Gorlin Formula Calculator (aortic and mitral valve area from catheterisation)

Understanding the Gorlin formula calculator — concept and principle

The Gorlin formula calculates the area of a narrowed (stenotic) aortic or mitral valve from measurements taken during cardiac catheterisation: cardiac output, heart rate, the time the valve is open in each beat and the mean pressure gradient across it. Cardiologists use it to grade valve stenosis when echocardiography is unclear.

Valve area from flow and pressure: with the default inputs the result is 0.64 cm² (200 ÷ 313 → severe).

How it is calculated

Flow across the valve (mL/s) = cardiac output (mL/min) ÷ (heart rate × period per beat)

Valve area (cm²) = flow ÷ (C × √mean gradient)

The period is the systolic ejection period (SEP) for the aortic valve or the diastolic filling period (DFP) for the mitral valve, in seconds per beat.
C is an empirical constant: 44.3 for the aortic valve and 37.7 (44.3 × 0.85) for the mitral valve.
The Hakki shortcut, area ≈ cardiac output (L/min) ÷ √gradient, is shown for comparison.

The principle

The formula comes from hydraulics. Flow through an opening equals area times velocity, and by Torricelli's law the velocity of a jet rises with the square root of the pressure drop. Rearranging gives area = flow ÷ (constant × √pressure). Blood only crosses the valve while it is open, so cardiac output is divided by the total opening time per minute to get the true flow rate during that time. The constant absorbs unit conversions, gravity and the narrowing of the jet beyond the opening.

Worked example

Default inputs: aortic valve, cardiac output 4.5 L/min, heart rate 75 bpm, SEP 0.30 s, mean gradient 50 mmHg.

Flow = 4,500 ÷ (75 × 0.30) = 4,500 ÷ 22.5 = 200 mL/s.
√50 = 7.071; 44.3 × 7.071 = 313.2.
Valve area = 200 ÷ 313.2 = 0.639 → 0.64 cm² → Severe (under 1.0 cm²).
Hakki = 4.5 ÷ 7.071 = 0.64 cm².

Each point is the calculator re-run with only “Heart rate (bpm)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Heart rate (bpm)	Valve area (cm²)
18.8	2.55
37.5	1.28
56.2	0.85
75	0.64
93.8	0.51
112	0.43
150	0.32

How to read the result

Where does your result fall?

Common grading: over 1.5 cm² mild, 1.0–1.5 cm² moderate, under 1.0 cm² severe. For aortic stenosis many guidelines also use an indexed area and the gradient. A small area with a low gradient and low output needs further study, as the valve may open more with higher flow.

Common mistakes

Using the aortic constant for the mitral valve.
Using forward cardiac output when there is also regurgitation, which understates true valve flow.
Entering the period per minute instead of per beat.

Keep in mind: This is a calculation aid for clinicians, not a diagnosis. Valve disease is assessed with the full catheter and echo data by a cardiology team.

Frequently asked questions

Why is the Gorlin formula less accurate at low cardiac output?

The empirical constant was derived at normal flows; at low flow the formula tends to underestimate the area.

When does the Hakki formula fail?

At fast or slow heart rates, when the opening period per minute differs from the usual value.

Is echo or catheter valve area preferred?

Echo is the first test; catheter measurement is used when echo results conflict with the clinical picture.

Sources: Gorlin R, Gorlin SG, "Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts", Am Heart J 1951;41:1–29 · Hakki AH et al., "A simplified valve formula for the calculation of stenotic cardiac valve areas", Circulation 1981;63:1050–1055 · Baumgartner H et al., EAE/ASE recommendations on valve stenosis, Eur J Echocardiogr 2009;10:1–25

Checked 9 Nov 2026. Gorlin R, Gorlin SG, “Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts”, Am Heart J 1951;41:1–29 (standard formula; constants 44.3 and 37.7 as tabulated in Open Exam Prep, “Valve Area, Bernoulli & Shunt Calculations”); Hakki AH et al., Circulation 1981;63:1050 (simplified formula, standard); severity bands from Baumgartner H et al., EAE/ASE 2009 valve stenosis recommendations.

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