Gorlin Valve Area Calculator
Gorlin Valve Area Calculator
Valve area by the Gorlin hydraulic formula — the catheter method, with the flow period that most calculators quietly get wrong and the low-flow failure that makes a normal valve look stenotic.
Gorlin valve area, aortic or mitral
Flow ÷ (44.3 × C × √gradient)Aortic valve, cardiac output 4.2 L/min, heart rate 72, systolic ejection period 0.31 s, mean gradient 44 mmHg
The hydraulic formula, its constants, and what it assumes
Aortic: C = 1.00, flow period = systolic ejection period
Mitral: C = 0.85, flow period = diastolic filling period, so 44.3 × 0.85 = 37.7 is often written as a single constant
- the numerator
- flow across the valve in mL per second, averaged over the period the valve is actually open. Cardiac output in mL/min divided by (seconds of flow per beat × beats per minute) gives mL per second of flow. Not mL per second averaged over the whole cycle, which would be three times smaller for an aortic valve
- 44.3
- the hydraulic constant, √(2g) with g taken as 980 cm/s². It comes from Torricelli’s relation between the velocity of flow through an orifice and the pressure head driving it, and √1960 = 44.27
- C, the empiric constant
- 1.00 for the aortic valve and 0.85 for the mitral. Gorlin and Gorlin introduced it as a discharge coefficient to reconcile the hydraulic calculation with mitral areas measured at operation. It is empirical: it was fitted, not derived, and 44.3 × 0.85 = 37.66 is why many texts print the mitral form with a constant of 37.7
- √(mean gradient)
- the MEAN gradient during the flow period, by planimetry of two simultaneous pressure traces. The square root halves the sensitivity to error in it: a 20% gradient error is a 10% area error, while a 20% error in the flow period or the cardiac output goes through in full
- the low-flow failure
- flow is in the numerator, so “the valve area may be erroneously calculated as stenotic if the flow across the valve is low (i.e. if the cardiac output is low)”. This is the formula’s central limitation and the reason low-flow, low-gradient aortic stenosis is a separate clinical problem rather than an arithmetic one
- regurgitation
- the cardiac output measured by thermodilution or Fick is FORWARD flow. Where the valve also leaks, the true transvalvular flow is larger, so the numerator is too small and the calculated area is an underestimate. The error is in the direction of over-diagnosing stenosis
- the Hakki simplification
- Hakki and colleagues showed that for the aortic valve the whole flow-period term nearly cancels, leaving area ≈ cardiac output ÷ √gradient. It was published for the PEAK-TO-PEAK gradient, so it is not interchangeable with the mean-gradient arithmetic on this page, and it is not computed here
- this is not the continuity equation
- the echocardiographic route multiplies the left ventricular outflow tract area by its velocity-time integral and divides by the velocity-time integral across the valve. It needs no cardiac output, no flow period and no empiric constant, and it is the method the 2020 ACC/AHA criteria are written around. Gorlin is the catheter method, used when a catheter study is being done anyway or when the echocardiographic and clinical pictures disagree
Worked example
Aortic valve, cardiac output 4.2 L/min, heart rate 72, systolic ejection period 0.31 s, mean gradient 44 mmHg
Seconds of ejection per minute = 0.31 × 72 = 22.32 s, which is 0.37 of each cardiac cycle
Flow during ejection = 4,200 mL/min ÷ 22.32 s = 188.2 mL/s
Denominator = 44.3 × 1.00 × √44 = 44.3 × 6.6332 = 293.85
188.2 ÷ 293.85 = 0.64 cm² — at or below the 1.0 cm² the 2020 ACC/AHA guideline gives for severe aortic stenosis
Now the low-flow failure, in one step. Drop the cardiac output to 2.5 L/min and hold everything else: the area becomes 0.38 cm². The valve has not changed. Raise the output to 7.0 L/min and it becomes 1.07 cm², above the severe threshold
The flow period goes through in full: use 0.25 s instead of 0.31 and the area becomes 0.79 cm², a quarter larger for a quarter shorter interval
The gradient does not, because of the square root: double it to 88 mmHg and the area falls only to 0.45 cm², which is the original divided by √2 rather than by 2
Switch to the mitral form with the same numbers — C = 0.85, so the combined constant becomes 37.66 — and the area rises to 0.75 cm², exactly 1 ÷ 0.85 = 1.176 times the aortic figure. That is the whole difference between the two forms of the equation
The two forms of the equation, and their constants
| Valve | Flow period | Empiric constant C | Combined constant |
|---|---|---|---|
| Aortic | Systolic ejection period | 1.00 | 44.3 × 1.00 = 44.3 |
| Mitral | Diastolic filling period | 0.85 | 44.3 × 0.85 = 37.65, printed as 37.7 |
