Quick answer: SV = 0.785 × d² × VTI, with the LVOT diameter d in cm and VTI in cm. A 2.0 cm LVOT with a VTI of 20 cm gives 62.8 mL. Multiply by heart rate for cardiac output. Normal LVOT VTI is 18–22 cm, normal SV 60–100 mL. Because d is squared, a 10% diameter error becomes a 21% stroke volume error.
Educational tool for clinicians and sonographers — not medical advice. These are published echocardiographic formulas. Haemodynamic assessment depends on image quality, correct sample-volume placement, rhythm, valve function and the whole clinical picture. Do not use this page to interpret your own echo results or to make a management decision.
Why a distance times an area gives a volume
The idea underneath this is simpler than the notation suggests, and it is worth stating plainly because it makes every downstream number make sense.
VTI is a distance. The Doppler trace plots blood velocity against time through one systole; the area under that curve is velocity multiplied by time, which is a length. It is the distance the column of blood travelled during that beat — typically about 20 cm. Sometimes called stroke distance, which is the more honest name.
So if you know how far the blood moved, and you know the cross-sectional area of the tube it moved through, the volume follows:
SV = CSA × VTI
CO = SV × HR ÷ 1000 (L/min)
CI = CO ÷ BSA · SVI = SV ÷ BSA
Worked example. LVOT diameter 2.0 cm, VTI 20 cm, heart rate 70:
- CSA = 0.7854 × 2.0² = 3.14 cm²
- SV = 3.14 × 20 = 62.8 mL
- CO = 62.8 × 70 ÷ 1000 = 4.40 L/min
It is the same cylinder volume calculation used everywhere else on this site — area times length — applied to a column of blood rather than a tank.
The diameter is squared, and that is the whole problem
This is the single most useful thing to internalise about the method, and it is why experienced echocardiographers are so fussy about one measurement.
VTI enters the formula linearly. Diameter enters it squared. So errors do not contribute equally:
| LVOT diameter | Error vs 2.0 cm | CSA | SV at VTI 20 | SV error |
|---|---|---|---|---|
| 1.8 cm | −10% | 2.54 cm² | 50.9 mL | −19% |
| 1.9 cm | −5% | 2.84 cm² | 56.7 mL | −9.8% |
| 2.0 cm | — | 3.14 cm² | 62.8 mL | — |
| 2.1 cm | +5% | 3.46 cm² | 69.3 mL | +10.3% |
| 2.2 cm | +10% | 3.80 cm² | 76.0 mL | +21% |
| 2.4 cm | +20% | 4.52 cm² | 90.5 mL | +44% |
Two millimetres — well within normal measurement variation on a zoomed image — moves the stroke volume from 51 to 76 mL. That range spans "low" to "comfortably normal" for the same patient on the same day.
What follows from it practically:
- Measure the diameter once, carefully. Zoomed parasternal long axis, mid-systole, inner edge to inner edge, within 0.5–1.0 cm of the aortic valve.
- For serial studies, reuse it. The LVOT does not change between this morning and this afternoon. Repeating only the VTI removes the dominant error source from the comparison.
- Track VTI alone for trends. Since CSA is constant within a patient, a change in VTI is a proportional change in stroke volume.
Normal LVOT VTI range and reference values
| Parameter | Typical adult range | Notes |
|---|---|---|
| LVOT diameter | 1.8–2.2 cm | Scales with body size; larger in men |
| LVOT CSA | 2.5–3.8 cm² | Derived, not measured directly |
| LVOT VTI | 18–22 cm | Falls with low output; rises with high output states |
| Stroke volume | 60–100 mL | |
| Stroke volume index | 33–47 mL/m² | <35 defines low-flow in aortic stenosis grading |
| Heart rate | 60–100 bpm | |
| Cardiac output | 4–8 L/min | Rises markedly in sepsis, pregnancy, anaemia |
| Cardiac index | 2.5–4.0 L/min/m² | The size-corrected figure for comparison |
Ranges are broad orientation figures from adult echocardiographic practice, not diagnostic thresholds. Values vary with age, sex, body size, loading conditions and the guideline being followed.
Why index to body surface area. A cardiac output of 5 L/min is generous in a 50 kg adult and marginal in a 110 kg one. Dividing by BSA removes body size from the comparison, which is why cardiac index rather than output is what gets compared between patients — the same reasoning behind height-adjusting kidney volume or scaling tidal volume to predicted body weight.
VTI variation and fluid responsiveness
In a mechanically ventilated patient, each positive-pressure breath transiently alters venous return and therefore stroke volume. If the ventricle is operating on the steep part of the Frank–Starling curve, that swing is large; if it is on the flat part, it is small.
Variation above roughly 12–15% is commonly taken as suggesting the patient may respond to a fluid bolus.
The assumptions matter more than the number. This measure is only interpretable under controlled mechanical ventilation with adequate tidal volumes, a regular cardiac rhythm, a closed chest, and without significant right ventricular failure. In a spontaneously breathing patient, in atrial fibrillation, or on low tidal volumes, respiratory VTI variation does not carry the same meaning — and reporting a percentage without those conditions being met is misleading. Passive leg raise with VTI measurement is often preferred precisely because it sidesteps most of them.
