Overview
Hemodynamics is the study of how blood moves through the heart and vessels, and it's quantified through a small set of interrelated measurements — output, pressure, resistance, and valve area — that together describe how efficiently the heart is functioning as a pump. This guide walks through eight calculators covering the core hemodynamic values used in cardiology, critical care, and echocardiography, from basic cardiac output to the invasive Gorlin formula used during catheterization.
This content is educational, not medical advice. Every formula covered here calculates a specific numeric value from measurements a clinician, sonographer, or monitoring device has already obtained — 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 standalone diagnosis. If you're trying to understand your own echocardiogram or catheterization report, bring these calculated values to a conversation with your cardiologist.
The eight tools below 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, and the three valve-area tools describe how much resistance a diseased heart valve is adding 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 simply as heart rate multiplied by stroke volume, with the result converted from milliliters to liters. A normal resting adult cardiac output falls between roughly 4 and 8 liters per minute, though this range rises substantially during exercise, fever, pregnancy, or anemia, since the heart compensates for increased oxygen demand or reduced oxygen-carrying capacity by pumping more blood per minute.
Cardiac output can fall for two very different reasons — a slow heart rate (bradycardia) or a small stroke volume (from weak contraction, valve disease, or reduced blood volume) — which is why it's rarely interpreted alone in a clinical setting. A cardiologist typically looks at cardiac output alongside heart rate and stroke volume individually to figure out which component is driving an abnormal result, since the treatment for a rate problem is very different from the treatment for 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 direct comparison.
Step 2: Adjust for Body Size with Cardiac Index
Cardiac index solves a specific limitation of cardiac output: a raw liters-per-minute number doesn't account for the fact that a larger body needs more blood flow than a smaller one to be equally well-perfused. Cardiac index divides cardiac output by body surface area (BSA), which is itself calculated from height and weight using the widely used Mosteller formula — the square root of (height in cm multiplied by weight in kg, divided by 3600).
A normal cardiac index falls 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, is the value typically used to diagnose cardiogenic shock in a critical care setting — a cardiac output that looks borderline-acceptable in a very large patient might represent a dangerously low cardiac index once body size is factored in. The relationship between the two values also means cardiac index will always be a smaller number than cardiac output for any patient with a BSA greater than 1.0 square meter, which describes almost all adults.
The Cardiac Index Calculator calculates BSA automatically from height and weight, then shows both cardiac output and cardiac index side by side with the normal 2.5-4.0 range for context.
Step 3: Measure Per-Beat Efficiency with Stroke Volume and Ejection Fraction
Stroke volume is the amount of blood the heart's main pumping chamber (the left ventricle) ejects with each heartbeat, calculated as the end-diastolic volume (the amount of blood in the ventricle right before it contracts) minus the end-systolic volume (what's left right after it contracts) — both typically measured by echocardiogram. From these same two numbers, ejection fraction is calculated as stroke volume divided by end-diastolic volume, expressed as a percentage, describing what proportion of the ventricle's blood is actually pumped out with each beat.
A normal ejection fraction falls roughly between 55% and 70%; values below that range, particularly below 40%, are associated with heart failure with reduced ejection fraction, one of the two major heart failure categories cardiologists distinguish between. It's worth noting that ejection fraction measures the fraction of blood ejected, not the absolute volume — a heart with a small end-diastolic volume and a normal ejection fraction percentage can still have an inadequate absolute stroke volume, which is one reason these values are interpreted together rather than in isolation.
The Stroke Volume Calculator takes end-diastolic and end-systolic volumes and returns both stroke volume and ejection fraction, along with an interpretation of where the ejection fraction falls relative to the normal range.
Step 4: Monitor Brain Blood Flow with Cerebral Perfusion Pressure
Cerebral perfusion pressure (CPP) estimates the net pressure actually driving blood flow into the brain, calculated as mean arterial pressure (MAP) minus intracranial pressure (ICP) — essentially the pressure pushing blood in, minus the pressure inside the skull pushing back. This calculation matters most in critical care settings like traumatic brain injury, stroke, or brain hemorrhage, where elevated intracranial pressure can meaningfully reduce the pressure gradient driving blood into brain tissue even when blood pressure itself looks normal.
The commonly used target range in critical care is 60 to 80 mmHg; a CPP that falls below roughly 60 mmHg raises concern for inadequate brain perfusion, while pushing MAP too high to compensate for elevated ICP carries its own risks, like worsening cerebral edema. Because CPP depends on two separately monitored values that can each change independently, critical care teams typically track both 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 and shows it against the standard 60-80 mmHg target range used in critical care.
Step 5: Assess Lung Circulation Resistance with Pulmonary Vascular Resistance
Pulmonary vascular resistance (PVR) measures how much resistance the blood encounters as it flows 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 = (mean PA pressure − wedge pressure) divided by cardiac output, expressed in Wood units, which can also be converted to dynes by multiplying by 80.
A normal PVR is generally under 2 Wood units; values elevated above roughly 2 to 3 Wood units indicate pulmonary hypertension, a condition where the right side of the heart has to work harder against increased resistance and can eventually fail if the elevated resistance isn't identified and treated. Because PVR requires invasive pressure measurements, it's typically calculated during a right heart catheterization procedure rather than estimated non-invasively, unlike several of the other hemodynamic 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 (PHT) 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 value after the mitral valve opens. A narrower, more stenotic valve takes longer for that pressure gradient to equalize, producing a longer PHT and, through the formula, a smaller calculated valve area.
Severity is generally graded as mild stenosis above 1.5 cm², moderate stenosis between 1.0 and 1.5 cm², and severe stenosis below 1.0 cm². The PHT method has known limitations in certain situations — such as immediately after a balloon valvuloplasty procedure or in patients with significant aortic regurgitation — where other echocardiographic or invasive methods may be more accurate, so it's typically one of several pieces of evidence a cardiologist considers 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, which relies on the physical principle that the volume of blood flowing through the left ventricular outflow tract (LVOT) just below the valve must equal the volume flowing through the valve itself. The equation needs three echocardiographic measurements: the LVOT diameter (used to calculate its cross-sectional area), the LVOT velocity-time integral (VTI), and the aortic valve VTI — valve area equals (LVOT area × LVOT VTI) divided by AV VTI.
Severity is generally classified as 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 have an outsized effect on the final result because the diameter is squared when calculating LVOT area, which is why this specific measurement is taken with particular 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 use during cardiac catheterization before echocardiography became widely available, and it's still used today when catheterization is already being performed for other reasons or when non-invasive estimates are 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 requires simultaneous invasive pressure and flow measurements, the Gorlin formula is more resource-intensive than echocardiographic methods like the continuity equation or pressure half-time method, which is why echo remains the first-line approach for most routine valve assessments. It remains valuable as a cross-check, particularly in cases where echocardiographic image quality is poor or where hemodynamic findings during catheterization don't match the non-invasive estimate.
The Gorlin Formula Calculator supports both mitral and aortic valve calculations from catheterization data, letting you 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 that is 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 be equal 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