Guideline thresholds, and which method they were written for
| Valve | Severe disease criteria | Method the criteria assume | Source |
|---|---|---|---|
| Aortic | Peak velocity at or above 4 m/s; mean gradient at or above 40 mmHg; valve area typically at or below 1.0 cm², or 0.6 cm²/m² indexed | Doppler echocardiography, with area by the continuity equation | 2020 ACC/AHA, Table 13 (stages of valvular aortic stenosis) |
| Mitral | Valve area at or below 1.5 cm²; diastolic pressure half-time at or above 150 ms | Doppler echocardiography, with area by planimetry or half-time | 2020 ACC/AHA, Table 16 (stages of mitral stenosis) |
| Either, by catheter | No separate guideline thresholds are published for Gorlin areas | Right and left heart catheterisation with simultaneous pressures and a measured cardiac output | Gorlin and Gorlin 1951 |
Torricelli, a fitted constant, and the flow period everyone gets wrong
Gorlin and Gorlin’s 1951 formula treats a stenotic valve as a hole in a plate. Torricelli’s relation gives the velocity of flow through an orifice from the pressure head driving it — velocity is the square root of twice the gravitational acceleration times the head — and flow divided by velocity gives the area. That is where the 44.3 comes from: it is √(2 × 980), the square root of twice the acceleration due to gravity in centimetres per second squared. Everything else is bookkeeping, except the empiric constant, which is not derived from anything: Gorlin and Gorlin added a discharge coefficient of 0.85 for the mitral valve to make the calculation agree with areas measured at operation, and that is why so many texts print the mitral form with 37.7 instead of 44.3.
The term most often got wrong is the flow period. The numerator is not the cardiac output expressed per second; it is the flow during the part of the cycle when the valve is open. An aortic valve is open for roughly a third of each cycle, so dividing the output by sixty rather than by the seconds of ejection per minute understates the flow threefold and the area with it. The flow period has to be measured on the pressure tracing, for the same beats as the gradient, and it goes through in full proportion: a 20% error in the ejection period is a 20% error in the valve area. The gradient is forgiving by comparison, because it sits under a square root — a 20% error there is a 10% error in the area.
The formula’s central limitation is that flow is in the numerator, so a low cardiac output computes a small area. A normally mobile valve in a failing ventricle can be reported as severely stenotic, which is the whole reason low-flow, low-gradient aortic stenosis exists as a clinical entity and is investigated with a dobutamine challenge rather than with a recalculation. Co-existing regurgitation does the same thing by a different route: thermodilution and Fick measure forward flow, so where the valve also leaks the true transvalvular flow is larger than the numerator and the area is too small again. Both errors point towards over-diagnosing stenosis.
It is worth being clear about what this page is. This is the catheter method. The guideline thresholds it bands against — 1.0 cm² for severe aortic stenosis, 1.5 cm² for severe mitral stenosis — come from the 2020 ACC/AHA valvular heart disease guideline, which grades aortic stenosis primarily on peak velocity and mean gradient and derives area from the echocardiographic continuity equation rather than from a catheter study. The continuity equation needs no cardiac output, no flow period and no fitted constant, which is why it has largely displaced Gorlin at the bedside. Gorlin retains a place when a catheter study is being done anyway and when the echocardiogram and the clinical picture disagree — and when they do, the disagreement is usually about flow. Every figure here is derived from other measurements, so it carries their errors as well as its own. A derived index is never more reliable than the least reliable number that went into it. A derived haemodynamic number is read alongside the patient — the history, the perfusion, the lactate, the trend across serial measurements — and never instead of them. It supports a clinician’s judgement rather than replacing it.
Frequently asked questions
What is the Gorlin formula for valve area?
Valve area in cm² is the flow across the valve in mL/s divided by 44.3 × C × the square root of the mean gradient in mmHg. The flow is the cardiac output in mL/min divided by the flow period in seconds per beat times the heart rate. C is 1.00 for the aortic valve and 0.85 for the mitral, and the flow period is the systolic ejection period for the aortic valve and the diastolic filling period for the mitral.