Common pitfalls
- Measuring diameter and VTI at different levels. The area and the velocity must come from the same point in the outflow tract. A diameter taken at the annulus with a VTI sampled 1 cm proximal breaks the continuity assumption.
- Outer-edge diameter measurement. Inner edge to inner edge, in mid-systole. Outer edge overestimates and the error is squared.
- Angle of insonation. Doppler underestimates velocity when the beam is not aligned with flow. Beyond about 20° the underestimate becomes material.
- Sample volume too close to the valve. Flow acceleration near the aortic valve inflates the VTI. Stay 0.5–1.0 cm proximal.
- Averaging too few beats in atrial fibrillation. Beat-to-beat stroke volume varies with the preceding R–R interval; average at least 5, ideally 10.
- Assuming a circular LVOT. The outflow tract is often mildly elliptical, so the circular-area assumption tends to underestimate. This is a recognised limitation of the method rather than a technique error, and it is one reason 3D or CT-derived areas differ.
- Applying it with a subaortic membrane or significant LVOT obstruction. The geometry the formula assumes no longer holds.
How to use this calculator
- Stroke volume & output — enter LVOT diameter and VTI. Add heart rate for cardiac output, and height and weight for the indexed values.
- VTI variation — enter the maximum and minimum VTI across the respiratory cycle.
- Check the sensitivity rows — the calculator shows what ±0.1 cm on the diameter would do to your result.
Frequently asked questions
How is stroke volume calculated from LVOT VTI?
Stroke volume equals the cross-sectional area of the left ventricular outflow tract multiplied by the velocity time integral. The area is π × radius², or equivalently 0.785 × diameter². A patient with a 2.0 cm LVOT diameter and a VTI of 20 cm has a stroke volume of 0.785 × 4 × 20, which is 62.8 mL.
What is a normal LVOT VTI?
Typically 18 to 22 cm in an adult with normal cardiac output at a normal heart rate. Values below about 18 suggest a low stroke volume, which may reflect hypovolaemia, poor left ventricular function or excessive afterload. Because VTI is the distance blood travels per beat, it falls when the ventricle ejects less, and it is often followed serially as a quick surrogate for stroke volume without repeating the diameter measurement.
Why is the LVOT diameter measurement so important?
Because it is squared in the area calculation, so any error in it is roughly doubled in the stroke volume. A 10% overestimate of the diameter produces a 21% overestimate of stroke volume and cardiac output. A measurement of 2.2 cm instead of 2.0 changes the calculated stroke volume from 62.8 to 76.0 mL for the same VTI. This is why the diameter is measured carefully, zoomed, inner edge to inner edge in mid-systole, and why serial studies often reuse the original diameter and only repeat the VTI.
What is the difference between VTI and stroke volume?
VTI is a distance, measured in centimetres, representing how far a column of blood travels through the outflow tract during one beat. Stroke volume is a volume, in millilitres, obtained by multiplying that distance by the cross-sectional area of the tract. VTI alone is useful for tracking change in a single patient because the area does not change, but it cannot be compared between patients with different outflow tract sizes.
What is the normal cardiac output and cardiac index?
Cardiac output in a resting adult is usually 4 to 8 L/min. Cardiac index, which is cardiac output divided by body surface area, is normally 2.5 to 4.0 L/min/m². Indexing to body size is what allows comparison between a small and a large patient, since a 5 L/min output means something quite different in a 50 kg person than in a 100 kg one.
Can LVOT VTI predict fluid responsiveness?
Respiratory variation in LVOT VTI is used as one indicator in mechanically ventilated patients, with variation above roughly 12–15% suggesting a patient may respond to a fluid bolus. The technique has important limitations: it assumes controlled mechanical ventilation with adequate tidal volumes, regular cardiac rhythm and no significant right ventricular failure. It is one input among several and its interpretation belongs with the clinician performing the assessment.
References & further reading
- Quiñones MA, Otto CM, Stoddard M, Waggoner A, Zoghbi WA. Recommendations for quantification of Doppler echocardiography: a report from the Doppler Quantification Task Force of the Nomenclature and Standards Committee of the American Society of Echocardiography. J Am Soc Echocardiogr 2002;15(2):167–184. PMID 11836492.
- Lang RM, Badano LP, Mor-Avi V, et al. Recommendations for cardiac chamber quantification by echocardiography in adults: an update from the American Society of Echocardiography and the European Association of Cardiovascular Imaging. Eur Heart J Cardiovasc Imaging 2015;16(3):233–270. doi:10.1093/ehjci/jev014
- Baumgartner H, Hung J, Bermejo J, et al. Recommendations on the echocardiographic assessment of aortic valve stenosis: a focused update from the European Association of Cardiovascular Imaging and the American Society of Echocardiography. J Am Soc Echocardiogr 2017;30(4):372–392. doi:10.1016/j.echo.2017.02.009
- Mosteller, R. D. (1987), "Simplified calculation of body-surface area", New England Journal of Medicine.
- Du Bois, D. & Du Bois, E. F. (1916) — the original body surface area formula.
Educational use only. This calculator reproduces published echocardiographic formulas. It is not a diagnostic tool and does not constitute medical advice. See our accuracy policy.