Gorlin Formula Calculator: Aortic and Mitral Valve Area
The Gorlin formula estimates the functional area of a stenotic cardiac valve from invasive hemodynamic measurements taken during cardiac catheterization. Enter cardiac output, heart rate, the ejection or filling period, and the mean pressure gradient to calculate aortic valve area (AVA) or mitral valve area (MVA). Stenosis severity is classified automatically using ACC/AHA grading criteria, and the Hakki approximation is shown alongside the full Gorlin result for comparison.
Formula
Worked example
A patient with cardiac output 5,000 mL/min, heart rate 75 bpm, systolic ejection period 0.33 s/beat, and mean aortic gradient 30 mmHg: sqrt(30) = 5.477; denominator = 44.3 x 75 x 0.33 x 5.477 = 6,000.7; AVA = 5,000 / 6,000.7 = 0.83 cm2, classified as severe aortic stenosis.
What is the Gorlin formula?
The Gorlin formula was derived in 1951 by Richard and Sylvia Gorlin, who applied principles of hydraulic flow to estimate the effective orifice area of a stenotic cardiac valve. The fundamental insight is that, for turbulent flow through a narrow orifice, the cross-sectional area is proportional to the volumetric flow rate divided by the square root of the driving pressure gradient. The formula requires four inputs measured at cardiac catheterization: cardiac output, heart rate, the duration of the flow period per beat (systolic ejection period for the aortic valve, diastolic filling period for the mitral valve), and the mean transvalvular pressure gradient. Two separate hydraulic constants were derived empirically: 44.3 for the aortic valve and 37.7 for the mitral valve, reflecting the different hemodynamic geometry at each site.
Aortic stenosis (AS): how to interpret the AVA result
The normal aortic valve area is approximately 3 to 4 cm2. Progressive calcification and leaflet fusion narrow the orifice, increasing the velocity and gradient across the valve. Mild aortic stenosis is an AVA above 1.5 cm2, moderate stenosis is 1.0 to 1.5 cm2, and severe stenosis is 1.0 cm2 or less. Most patients with severe AS develop symptoms (angina, syncope, heart failure) within five years, and symptomatic severe AS carries a mortality of around 50 percent at two years without intervention. The current ACC/AHA guidelines list aortic valve replacement or transcatheter aortic valve implantation (TAVI) as a class I recommendation for symptomatic severe AS. In patients with low ejection fraction and low gradient ("low-flow, low-gradient" AS), the Gorlin formula can underestimate AVA because flow-dependent components of the equation are reduced; dobutamine stress echocardiography is the preferred adjunct in that context.
Mitral stenosis (MS): how to interpret the MVA result
The normal mitral valve area is 4 to 6 cm2. Rheumatic fever is the dominant global cause of mitral stenosis, with progressive thickening and fusion of the leaflets and subvalvular apparatus over decades. The Gorlin constant for the mitral valve (37.7) differs from the aortic constant because the pressure gradient is measured during diastolic filling rather than systolic ejection. Mild MS is an MVA above 1.5 cm2, moderate MS is 1.0 to 1.5 cm2, and severe MS is below 1.0 cm2 with a mean gradient above 10 mmHg. Percutaneous mitral balloon commissurotomy (PMBC) is the preferred intervention when anatomy is suitable; surgical valve repair or replacement is indicated when PMBC is contraindicated.
The Hakki approximation and when to use it
In 1981, Hakki and colleagues showed that the complex Gorlin denominator simplifies substantially at a heart rate near 70 to 80 bpm: for aortic stenosis, AVA approximately equals cardiac output in L/min divided by the square root of the mean gradient, and for mitral stenosis a factor of 0.85 is added in the denominator. The Hakki formula is useful as a bedside check and quick comparison, but it is less accurate when heart rate deviates significantly from 75 bpm, because the systolic ejection period changes non-linearly with rate. When the Gorlin and Hakki results differ by more than 0.2 cm2, verify that the ejection period was measured accurately and that the heart rate at the time of catheterization was typical for that patient.
Limitations of the Gorlin formula and how to cross-check results
Three well-established limitations affect clinical reliability. First, flow dependency: the Gorlin AVA is smaller at lower cardiac outputs, so patients with a reduced ejection fraction may appear to have more severe stenosis than they do. A cardiac output below 2,500 mL/min (or 2.5 L/min) is the conventional threshold for concern. Second, the formula was derived using mitral stenosis patients in the 1951 paper, so the aortic constant was extrapolated rather than directly measured. Third, simultaneous measurements of cardiac output and pressure gradient are required; non-simultaneous or averaged measurements introduce error. Echocardiographic continuity-equation area and direct planimetry of the valve orifice by transesophageal echo or CT are valuable cross-checks and should be reconciled with the Gorlin result before treatment decisions are made.
