# Acoustic Impedance Calculator

URL: https://speedycalculator.com/calculators/physics/acoustic-impedance/
Last updated: 2026-10-30

> The acoustic impedance calculator finds a material's characteristic acoustic impedance Z = ρc and the fraction of sound energy reflected and transmitted at the boundary between two materials.

## Inputs

- Material 1
- Density ρ₁ (kg/m³, g/cm³, g/mL, lb/ft³, lb/in³)
- Speed of sound c₁ (m/s, km/h, mph, ft/s, knots)
- Material 2
- Density ρ₂ (kg/m³, g/cm³, g/mL, lb/ft³, lb/in³)
- Speed of sound c₂ (m/s, km/h, mph, ft/s, knots)

## Results

- Impedance of material 1
- Impedance of material 2
- Intensity reflection coefficient
- Intensity transmission coefficient
- Pressure reflection coefficient

## Formula

```
Z = ρ·c,  R = ((Z₂ − Z₁)/(Z₂ + Z₁))²,  T = 1 − R = 4Z₁Z₂/(Z₁ + Z₂)²
```

## Explanation

Acoustic impedance measures how much a material resists sound passing through it. When sound meets a boundary between materials with very different impedances – air and skin, water and steel – most of it reflects. That is why ultrasound scans need gel between the probe and the skin.

### How to use the Acoustic Impedance Calculator

- **Material 1**
- **Density ρ₁**
- **Speed of sound c₁**
- **Material 2**
- **Density ρ₂**
- **Speed of sound c₂**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose both materials from the list or enter a custom density and speed of sound. Impedance is shown in MRayl (10⁶ kg/(m²·s)).

### Inputs explained

FieldWhat to enterMaterial 1Choose one: Air, Fresh water, Seawater, Blood …Density ρ₁Units: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³Speed of sound c₁Units: m/s, km/h, mph, ft/s, knotsMaterial 2Choose one: Air, Fresh water, Seawater, Blood …Density ρ₂Units: kg/m³, g/cm³, g/mL, lb/ft³, lb/in³Speed of sound c₂Units: m/s, km/h, mph, ft/s, knots

### What each result means

- **Intensity reflection coefficient** = (([Impedance of material 2] - [Impedance of material 1])÷([Impedance of material 2] + [Impedance of material 1]))^2×100
- **Intensity transmission coefficient** = 4×[Impedance of material 1]×[Impedance of material 2]÷([Impedance of material 1] + [Impedance of material 2])^2×100
- **Pressure reflection coefficient** = ([Impedance of material 2] - [Impedance of material 1])÷([Impedance of material 2] + [Impedance of material 1])

### Example values

How the main result changes when **Density ρ₁** changes and everything else stays at the example values above:

Density ρ₁ (kg/m³)Intensity reflection coefficient (%)5000.47867500.47861,0000.47861,2500.47861,5000.47862,0000.4786

## Worked example

Inputs — Material 1: Fresh water; Material 2: Muscle.

Results — Impedance of material 1 = 1.48 MRayl; Impedance of material 2 = 1.7 MRayl; **Intensity reflection coefficient = 0.4786 %**; Intensity transmission coefficient = 99.5214 %; Pressure reflection coefficient = 0.06918.

## Key terms

- **Characteristic impedance**: Product of density and sound speed.

## FAQ

**What is a rayl?**
The unit of acoustic impedance, 1 kg/(m²·s).

**Why is ultrasound gel needed?**
Air between the probe and skin would reflect almost all of the sound.

**Why can't you hear people underwater well?**
Air and water impedances differ by a factor of about 3,600, so 99.9% of sound reflects.

**What does a negative pressure reflection mean?**
The reflected wave is inverted (going to a lower impedance).


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)