Where does the 44.3 in the Gorlin formula come from?
It is the hydraulic term √(2g) with g taken as 980 cm/s², from Torricelli’s relation between flow velocity through an orifice and the pressure head driving it: √1960 = 44.27. The mitral version is often printed with 37.7 instead, which is the same constant multiplied by the mitral empiric constant of 0.85 — 44.3 × 0.85 = 37.66. They are not two different formulas.
Why does a low cardiac output make a valve look stenotic?
Because flow is in the numerator. Halve the cardiac output with the gradient and flow period unchanged and the calculated area halves, with no change in the valve. In this page’s worked example dropping the output from 4.2 to 2.5 L/min takes the area from 0.64 to 0.38 cm². This is the formula’s best-documented limitation and the reason low-flow, low-gradient aortic stenosis is investigated with a dobutamine challenge rather than by recalculating.
Is this the same as the continuity equation?
No, and the difference matters. The continuity equation is the echocardiographic method: outflow tract area times its velocity-time integral, divided by the velocity-time integral across the valve. It needs no cardiac output, no flow period and no empiric constant, and it is the method the 2020 ACC/AHA criteria are written around. This page implements Gorlin, the catheter method.
What valve area counts as severe stenosis?
The 2020 ACC/AHA valvular heart disease guideline gives severe aortic stenosis as a peak velocity at or above 4 m/s and a mean gradient at or above 40 mmHg, with a valve area that “typically is ≤1.0 cm2 (or AVAi 0.6 cm2/m2)”, and severe mitral stenosis as a valve area at or below 1.5 cm² with a diastolic pressure half-time at or above 150 ms. Those criteria were written for echocardiographic measurements; no separate thresholds are published for Gorlin areas, which are read against them by convention.
Related calculators
References
- Gorlin R, Gorlin SG. Hydraulic formula for calculation of the area of the stenotic mitral valve, other cardiac valves, and central circulatory shunts. I. Am Heart J. 1951;41(1):1–29. The derivation source. It was NOT reachable from here: the formula, the 44.3 and the empiric constants on this page come from two independent reproductions that agree to the digit, cited below, and no worked example from the original has been recomputed.
- Gorlin Formula for Valve Area, in a clinical calculator reference reproducing the 1951 equation as “VA = [CO/(SEP*HR)]/[44.3*C*(DELTAP)½]” with “C = 1 for the AV and 0.85 for the MV” and SEP as “LV ejection time (sec)”.
- Ask the Clinical Instructor: valve area calculation. Cath Lab Digest. Prints both forms as a catheter report uses them: aortic over “44.3 x √ of mean valve gradient”, mitral over “37.7 x √ of mean valve gradient” — 37.7 being 44.3 × 0.85, the mitral empiric constant folded into the hydraulic one.
- Hakki AH, Iskandrian AS, Bemis CE, et al. A simplified valve formula for the calculation of stenotic cardiac valve areas. Circulation. 1981;63(5):1050–5. The simplification in which the whole flow-period term collapses, leaving valve area ≈ cardiac output ÷ √gradient. Cited here for what it is; it was published for the peak-to-peak gradient, so it is not interchangeable with the mean-gradient arithmetic this page performs.
- Otto CM, Nishimura RA, Bonow RO, et al. 2020 ACC/AHA Guideline for the Management of Patients With Valvular Heart Disease. Circulation. 2021;143(5):e72–e227. Table 13: severe aortic stenosis is Vmax “≥4 m/s”, mean gradient “≥40 mm Hg”, area that “typically is ≤1.0 cm2 (or AVAi 0.6 cm2/m2)”. Table 16: severe mitral stenosis is an area “≤1.5 cm2” with a diastolic pressure half-time “≥150 ms”.
- Aortic valve area calculation. Wikipedia. States the Gorlin equation’s central limitation plainly — “the valve area may be erroneously calculated as stenotic if the flow across the valve is low (i.e. if the cardiac output is low)” — and gives the Hakki simplification’s provenance.
Not medical advice. For healthcare professionals and education. Reference intervals vary by laboratory and assay — always use your own laboratory's. Never base a dose or a treatment decision on this page alone. Full disclaimer at calcengines.com/disclaimer/