Helmholtz Resonator Calculator — Resonant Frequency of a Cavity
Find the natural resonant frequency of any Helmholtz resonator — from a glass bottle to a speaker cabinet port. Enter the cavity volume, neck (port) length and radius, and the ambient temperature.
L
cm
cm
°C
Frequency at which the cavity resonates (Helmholtz formula)
- 1
Speed of sound
c = 331.3 × √(1 + 20 ÷ 273.15) = 343.2 m/s - 2
Neck cross-section area (A = πr²)
A = π × (1 cm)² = 3.1416 cm² - 3
Effective neck length (L + 1.2r)
L_eff = 5 + 1.2 × 1 = 6.2 cmEnd correction accounts for the air just outside the neck that also oscillates. - 4
Resonant frequency
f₀ = (c ÷ 2π) × √(A ÷ (V × L_eff)) = 123All values in SI: c (m/s), A (m²), V (m³), L_eff (m).
How does this calculator work?
The Helmholtz resonant frequency is f₀ = (c/2π)√(A/(V·L_eff)), where A = πr² is the neck area, V is the cavity volume, L_eff = L + 1.2r is the effective neck length (including end correction), and c is the speed of sound. A larger cavity or longer neck lowers the pitch; a wider neck raises it.
Formula
How this is calculated
A Helmholtz resonator consists of a rigid-walled cavity connected to the outside by a short, narrow neck (or port). When air in the neck is displaced, the springiness of the air inside the cavity acts like a restoring force — pushing the neck air back and causing it to oscillate at a characteristic resonant frequency, just as a mass on a spring has a natural frequency.
The resonant frequency is f₀ = (c / 2π) × √(A / (V × L_eff)), where c is the speed of sound in air, A is the cross-sectional area of the neck (π r²), V is the internal volume of the cavity, and L_eff is the effective length of the neck. The effective length is slightly longer than the physical neck because air just outside each opening also moves with it — an "end correction" of approximately 0.6r per open end (1.2r total for both ends) is added: L_eff = L + 1.2r. A larger cavity or longer neck lowers the frequency; a wider neck raises it.
The speed of sound depends on temperature: c ≈ 331.3 × √(1 + T/273.15) m/s, so warm air gives a slightly higher resonant frequency. Real resonators may deviate from this ideal model when the cavity is not rigid, the neck is not uniform, or when the frequency is high enough that the cavity dimensions are no longer much smaller than the wavelength.
Frequently asked questions
The bottle acts as a Helmholtz resonator. Blowing across the neck creates a turbulent jet that periodically excites air in and out of the neck at the resonant frequency determined by the bottle's volume and neck dimensions. Filling the bottle with water reduces the cavity volume and raises the pitch.
Bass-reflex (ported) speaker enclosures use a Helmholtz resonator principle. The port is tuned to a specific frequency to reinforce bass output just below the point where the speaker driver rolls off, extending low-frequency response.
Air at the opening of the neck does not abruptly stop — a small volume of air just outside the neck also participates in the oscillation, making the effective length slightly longer than the physical neck. An end correction of about 0.6r per open end (where r is the neck radius) is added to account for this.
Also known as
TG we-Calculate Editorial Team. (2026). Helmholtz Resonator Calculator — Resonant Frequency of a Cavity [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/helmholtz-resonator-calculator
TG we-Calculate Editorial Team. "Helmholtz Resonator Calculator — Resonant Frequency of a Cavity." TG we-Calculate. 2026. https://we-calculate.com/calculator/helmholtz-resonator-calculator.
TG we-Calculate Editorial Team, "Helmholtz Resonator Calculator — Resonant Frequency of a Cavity," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/helmholtz-resonator-calculator
@misc{wecalculate_helmholtz_resonator_calculator, title = {Helmholtz Resonator Calculator — Resonant Frequency of a Cavity}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/helmholtz-resonator-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?