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Acoustic Impedance Calculator

Enter the density and speed of sound to get the acoustic impedance.

How it is calculated

The tool multiplies two properties of the medium: Z = ρ × c, where ρ is the density in kg/m³ and c is the speed of sound in the medium in m/s. The product is in kg/(m²·s), which is called a rayl, and it is rounded to a whole number. Both inputs must be above zero. It is a property of one material only; the tool does not compare two media. To judge how much sound crosses a boundary you would calculate Z for both sides and compare them, for example with the standard intensity reflection coefficient R = ((Z₂ − Z₁) ÷ (Z₂ + Z₁))², which is not computed here.

Worked example

Fresh water at about 20 °C has a density of 998 kg/m³ and a speed of sound of 1,482 m/s. Z = 998 × 1,482 = 1,479,036, shown as 1,479,036 rayl (about 1.48 million rayl). For comparison, air at 1.2 kg/m³ and 343 m/s gives only 412 rayl. Putting these into the reflection formula gives ((1,479,036 − 412) ÷ (1,479,036 + 412))² ≈ 0.9989, so roughly 99.9% of the sound intensity is reflected at an air-water boundary, which is why a coupling gel matters in ultrasound.

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Common mistakes

  • Entering density in g/cm³ (water = 1) instead of kg/m³ (water = 1000). The result would be 1,000 times too small.
  • Entering the speed in km/s or ft/s. It must be m/s; water is about 1,482, not 1.482.
  • Using the speed of sound in air for a liquid or solid. The speed has to be that of the same medium as the density.
  • Comparing a value in rayl with one in MRayl. 1 MRayl is 1,000,000 rayl; published tables for tissue usually quote MRayl, so convert before comparing.
  • Treating one density and speed as constant. Both change with temperature, so the result is only valid for the conditions your numbers came from.

About this calculator

This calculator finds the characteristic acoustic impedance of a medium, Z = ρ × c — density multiplied by the speed of sound through that medium — expressed in rayls (kg/m²·s). It's a property of the material itself, describing how much it resists the passage of a sound wave.

Acoustic impedance governs what happens at the boundary between two media: the bigger the impedance mismatch, the more sound energy reflects rather than transmits across it, which is exactly why an ultrasound gel is used to bridge the impedance gap between air and skin, and why bone and soft tissue show up so differently on an ultrasound image. It's a core parameter in medical ultrasound, sonar, and architectural and materials acoustics wherever engineers need to predict reflection and transmission at an interface.

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Comments (1)

  • Editorial team

    What decides how much sound crosses a boundary is the ratio of the two impedances, not the size of either one. Water and soft tissue are close, so energy passes; air and water are about 3,600 times apart, so it mostly bounces. Run the calculator once for each medium and compare the two numbers. Which pair of materials are you trying to match, and in which application?

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