Overview
Hemodynamics is the study of how blood moves through the heart and vessels, quantified through a small set of related measurements, output, pressure, resistance, valve area, that together describe how well the heart works as a pump. This guide walks through eight calculators covering the core hemodynamic values used in cardiology, critical care, and echocardiography, starting with basic cardiac output and ending with the invasive Gorlin formula used during catheterization.
This content is educational, not medical advice. Every formula here calculates a specific numeric value from measurements a clinician, sonographer, or monitoring device has already taken. None of these calculators measure anything directly, diagnose a condition, or replace interpretation by a qualified healthcare professional who has the patient's full clinical picture. A value outside the typical reference range is a starting point for further evaluation, not a diagnosis on its own. If you're trying to make sense of your own echocardiogram or catheterization report, bring these calculated values to your cardiologist.
The eight tools build on each other. Cardiac output and cardiac index describe overall pump performance. Stroke volume and ejection fraction describe per-beat efficiency. Cerebral perfusion pressure and pulmonary vascular resistance describe pressure relationships in two specific circulations. The three valve-area tools describe how much resistance a diseased heart valve adds to the system.
Step 1: Calculate Overall Pump Performance with Cardiac Output
Cardiac output is the total volume of blood the heart pumps in one minute, calculated as heart rate multiplied by stroke volume, converted from milliliters to liters. A normal resting adult cardiac output sits between roughly 4 and 8 liters per minute, though it climbs substantially during exercise, fever, pregnancy, or anemia, since the heart compensates for higher oxygen demand or reduced oxygen-carrying capacity by pumping more per minute.
Cardiac output can fall for two very different reasons: a slow heart rate, or a small stroke volume from weak contraction, valve disease, or reduced blood volume. That's why clinicians rarely interpret it alone. A cardiologist typically checks cardiac output alongside heart rate and stroke volume individually to work out which component is driving an abnormal result, since treating a rate problem looks nothing like treating a volume or contractility problem.
The Cardiac Output Calculator takes heart rate and stroke volume and returns cardiac output in liters per minute, with the normal resting range shown for comparison.
Step 2: Adjust for Body Size with Cardiac Index
Cardiac index fixes a specific limitation in cardiac output: a raw liters-per-minute number ignores the fact that a larger body needs more blood flow than a smaller one to stay equally well-perfused. Cardiac index divides cardiac output by body surface area, itself calculated from height and weight using the widely used Mosteller formula, the square root of (height in cm times weight in kg, divided by 3600).
A normal cardiac index runs between about 2.5 and 4.0 liters per minute per square meter, and this normalization is exactly why cardiac index, not raw cardiac output, gets used to diagnose cardiogenic shock in critical care. A cardiac output that looks borderline-acceptable in a very large patient might actually represent a dangerously low cardiac index once body size enters the picture. The relationship also means cardiac index will always read lower than cardiac output for any patient with a BSA over 1.0 square meter, which covers nearly all adults.
The Cardiac Index Calculator calculates BSA automatically from height and weight, then shows both cardiac output and cardiac index side by side against the normal 2.5-4.0 range.
Step 3: Measure Per-Beat Efficiency with Stroke Volume and Ejection Fraction
Stroke volume is the amount of blood the left ventricle ejects with each heartbeat, calculated as end-diastolic volume (blood in the ventricle right before it contracts) minus end-systolic volume (what's left right after), both typically measured by echocardiogram. From those same two numbers, ejection fraction comes out as stroke volume divided by end-diastolic volume, expressed as a percentage, describing what share of the ventricle's blood actually gets pumped out each beat.
A normal ejection fraction sits roughly between 55% and 70%. Values below that, particularly below 40%, track with heart failure with reduced ejection fraction, one of the two major heart failure categories cardiologists distinguish. Ejection fraction measures a fraction of blood ejected, not an absolute volume, so a heart with a small end-diastolic volume and a normal ejection fraction percentage can still deliver an inadequate absolute stroke volume. That's one reason these values get read together instead of separately.
The Stroke Volume Calculator takes end-diastolic and end-systolic volumes and returns both stroke volume and ejection fraction, plus an interpretation of where ejection fraction falls relative to normal.
Step 4: Monitor Brain Blood Flow with Cerebral Perfusion Pressure
Cerebral perfusion pressure (CPP) estimates the net pressure actually driving blood into the brain, calculated as mean arterial pressure minus intracranial pressure, essentially the pressure pushing blood in minus the pressure inside the skull pushing back. This matters most in critical care settings like traumatic brain injury, stroke, or brain hemorrhage, where elevated intracranial pressure can meaningfully cut the gradient driving blood into brain tissue even when blood pressure itself looks fine.
The commonly used critical care target is 60 to 80 mmHg. A CPP below roughly 60 mmHg raises concern for inadequate brain perfusion, while pushing MAP too high to compensate for elevated ICP carries its own risk, worsening cerebral edema among them. Because CPP depends on two separately monitored values that can each shift independently, critical care teams typically track MAP and ICP continuously rather than checking CPP as a single periodic snapshot.