ACC/AHA stenosis severity grading by valve area
| Severity | AVA (cm²) | MVA (cm²) | Mean gradient (mmHg) | Clinical implication |
|---|---|---|---|---|
| Normal | 3.0 - 4.0 | 4.0 - 6.0 | <10 | No obstruction to flow |
| Mild | >1.5 | >1.5 | 10 - 25 | Surveillance; no intervention indicated |
| Moderate | 1.0 - 1.5 | 1.0 - 1.5 | 25 - 40 | Closer surveillance; consider intervention if symptomatic |
| Severe | ≤1.0 | <1.0 | >40 (AS) / >10 (MS) | Intervention indicated in symptomatic patients |
Based on ACC/AHA 2014 Valvular Heart Disease guidelines. Mean gradient and velocity thresholds are echocardiographic values and are shown for cross-reference only.
Frequently asked questions
What units does the Gorlin formula use for cardiac output?
The classic Gorlin equation as published by Gorlin and Gorlin uses cardiac output in mL/min (millilitres per minute), not L/min. If your catheterization report states cardiac output in L/min, multiply by 1,000 before entering it here. For example, a cardiac output of 5.0 L/min becomes 5,000 mL/min. Using L/min directly without conversion will produce a valve area roughly 1,000 times too small, which is a common calculation error.
What is the systolic ejection period and how is it measured?
The systolic ejection period (SEP) is the duration in seconds from the opening to the closing of the aortic valve during each heartbeat. It is measured from the aortic or left ventricular pressure tracing obtained at catheterization: specifically, from the point where left ventricular pressure exceeds aortic diastolic pressure (valve opens) to the incisura on the aortic tracing (valve closes). At a heart rate of 75 bpm it is typically around 0.30 to 0.38 seconds. For the mitral valve, the analogous measure is the diastolic filling period (DFP), from mitral valve opening to closure.
Why does the Gorlin formula use the MEAN gradient, not the peak gradient?
The mean transvalvular gradient represents the time-averaged pressure difference across the valve throughout the entire flow period, which is the physically correct driving force for the hydraulic flow calculation. The peak-to-peak gradient (the difference between peak left ventricular pressure and peak aortic pressure) does not occur simultaneously in time, is not a true instantaneous gradient, and systematically underestimates the hemodynamic burden. Most catheterization laboratories report both, but only the mean gradient should be entered into the Gorlin formula.
What is "low-flow, low-gradient" aortic stenosis and why does it matter?
Low-flow, low-gradient (LFLG) aortic stenosis describes a subset of patients with a small calculated valve area (below 1.0 cm2) but a mean gradient below 40 mmHg, despite a reduced cardiac output. Because the Gorlin AVA is flow-dependent, a reduced cardiac output caused by a weakened left ventricle (ejection fraction below 40%) will produce a smaller calculated area even if the valve is only moderately stenosed. Dobutamine challenge during catheterization is the standard way to differentiate true severe stenosis from pseudo-severe stenosis in this scenario: if the valve area increases above 1.0 cm2 when output rises with dobutamine, the stenosis was likely pseudo-severe.
How does the Gorlin formula compare to echocardiographic valve area measurement?
The Gorlin formula uses invasive catheterization data; echocardiography uses the continuity equation (AVA = LVOT area x LVOT VTI / AV VTI) or direct planimetry. Agreement between methods is generally good in patients with normal cardiac output, but diverges in low-flow states and when significant aortic regurgitation is present. Current guidelines recommend reconciling catheterization-derived and echo-derived valve areas rather than treating either as a gold standard, especially when clinical presentation and measured area are discordant.
What is the Hakki formula and how is it different?
The Hakki formula (1981) is a simplified version: AVA (cm2) = cardiac output (L/min) / square root of mean gradient for aortic stenosis. It effectively assumes that heart rate multiplied by systolic ejection period is approximately constant near a rate of 75 bpm, which simplifies the Gorlin denominator to just the Gorlin constant times the square root of the gradient. The result approximates the Gorlin value within 0.1 to 0.2 cm2 at typical resting heart rates but diverges more at rates below 50 or above 100 bpm. This calculator shows both results so you can check for discrepancies.
Can the Gorlin formula be used for other valves such as the tricuspid or pulmonic?
Yes, though it is far less commonly applied. The mitral constant (37.7) and the same diastolic filling period approach are sometimes used for tricuspid stenosis, with normal tricuspid valve area being approximately 7 to 9 cm2. The pulmonic valve is very rarely stenotic in adults. This calculator focuses on aortic and mitral applications, which account for the overwhelming majority of clinical use.
Sources
- Gorlin R, Gorlin SG. Hydraulic formula for calculation of stenotic mitral valve, other cardiac valves and central circulatory shunts. Am Heart J. 1951;41(1):1-29.
- Nishimura RA, et al. 2014 AHA/ACC Guideline for the Management of Patients With Valvular Heart Disease. J Am Coll Cardiol. 2014;63(22):e57-e185.
- Hakki AH, et al. A simplified valve formula for the calculation of stenotic cardiac valve areas. Circulation. 1981;63(5):1050-1055.