How this instrument works
A stenotic valve is a narrowed opening the heart has to push blood through, and the Gorlin equation estimates how narrow. It treats the valve as an orifice in a pipe: a known flow crosses it, a measurable pressure drop appears on the far side, and the orifice equation from basic fluid dynamics ties the two together. Flow rate first — cardiac output divided by how many seconds per minute the valve actually stays open — then valve area, dividing that flow rate by a constant, the valve's own coefficient, and the square root of the mean pressure gradient. Bernoulli's principle sits underneath the whole calculation: faster flow through a smaller opening costs a larger pressure drop, so the drop itself becomes a measuring stick for the opening's size.
Richard Gorlin and Sol Gorlin, a physiologist and an engineer working together, published the formula in 1951 after studying blood flow across diseased valves at catheterization. Their original mitral constant, fit empirically against measured valve areas at autopsy and surgery, came out to 0.7. Two decades later, in 1972, Cohen and Gorlin revised that mitral constant upward to 0.85, a change now built into essentially every modern implementation of the equation, including this one. The aortic and pulmonic constant of 1.0, by contrast, was never re-derived from a comparable dataset the way the mitral constant was — it was adopted by convention, treated as close enough to the mitral coefficient's logic to stand without its own dedicated study.
The equation needs cardiac output, the flow period per beat, heart rate, and the mean pressure gradient across the valve — numbers traditionally gathered during cardiac catheterization, though echocardiography now supplies most of them noninvasively for the aortic valve via the continuity equation and for the mitral valve via pressure half-time (a simpler shortcut covered in its own instrument on this site). One honest limitation worth stating plainly: the constant in the denominator assumes something close to normal flow. Push cardiac output well below typical resting values and the calculated area drifts smaller than the valve's true anatomic opening, understating severity at exactly the low-flow states where getting the number right matters most.
- Enter Cardiac output in litres per minute — the total blood volume the heart pumps each minute.
- Enter Flow period, the number of seconds per beat the valve is actually open and passing flow.
- Enter Heart rate in beats per minute.
- Enter Mean gradient, the average pressure drop across the valve in mmHg.
- Choose the Valve: aortic or pulmonic uses a constant of 1.0, mitral or tricuspid uses 0.85 — then read Flow rate and Valve area from the working block.
Worked example — 5 L/min, 70 bpm, 20 mmHg gradient, aortic valve
Cardiac output of 5 L/min, a flow period of 0.35 seconds per beat, a heart rate of 70 bpm, aortic valve. Flow rate first: 5 × 1000 = 5000, divided by (0.35 × 70 = 24.5), gives 204.1 mL/sec. Valve area next: 204.1 divided by (44.3 × 1.0 × √20), and √20 is about 4.47, so the denominator is roughly 198.1. That leaves 204.1 ÷ 198.1 ≈ 1.03 cm² — in the range read as severe aortic stenosis.
Swap in a mitral case and nothing about the arithmetic changes, only the constant: cardiac output 4 L/min, flow period 0.30 seconds, heart rate 80 bpm, mean gradient 15 mmHg, mitral valve (constant 0.85). Flow rate comes to 4000 ÷ 24 = 166.7 mL/sec; valve area comes to 166.7 ÷ (44.3 × 0.85 × √15 ≈ 145.8) ≈ 1.14 cm² — also read as severe, this time for mitral stenosis, on a different numeric scale than the aortic case above.
Questions
What does the Gorlin equation actually measure?
It backs out an opening's cross-sectional area from two things a catheter or an echocardiogram can measure directly: how much blood crosses the valve per second, and how much pressure that flow costs to push through. The physics is the same as sizing a hole in a pipe from its flow and pressure drop — the valve just happens to be made of tissue and opening sixty-plus times a minute.
Why does the mitral constant read 0.85 instead of the original 0.7?
Gorlin and Gorlin's 1951 paper fit 0.7 to their own dataset of diseased mitral valves. Cohen and Gorlin revisited the constant in 1972 and found 0.85 tracked measured valve areas more closely, and that revised figure is what nearly every clinical calculator, including this one, now uses by default. The lesson generalizes: an empirical constant is only as good as the population it was fit against, and later work with better measurement tools can and does move it.
Where does the aortic constant of 1.0 come from?
Less rigorously than the mitral constant. Gorlin and Gorlin's original paper extended the same reasoning to the aortic and pulmonic orifice rather than fitting it against its own dedicated dataset the way the mitral value was later refined. It has held up well in practice, but it rests on convention more than on the kind of empirical re-derivation the mitral constant received in 1972.
What valve area counts as severe stenosis?
Conventionally, an aortic valve area under roughly 1.0 cm² and a mitral valve area under roughly 1.0 cm² are both read as severe; mitral areas between about 1.0 and 1.5 cm² are typically called moderate. Those cutoffs come from cardiology society guidelines built on outcomes data, not from the Gorlin paper itself — the equation supplies the number, the guideline supplies the label.
Does this calculation require cardiac catheterization?
Historically, yes — cardiac output, flow period, and mean gradient were all catheter measurements, and the formula was built around that data. Echocardiography now estimates most of the same quantities noninvasively, though for a quick mitral-specific answer without the flow and cardiac-output inputs at all, the pressure half-time method, this site's other mitral valve area instrument, trades some precision for a single Doppler timing measurement.
What is the real limitation of the Gorlin equation?
It assumes something near-normal cardiac output. In low-flow states — a weak left ventricle pushing less blood per beat — the calculated valve area comes out smaller than the valve's true anatomic opening, because the constant in the denominator was fit under closer-to-normal flow conditions. A patient can look like they have worse stenosis than they actually do simply because their heart is pumping less blood, which is why cardiologists cross-check a low Gorlin-derived area against flow status before calling severe disease.
References
- Gorlin R, Gorlin SG, 1951, Am Heart J — original hydraulic formula (PubMed)
- Cohen MV, Gorlin R, 1972, Am Heart J — revised mitral constant (PubMed)
Read this first: This instrument computes a screening figure from population formulas — it is not a diagnosis, and it cannot see the whole picture a clinician can. Use it to inform a conversation, not to replace one.