Understanding the various cardiac output formulas and cardiac output equations is essential for anyone involved in cardiovascular assessment. This comprehensive guide breaks down the key formulas used to calculate cardiac output (CO), including their derivations (where applicable simplified for clarity), clinical applications, and links to our specific calculators. We’ll cover the basic CO = HR × SV, the Fick principle, Doppler echocardiography method, and the thermodilution method. A downloadable cheat sheet will summarize these for quick reference.

Cardiac Output Formulas Explained

1. The Fundamental Cardiac Output Formula

This is the most basic and universally understood equation for cardiac output.

CO = HR × SV

  • CO: Cardiac Output (L/min or mL/min)
  • HR: Heart Rate (beats/min)
  • SV: Stroke Volume (L/beat or mL/beat) – the volume of blood pumped per beat.

Derivation: This formula is definitional. If the heart beats ‘HR’ times a minute, and each beat ejects ‘SV’ volume of blood, then the total volume per minute is simply their product.

Application: Conceptually underpins all other methods. Directly calculable if HR and SV are known (e.g., SV from our Stroke Volume Calculator). You can learn more about how to calculate CO using this basic method.

2. The Fick Principle Formula

The Fick principle states that blood flow across an organ (or the whole body) is proportional to the oxygen consumption (or any marker substance uptake) divided by the arteriovenous oxygen difference.

    \[ \text{CO} = \frac{\text{VO}_2}{\text{CaO}_2 - \text{CvO}_2} \]

  • CO: Cardiac Output (typically L/min)
  • VO2: Oxygen consumption by the body (mL O2/min)
  • CaO2: Arterial oxygen content (mL O2/dL blood or mL O2/L blood)
  • CvO2: Mixed venous oxygen content (mL O2/dL blood or mL O2/L blood)

Unit Note: If CaO2 and CvO2 are in mL/dL, the denominator difference needs to be multiplied by 10 to convert to mL/L for CO in L/min. Our Fick Method Calculator handles units.

Derivation (Conceptual):
Total O2 consumed by tissues (VO2) must equal the O2 delivered by arterial blood minus the O2 remaining in venous blood.
O2 Delivered = CO × CaO2
O2 Remaining = CO × CvO2
VO2 = (CO × CaO2) – (CO × CvO2) = CO × (CaO2 – CvO2)
Rearranging gives the Fick formula.

Application: Considered a gold standard, especially direct Fick (measured VO2). Used in cardiac catheterization labs and research. Invasive due to need for mixed venous blood sampling. A comparison between Doppler and Fick is available.

3. Doppler Echocardiography Formula (LVOT Method)

This non-invasive method uses ultrasound to measure blood flow velocity and dimensions.

Step 1: Calculate Stroke Volume (SV)

    \[ \text{CSALVOT} = \pi \times \left( \frac{D_{\text{LVOT}}}{2} \right)^2 \quad \text{or} \quad \text{CSALVOT} = 0.785 \times D_{\text{LVOT}}^2 \]

    \[ \text{SV} = \text{CSALVOT} \times \text{VTI}_{\text{LVOT}} \]

Step 2: Calculate Cardiac Output (CO)

CO = SV × HR

  • CSALVOT: Cross-sectional area of the Left Ventricular Outflow Tract (cm2)
  • DLVOT: Diameter of the LVOT (cm)
  • VTILVOT: Velocity Time Integral across the LVOT (cm) – distance blood travels per beat
  • SV: Stroke Volume (mL, since CSA in cm2 and VTI in cm gives cm3 = mL)
  • HR: Heart Rate (bpm)
  • CO: Cardiac Output (mL/min, then convert to L/min)

Derivation: Based on the hydraulic principle that flow (SV) through a tube (LVOT) is the product of its cross-sectional area and the mean distance traveled by the fluid column (VTI) per cycle.

Application: Widely used non-invasive method in clinical practice. Relies on accurate echocardiographic measurements. See our Doppler Echo CO Calculator.

4. Thermodilution Formula (Stewart-Hamilton Equation)

This invasive method uses an indicator (cold saline) injected into the circulation.

    \[ \text{CO} = \frac{V_i \times (T_b - T_i) \times K_1 \times K_2}{\int \Delta T_b(t) \, dt} \]

  • CO: Cardiac Output (L/min)
  • Vi: Volume of injectate (mL)
  • Tb: Blood temperature (°C)
  • Ti: Injectate temperature (°C)
  • K1: Density factor (product of specific gravity and specific heat for injectate and blood)
  • K2: Computation constant (accounts for catheter dead space, injectate warming during injection, unit conversions; e.g., 60 for seconds to minutes, 1.08 for K1 if injectate is 5% dextrose and blood). This constant is often embedded in the monitoring device specific to the catheter and injectate volume/type.
  • ∫ΔTb(t)dt: Area under the temperature change curve (°C × sec).

Derivation: Based on conservation of indicator. The total amount of “cold” injected is distributed through the cardiac output over time. The integral of temperature change reflects this distribution. The actual derivation is complex and involves principles of indicator dilution theory developed by Stewart and Hamilton.

Application: Common in ICUs using pulmonary artery catheters. Considered a clinical gold standard. Our Thermodilution Calculator page discusses its principles.

Downloadable Cardiac Output Formulas Cheat Sheet

For a quick reference to these key formulas, their components, and typical units, download our cheat sheet:

Download CO Formulas Cheat Sheet (PDF)

Choosing and Applying Formulas

The selection of a cardiac output formula depends on the clinical setting, available technology, patient condition, and whether an invasive or non-invasive approach is preferred. Each formula has its strengths and limitations. Understanding the underlying principles, as outlined here and in more detail on the specific calculator pages (e.g., for Fick, Doppler, or Thermodilution), is key to accurate application and interpretation.

For a comparison of these methods, see our article on Cardiac Output Calculator Comparison. Further exploration of advanced monitoring techniques builds upon these foundational formulas.

For detailed physiological understanding, consult authoritative texts like “Berne & Levy Physiology” or resources from the Cardiovascular Physiology Concepts website by Dr. Richard E. Klabunde.