physiology of medicine, nursing and sports science. The Fick principle is a fine example of the engineering idea "replace a quantity you cannot measure with a combination of quantities you can", and it appears in every textbook as an application of conservation of mass. This tool lets students vary each quantity with a slider and feel the proportional and inverse relationships in the equation directly.
Exercise physiology and cardiorespiratory fitness: When exercise begins, tissue oxygen demand rises sharply and cardiac output increases from a resting 5 L/min to 20-25 L/min in a trained person. This happens not only through a higher heart rate but also through a wider arteriovenous oxygen difference and a higher extraction ratio. The Fick equation CO = V̇O₂/(Ca−Cv) shows that the maximum oxygen uptake (V̇O₂max) is set by "maximum cardiac output times maximum a-v difference", giving a framework for understanding endurance-training adaptations.
Dilution methods as measurement principles: The same "conservation of a tracer" idea behind the Fick principle is also the basis of dye-dilution (inject a dye and read the flow from the downstream concentration-time curve) and thermodilution (inject cold saline and track the temperature change). Only the tracer differs — oxygen, dye, or heat — while the skeleton of using a conservation law to back out the flow is shared. This tool deals with the most classical form, the oxygen method.
Modelling the heart as a biological pump: Viewing the heart as a periodic flow source is the starting point of haemodynamic numerical simulation, from zero-dimensional lumped-parameter models to one-dimensional wave models. The relationship between cardiac output, stroke volume and heart rate provides the basic parameters when setting boundary and input conditions for such models, and serves as an entry point into CAE-style cardiovascular modelling.
Common Misconceptions and Pitfalls
A common confusion is mixing up oxygen content and oxygen saturation (SpO₂). The Ca and Cv you enter here are the volume of oxygen contained in one litre of blood (mL/L), which is not the same thing as saturation (%). Oxygen content is roughly "haemoglobin concentration × saturation × 1.34", so in anaemia, with little haemoglobin, the content is low even at 100% saturation. Mistaking saturation for content makes the Fick calculation completely wrong, because it is content, not saturation, that enters the equation.
Next, assuming the arteriovenous oxygen difference can be driven to zero. On paper, bringing Ca and Cv arbitrarily close makes the cardiac output diverge to infinity. But in a living body the tissues always consume some oxygen, so Cv never equals Ca. This tool restricts the input ranges so that Ca > Cv always holds, avoiding the non-physical state of a zero or negative difference. The reason the numbers do not blow up at extreme settings is that this physical constraint is built in.
Finally, this is an educational simulator, not a medical device or medical advice. Real cardiac-output measurement is performed by healthcare professionals using alveolar-gas and blood-gas analysis or thermodilution catheters, with many prerequisites such as ensuring rest and managing measurement error. The 1.8 m² body surface area and the constants in this tool are representative values and are not guaranteed to apply to any specific individual. The displayed "classification" is only a rough guide to help understanding of the principle and must never be used for diagnostic or treatment decisions.
How to Use
Enter oxygen consumption (VO₂) in mL/min—typical resting value is 250 mL/min for a 70 kg adult.
Input arterial oxygen content (CaO₂) in mL/L—normal range 190–210 mL/L depending on hemoglobin and SpO₂.
Input venous oxygen content (CvO₂) in mL/L—typically 140–150 mL/L at rest.
Enter heart rate (HR) in beats/min to calculate stroke volume automatically.