How this calculator works
A port and the air in the box form a Helmholtz resonator, the same arrangement as a bottle you blow across. The air in the port moves as one mass and the air in the box acts as a spring, giving a tuning frequency that depends on the port area, the port length and the box volume. Longer ports and smaller boxes tune lower; a wider port tunes higher for the same length. The effective length is a little longer than the physical tube because air just outside both ends moves too, and the usual convention adds 0.732 diameters for one flanged end. A port tuned near the driver's resonance reinforces the low bass and protects the cone from over-excursion below tuning.
Formula
tuning frequency f = (c / 2 pi) x square root of (A / (V x (L + 0.732 D))), where c is 343 m/s, A is the total port area, V the box volume and L the physical port length. Solving for length: L = c^2 A / (4 pi^2 f^2 V) - 0.732 D. Total area A = number of ports x pi x D^2 / 4.
Worked example
A 50 litre box with a single 10 cm port tuned to 35 Hz. The area is pi x 0.1^2 / 4 = 0.007854 m². The effective length is 343^2 x 0.007854 / (4 pi^2 x 35^2 x 0.05) = 0.3821 m. Subtracting the end correction of 0.732 x 0.1 = 0.0732 m gives a physical port length of 0.3089 m, about 30.9 cm.
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Frequently asked questions
Why does the port length have an end correction?
The air outside the port also moves with the air inside, so the acoustic length is longer than the tube. A flanged end adds roughly 0.732 diameters and a free end about 0.613, in the usual convention. Real cabinets are not perfect flanges, so measure the tuning or adjust the port length after assembly.
What happens if the port is too small?
A small port moves air quickly, which produces chuffing and compression at high levels. As a rule of thumb, keep the air speed below about 5 percent of the speed of sound, or roughly 17 m/s, at the tuning frequency and at maximum output. More ports or a wider port reduce the speed but need a longer tube for the same tuning.
Why does the formula fail for very small boxes or high tuning?
The end correction can exceed the required effective length, which would need a negative port length. That means the box is too small for that tuning and port size, and no real port can reach it. Increase the volume, lower the port area or tune higher.
Does the port have to be a tube?
No. Slot ports and rectangular vents work the same way if you use the area and the equivalent diameter. The end correction depends on the shape, so a slot with a large perimeter behaves a little differently. The simple round-port formula is the standard starting point.