The Cerebral Perfusion Pressure Calculator calculates CPP instantly from MAP and ICP, shown against the standard 60-80 mmHg critical care target.
Step 5: Assess Lung Circulation Resistance with Pulmonary Vascular Resistance
Pulmonary vascular resistance (PVR) measures how much resistance blood meets flowing through the lungs, calculated from three values typically obtained during right heart catheterization: mean pulmonary artery pressure, pulmonary capillary wedge pressure (a proxy for left atrial pressure), and cardiac output. The formula is PVR equals (mean PA pressure minus wedge pressure) divided by cardiac output, expressed in Wood units, convertible to dynes by multiplying by 80.
A normal PVR generally stays under 2 Wood units. Values above roughly 2 to 3 Wood units indicate pulmonary hypertension, a condition where the right side of the heart works harder against increased resistance and can eventually fail if that resistance goes unidentified and untreated. Because PVR needs invasive pressure measurements, it typically gets calculated during right heart catheterization rather than estimated non-invasively, unlike several other values in this guide.
The PVR Calculator converts the three catheterization values into PVR in both Wood units and dynes, with the normal range shown for comparison.
Step 6: Grade Mitral Stenosis with Mitral Valve Area
Mitral valve area is most commonly estimated non-invasively using the pressure half-time method on Doppler echocardiography: valve area equals 220 divided by the pressure half-time in milliseconds, where PHT is the time it takes the pressure gradient across the valve to fall to half its initial peak after the mitral valve opens. A narrower, more stenotic valve takes longer for that gradient to equalize, producing a longer PHT and, through the formula, a smaller calculated valve area.
Severity is generally graded mild above 1.5 cm², moderate between 1.0 and 1.5 cm², and severe below 1.0 cm². The PHT method has known blind spots in certain situations, immediately after a balloon valvuloplasty procedure, or in patients with significant aortic regurgitation, where other echocardiographic or invasive methods read more accurately, so it's typically one of several pieces of evidence a cardiologist weighs together.
The Mitral Valve Area Calculator converts a single pressure half-time measurement into valve area and its corresponding stenosis severity grade.
Step 7: Grade Aortic Stenosis with Aortic Valve Area
Aortic valve area is calculated using the continuity equation, built on the physical principle that the volume of blood flowing through the left ventricular outflow tract (LVOT) just below the valve has to equal the volume flowing through the valve itself. The equation needs three echocardiographic measurements: the LVOT diameter (for its cross-sectional area), the LVOT velocity-time integral (VTI), and the aortic valve VTI. Valve area equals (LVOT area times LVOT VTI) divided by AV VTI.
Severity is generally classified mild above 1.5 cm², moderate between 1.0 and 1.5 cm², and severe below 1.0 cm², with severe aortic stenosis often prompting evaluation for valve replacement or repair depending on symptoms and overall clinical status. Small errors in measuring LVOT diameter carry outsized weight in the final result, because the diameter gets squared when calculating LVOT area. That's why this particular measurement is taken with extra care during the echocardiogram.
The Aortic Valve Area Calculator takes all three continuity equation inputs and returns both the calculated valve area and its severity classification.
Step 8: Understand the Invasive Gold Standard with the Gorlin Formula
The Gorlin formula was the original method for calculating valve area, developed for cardiac catheterization before echocardiography became widely available. It's still used today when catheterization is already underway for other reasons, or when non-invasive estimates come back inconclusive. It calculates valve area from cardiac output, heart rate, the systolic ejection period (the fraction of each cardiac cycle spent actively ejecting blood), and the mean pressure gradient measured directly across the valve during catheterization.
Because it needs simultaneous invasive pressure and flow measurements, the Gorlin formula demands more resources than echocardiographic methods like the continuity equation or pressure half-time method, which is why echo stays first-line for most routine valve assessments. It still earns its keep as a cross-check, particularly when echocardiographic image quality is poor or when catheterization findings don't match the non-invasive estimate.
The Gorlin Formula Calculator supports both mitral and aortic valve calculations from catheterization data, so you can cross-check a result against the echo-based Mitral Valve Area Calculator or Aortic Valve Area Calculator.
Key Terms
- MAP - Mean Arterial Pressure, the average pressure in the arteries during one full cardiac cycle, used as one half of the cerebral perfusion pressure calculation.
- Body Surface Area (BSA) - an estimate of total body surface derived from height and weight, used to normalize measurements like cardiac output across different body sizes.
- Ejection Fraction - the percentage of blood in the left ventricle pumped out with each heartbeat, a key marker of heart pump function.
- Wood Unit - the standard unit for expressing pulmonary vascular resistance, calculated as a pressure difference divided by flow.
- Continuity Equation - a physical principle stating that blood flow volume must match on both sides of a valve, used to calculate aortic valve area non-invasively.
- Pressure Half-Time (PHT) - the time it takes a pressure gradient across a heart valve to fall to half its peak value, used to estimate mitral valve area.
- Intracranial Pressure (ICP) - the pressure inside the skull, which factors directly into how much net pressure is available to perfuse the brain.