Canonical: https://echosuite.app/guides/doppler-equation/

# Doppler equation calculator

Explore doppler equation with the method’s inputs, acquisition guidance and source references. Open the calculator to enter measurements or try an illustrative worked example.

Created by [Mohammed Kamareddine, MD](https://echosuite.app/about/) · [Sources & educational scope](https://echosuite.app/about/)

[Open interactive calculator →](https://echosuite.app/calculators/#doppler-equation)

## Method

Δf = 2fₜv cosθ/c; v = |Δf|c/(2fₜ cosθ)

Use the measurement units shown below. Some fields apply only to a selected method or condition; follow the interactive tool’s method choices. The interactive tool keeps missing measurements incomplete and provides its method-specific results and reference context.

## Measurements and acquisition

### Solve for

Enter the measured value in the displayed unit

- Velocity
- Frequency shift
- Confirm the variable matches the selected formula.
- Use the unit displayed beside the field.
- Keep measurements from the same representative hemodynamic state.

### Shift magnitude · |Δf|  kHz

Enter the measured value in the displayed unit

- Confirm the variable matches the selected formula.
- Use the unit displayed beside the field.
- Keep measurements from the same representative hemodynamic state.

### Blood speed · v  m/s

Enter the measured value in the displayed unit

- Confirm the variable matches the selected formula.
- Use the unit displayed beside the field.
- Keep measurements from the same representative hemodynamic state.

### Transmit frequency · fₜ  MHz

Enter the measured value in the displayed unit

- Confirm the variable matches the selected formula.
- Use the unit displayed beside the field.
- Keep measurements from the same representative hemodynamic state.

### Beam-to-flow angle · θ  °

Enter the measured value in the displayed unit

- Confirm the variable matches the selected formula.
- Use the unit displayed beside the field.
- Keep measurements from the same representative hemodynamic state.

### Sound speed · c  m/s

Enter the measured value in the displayed unit

- Confirm the variable matches the selected formula.
- Use the unit displayed beside the field.
- Keep measurements from the same representative hemodynamic state.

## Sources and method context

ASE · 2019 · Doppler equation and cardiac spectral acquisition · ASE Comprehensive TTE · spectral Doppler, p. 42; Manual of Neurosonology (2016), Fig. 1.5

[Primary reference](https://www.asecho.org/wp-content/uploads/2019/01/2019_Comprehensive-TTE.pdf)

- Alignment in echocardiography · ASE Comprehensive TTE (2019), p. 42

Detected velocity depends on cosine of the beam-to-flow angle. Improve alignment and compare windows rather than using angle correction; choose a well-acquired maximum-velocity signal.

- Equation and sign · Cambridge, Manual of Neurosonology (2016), pp. 4–5, Fig. 1.5

Frequency shift is proportional to transmitted frequency, flow speed and cosine of the angle. Perpendicular flow has zero axial shift.

- Two Doppler interactions · OpenStax College Physics 2e §17.7, Doppler-shifted ultrasound and Example 17.8

A moving scatterer first receives sound and then acts as a moving source. In the low-speed approximation each contributes half of the total echo shift.

Catalogue review status: Source mapped · clinical sign-off pending

These pages describe the educational tool. Interpret measurements with the complete clinical context and the method’s acquisition limitations.

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