What it does
An ultrasound scanner sends short pulses of sound into the body and listens for echoes. How strong an echo is, how deep you can see and how fine a detail you can resolve all follow from a few simple formulas. This calculator puts them in one place: give the probe frequency, the pulse length and size, and the two materials either side of a boundary, and it works out the acoustic impedance, the share of the sound reflected and transmitted, the attenuation on the way down and back, the resolution, the beam shape, the timing and the Doppler shift.
How to use it
- Enter the frequency in MHz, the number of cycles per pulse, the transducer diameter, the depth of the boundary and the system’s dynamic range.
- Choose medium 1 (where the pulse travels) and medium 2 (beyond the boundary) from the list, or type your own density, speed of sound and attenuation. Typing a value switches that medium to “My own values”.
- Give the angle of incidence if the beam meets the boundary at a slant.
- For Doppler, give the speed of the blood or tissue and the angle between beam and flow.
- Read the four groups of results and the two charts, and download a CSV or a report.
What the results mean
- Impedance Z = ρc. Echoes come from changes in Z. The intensity reflected at normal incidence is ((Z₂ − Z₁)/(Z₂ + Z₁))². Soft tissue against air reflects almost everything, which is why gel is used.
- Oblique incidence bends the transmitted beam (Snell’s law); beyond the critical angle nothing gets through.
- Attenuation grows with frequency and depth. The echo has to come back too, so the round trip counts twice. The half-value layer halves the intensity; the deepest useful echo is where the round-trip loss uses up the dynamic range.
- Axial resolution is half the pulse length: shorter pulses and higher frequencies separate closer reflectors along the beam.
- Near-field length D²/4λ is where an unfocused disc’s beam is narrowest; beyond it the beam spreads by the divergence angle.
- Highest PRF keeps one pulse in flight at a time; in pulsed Doppler half of it is the highest shift you can measure without aliasing.
Worked example
With the defaults (5 MHz, 3 cycles, 10 mm disc, a boundary 10 cm deep from average soft tissue to cortical bone, normal incidence) the page shows impedances of 1.632 MRayl and 7.600 MRayl, 41.8 % reflected and 58.2 % transmitted, and a critical angle of 22.64°. The loss to the boundary is 25 dB one way, so the echo comes back 53.8 dB down, inside the 60 dB dynamic range. The wavelength is 0.308 mm, the axial resolution 0.462 mm, the near-field length 8.12 cm and the echo returns after 129.9 µs, allowing a PRF of up to 7.70 kHz. Blood at 50 cm/s at 60° gives a Doppler shift of 1623 Hz, and speeds up to 119 cm/s can be measured before aliasing.
Tips
- Try a 10 MHz probe: resolution halves to 0.231 mm but the deepest useful echo drops from 12 cm to 6 cm.
- Set the incidence angle above 22.64° for soft tissue to bone and the boundary becomes a perfect mirror.
FAQ
Where do the material values come from? They are rounded, illustrative values of the kind found in teaching texts. Real tissue varies; type your own if you have measurements.
Is this a safety tool? No. It does not compute thermal or mechanical indices or exposure. It is for study and planning, not a substitute for professional judgement.
Where the numbers come from
- Acoustic impedance, plane-wave reflection and transmission (normal and oblique, with Snell's law), attenuation in dB/cm/MHz, axial resolution, near-field length D²/4λ, divergence sin θ = 1.22 λ/D, range equation and the Doppler equation: standard diagnostic ultrasound physics, for example Hoskins, P., Martin, K. and Thrush, A. (eds), Diagnostic Ultrasound: Physics and Equipment.
- Checked against an independent numpy script written for the tests and the textbook result that soft tissue to air reflects about 99.9 %.
- Material values are rounded, illustrative teaching values (not measured data), editable.
Standard scientific values, such as constants, atomic weights and melting points, are facts found in every textbook; we name where ours were checked. If you are an author or publisher and want a value, a credit or a table changed or removed, tell us and we will act quickly.
Last updated 2026-11-09.