Acoustic Impedance Calculator
The acoustic impedance of two media from their density and speed of sound, and the share of sound energy reflected and transmitted at the boundary between them.
Acoustic impedance is density × speed of sound, in rayls.
How the acoustic impedance calculator works
Acoustic impedance is density × speed of sound, in rayls. When sound meets a boundary, the reflected fraction of its energy is ((Z₂ − Z₁) ÷ (Z₂ + Z₁))²: media with similar impedance pass sound freely, very different ones reflect almost all of it — which is why ultrasound needs gel between probe and skin and why you hear little from underwater.
Formula: Z = ρ × c; R = ((Z₂ − Z₁) ÷ (Z₂ + Z₁))²; T = 1 − R
Worked examples
| Inputs | Energy reflected at the boundary (%) | Note |
|---|---|---|
| Air to water | 99.889 | 99.89% reflected |
| Soft tissue to bone | 37.064 | 38% reflected |
| Identical media | 0 | 0% reflected |
FAQFrequently asked questions
What are typical acoustic impedances?
Air about 410 rayl, water 1.48 MRayl, soft tissue 1.6 MRayl, bone 6–8 MRayl, steel 45 MRayl. The air–water pair is the classic mismatch: 99.9% of sound energy reflects.
Why does ultrasound need gel?
Air trapped between the probe and the skin would reflect almost everything before it entered the body. Gel has an impedance close to tissue, so the sound passes in and, on the way back, out.
Is this energy or amplitude?
Energy (intensity). The amplitude reflection coefficient is (Z₂ − Z₁) ÷ (Z₂ + Z₁) without the square; the calculator reports the squared, energy form, which is what a decibel loss describes.
Does the angle of incidence matter?
These formulas are for sound arriving at right angles to the boundary. At oblique angles the reflection rises, and above a critical angle it can become total, just as with light.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.