# Helmholtz Resonator Calculator

URL: https://speedycalculator.com/calculators/physics/helmholtz-resonator/
Last updated: 2026-10-30

> The Helmholtz resonator calculator finds the resonant frequency of a cavity with a neck – a bottle, guitar body, bass port or exhaust silencer – from the cavity volume, the neck area and length, and the end correction.

## Inputs

- Cavity shape
- Cavity volume V (L, mL, m³, US gal, ft³)
- Box length (cm, mm, m, in, ft)
- Box width (cm, mm, m, in, ft)
- Box height (cm, mm, m, in, ft)
- Cavity diameter (cm, mm, m, in, ft)
- Cylinder height (cm, mm, m, in, ft)
- Opening shape
- Opening area (cm², mm², m², in²)
- Opening diameter (cm, mm, m, in, ft)
- Opening width (cm, mm, m, in, ft)
- Opening height (cm, mm, m, in, ft)
- Neck length L (cm, mm, m, in, ft)
- End correction
- Speed of sound
- Custom speed of sound (m/s, km/h, mph, ft/s, knots)

## Results

- Effective neck length
- Cavity volume
- Resonant frequency f

## Formula

```
f = (c/2π)·√(A / (V·L_eff)),  L_eff = L + end correction (0.6r per free end, 0.85r per flanged end)
```

## Explanation

Blowing across a bottle produces a tone: the air in the neck bounces like a mass on the spring of the air in the cavity. Loudspeaker ports, guitar sound holes, car intakes and noise silencers are all tuned Helmholtz resonators.

### How to use the Helmholtz Resonator Calculator

- **Cavity shape**
- **Cavity volume V**
- **Box length**
- **Box width**
- **Box height**
- **Cavity diameter**
- **Cylinder height**
- **Opening shape**
- **Opening area**
- **Opening diameter**
- **Opening width**
- **Opening height**
- **Neck length L**
- **End correction**
- **Speed of sound**
- **Custom speed of sound**

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

### How it works

Choose the cavity and opening shapes and enter the dimensions. Pick the end correction that matches your neck (a flanged end sits flush with a large surface).

### Inputs explained

FieldWhat to enterCavity shapeChoose one: Arbitrary (volume), Box, Sphere, CylinderCavity volume VUnits: L, mL, m³, US gal, ft³Box lengthUnits: cm, mm, m, in, ftBox widthUnits: cm, mm, m, in, ftBox heightUnits: cm, mm, m, in, ftCavity diameterUnits: cm, mm, m, in, ftCylinder heightUnits: cm, mm, m, in, ftOpening shapeChoose one: Arbitrary (area), Circle, RectangleOpening areaUnits: cm², mm², m², in²Opening diameterUnits: cm, mm, m, in, ftOpening widthUnits: cm, mm, m, in, ftOpening heightUnits: cm, mm, m, in, ftNeck length LUnits: cm, mm, m, in, ftEnd correctionChoose one: Both ends free (1.2r), One end flanged (1.45r), Both ends flanged (1.7r), NoneSpeed of soundChoose one: Air at 0 °C, Air at 20 °C, Air at 40 °C, Helium at 20 °C …Custom speed of soundUnits: m/s, km/h, mph, ft/s, knots

### What each result means

- **Effective neck length** = [Neck length L] + [End correction]×sqrt([Opening area]÷pi)
- **Cavity volume** = [Cavity volume]
- **Resonant frequency f** = [c]÷(2×pi)×sqrt([Opening area]÷([Cavity volume]×[Effective neck length]))

### Example values

How the main result changes when **Cavity volume V** changes and everything else stays at the example values above:

Cavity volume V (L)Resonant frequency f (Hz)0.375180.14050.5625147.08410.75127.37860.9375113.93091.13104.00421.590.0703

## Worked example

Inputs — Cavity shape: Arbitrary (volume); Cavity volume V: 0.75 L; Opening shape: Circle; Opening diameter: 2.2 cm; Neck length L: 8 cm; End correction: Both ends free (1.2r); Speed of sound: Air at 20 °C.

Results — Effective neck length = 9.32 cm; Cavity volume = 0.75 L; **Resonant frequency f = 127.37859 Hz**.

## Key terms

- **Helmholtz resonance**: Air-mass-on-air-spring oscillation of a cavity with a neck.

## FAQ

**Why does a half-empty bottle sound higher?**
The air volume is smaller, so the resonance rises.

**How are loudspeaker ports tuned?**
By choosing the port area and length to set the box resonance.

**What is the end correction?**
Air just outside the neck also moves, making the neck act longer.

**Is the formula exact?**
It assumes the cavity is much larger than the neck and the wavelength much longer than the resonator.


## 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)