Interactive tools

Calculators & quick reference.

Drag the sliders to build intuition for the relationships that run through the whole curriculum — from the wave equation to bedside hemodynamics. Every formula is the real one taught in the lessons.

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Wavelength in soft tissue

λ = 1.54 / f

Frequency: 5 MHz

λ = 0.31 mmHigher frequency → shorter wavelength → finer axial resolution, but more attenuation and shallower penetration.

Axial resolution

axial res = (n × λ) / 2, λ = 1.54 / f

Frequency: 5 MHzCycles per pulse: 2

0.31 mmShorter pulses (higher frequency, fewer cycles, heavier damping) improve axial resolution. It is independent of depth.

Soft-tissue attenuation (one-way)

attenuation (dB) = 0.5 × f × depth

Frequency: 5 MHzDepth: 4 cm

10.0 dB one-way≈ 20.0 dB round-trip. Attenuation rises with both frequency and depth — the limit on penetration.

Doppler shift

Δf = (2 · f₀ · v · cosθ) / c

Transmit freq: 5 MHzVelocity: 1 m/sInsonation angle: 60 °

Δf = 3.25 kHzVelocity ∝ 1/cosθ, so error explodes as the angle approaches 90°. Standardize ≤ 60°.

Mechanical index (MI)

MI = p_r / √f_c

Peak rarefactional pressure: 1.5 MPaCentre frequency: 3 MHz

MI = 0.87Estimates non-thermal (cavitation) risk. FDA caps output at MI ≤ 1.9; keep it as low as reasonable (ALARA).

Ejection fraction (Simpson)

EF = (EDV − ESV) / EDV × 100%

End-diastolic volume: 120 mLEnd-systolic volume: 50 mL

EF = 58%Stroke volume 70 mL · ASE category: normal.

Simplified Bernoulli gradient

ΔP = 4 · v²

Peak velocity: 3 m/s

ΔP = 36 mmHgValid when the proximal velocity is small (< ~1 m/s). Used for valvular and stenotic pressure gradients.

IVC → right atrial pressure

IVC diameter + collapse → RAP (ASE)

IVC diameter: 2 cmRespiratory collapse: 50 %

RAP ≈ 8 mmHgIntermediate values fall between the two ASE categories (range 5–10 mmHg).

Abdominal aorta — AAA classifier

max AP diameter, outer-to-outer

AP diameter: 2.5 cm

2.5 cm — normalNormal infrarenal aorta is < 3 cm.

Educational tools only — always confirm clinical thresholds against current guideline publications before patient care.