Formula
A bass-reflex port is a Helmholtz resonator. The air in the box is the spring. The air in the port is the mass. Together they resonate at the tuning frequency Fb, which is where a vented box hands off from the port to the driver. This port calculator, and the port mode on the subwoofer box page, use the same equation. The speed of sound is 343 m/s at the 20 °C default.
Lv = c² Sp / (4 π² Fb² Vb) − k de
Fb = (c / 2π) √(Sp / (Vb (L + k de)))
End correction
The air just outside each end moves with the port, so the acoustic length is longer than the tube. A flanged end, the usual outside face of a baffle, adds about 0.425 diameters. A free end adds about 0.307 diameters. One of each, a port mounted flush, is k = 0.732. Both ends flanged, a slot built against the box walls or a tube with an inside flange, is 0.85. Both ends free, an unflanged tube or a bottle neck in open air, is 0.614. A round port uses its inside diameter. A slot uses the equivalent diameter 2 √(area / π).
Choosing a tuning frequency
Fb comes from the driver, not from a round number. The subwoofer box calculator starts a ported box from D. B. Keele’s QB3 alignment of Fs, Qts, and Vas. That volume and tuning are a place to begin. A home subwoofer is often somewhere from about 20 to 35 Hz. Car boxes are often about 30 to 40 Hz, because the cabin raises the low end as the wavelength gets long compared with the cabin. This page does not add a cabin-gain curve. There is no single number for it.
Port area, velocity, and why a bigger port is longer
The same tuning with more area needs a longer tube. That is the trade. Peak port velocity is 2π Fb Sd Xmax divided by the total open area. Above about 17 m/s a home port usually starts to chuff. Car-audio builds often accept 25 to 30 m/s. A flare at the ends lowers that noise. It also changes the end correction a little. Use the narrowest diameter, leave a little extra length, and trim to the tuning you measure. Compression shows up when the port is too small for the excursion: the output stops rising with the cone.
v = 2 π Fb Sd Xmax / Sp
Sp min = 2 π Fb Sd Xmax / v max
Round ports, slot ports, and more than one
A round port is a tube. A slot port is a rectangular duct, often using a box wall as one side, which is why both-flanged is the usual end correction there. Several identical ports share one tuning. The area in the formula is the sum, and each port is cut to that same length. Two ports of half the area are shorter than one port of the whole area, and each one is faster if you were counting on the larger tube. The first example here, 50 litres at 35 Hz with one 10 cm port, is 30.9 cm. Both ends flanged it is 29.7 cm. Both ends free it is 32.1 cm.
The air in the port, and the box around it
Port air is not part of the net box. Displacement is the number of ports times the area of one times the physical length. A slot divider, thickness times length times slot height, displaces a bit more and belongs in the same subtraction. Put that volume back into the subwoofer box calculator so the gross box grows enough to leave the net volume you tuned. The 5 by 30 cm slot in 85 litres holds 5.73 litres of air at the calculated length.
Pipe resonance, clearance, and a measured tuning
The port is also a pipe. The first half-wave resonance is c / (2 (Lv + k de)). For the 50 litre example it lands near 449 Hz. Keep that peak well above the subwoofer’s low-pass. Below about 250 Hz it is close enough to the passband to matter. The inner end wants about one diameter of open air before the back or side wall. Closer than that, the port stops behaving like the formula. If it will not fit straight, use an elbow, fold the slot, add ports, or live with a smaller area.
The tuning you built is the impedance minimum between the two peaks, not the number on this page. Cut long, measure, and shorten. A ported box unloads below Fb, so the tuning is part of the design and not a trim to hide afterward.
A Helmholtz resonator that is not a speaker
The same tuning equation is a cavity and a neck: a bottle, a bass trap, a resonator box. A 750 mL cavity, a 2 cm neck, 7.5 cm long, both ends free, is 119.6 Hz. That is the acoustic formula only. Nothing here sizes an exhaust, an engine, or a life-safety system. Speaker wiring and a wooden box are not an electrical code either. Assume the end correction you picked and a rigid sealed cavity, then check the result with a model or a measurement.
Worked examples
50 L, 35 Hz, one 10 cm round port, one flange and one free end. 30.9 cm (0.3089 m). The subwoofer box calculator returns the same length.
The same port, both ends flanged. 29.7 cm. Both ends free. 32.1 cm.
80 L, 32 Hz, two 7.5 cm ports, one flange and one free end. 26.7 cm each (0.2665 m).
Slot 5 cm × 30 cm, 85 L, 33 Hz, one flange and one free end. Area 150 cm², equivalent diameter 13.82 cm, length 38.2 cm (0.3818 m), air 5.73 L.
2.5 ft³ (70.79 L), 32 Hz, one 4 in port. 10.19 in (25.9 cm).
50 L, one 10 cm port, 30 cm long, one flange and one free end. Tuning 35.4 Hz.
Pipe resonance of the first port. 449 Hz.
Sd 500 cm², Xmax 12 mm, 35 Hz, one 10 cm port. 16.8 m/s. Minimum area at 17 m/s is 77.6 cm², a 9.94 cm round port.
750 mL, 2 cm neck, 7.5 cm, both ends free. 119.6 Hz.
Reference
The checks for this page. c = 343 m/s. One flanged end and one free end unless noted.
| Case | Result |
|---|---|
| 50 L, 35 Hz, 10 cm | 30.9 cm · 0.3089 m |
| Both flanged / both free | 29.7 cm · 32.1 cm |
| Two 7.5 cm, 80 L, 32 Hz | 26.7 cm each |
| 5 × 30 cm slot, 85 L, 33 Hz | 38.2 cm · 5.73 L of air |
| 2.5 ft³, 4 in, 32 Hz | 10.19 in · 25.9 cm |
| 30 cm tube, 50 L, 10 cm | 35.4 Hz |
| Pipe, first example | 449 Hz |
| Sd 500 cm², Xmax 12 mm | 16.8 m/s · min 77.6 cm² · 9.94 cm |
| 750 mL bottle | 119.6 Hz |
Questions
How long should my subwoofer port be?
It depends on the net volume, the tuning, and the port area. One 10 cm round port in a 50 litre box at 35 Hz, with one flanged end and one free end, is 30.9 cm long. A home sub is often tuned around 20 to 35 Hz. A car box is often 30 to 40 Hz, and the cabin adds bass the formula does not include. Start from the driver’s Thiele-Small alignment on the subwoofer box calculator, then trim to a measured tuning.
How do I calculate slot port length?
A slot uses the same Helmholtz length as a round port. Area is width times height, and the end correction uses the equivalent diameter 2 √(area / π). A 5 cm by 30 cm slot is 150 cm², about 13.82 cm across. In 85 litres at 33 Hz, one flanged end and one free end, each port is 38.2 cm and holds 5.73 litres of air. A slot built against the box walls is often both ends flanged, which shortens it.
Does port length or port area change the tuning?
Both. A longer port, or a smaller area, tunes lower. A shorter port, or a bigger area, tunes higher. The length in the formula is the physical length plus the end correction, so the ends matter as much as the tube you cut. Fifty litres, one 10 cm port, and a 30 cm tube with one flange and one free end tune to about 35.4 Hz.
How big should the port be?
Big enough that the air stays quiet. Peak velocity is 2π Fb Sd Xmax divided by the total port area. A 500 cm² cone, 12 mm of Xmax, 35 Hz, and one 10 cm port is 16.8 m/s, just under the 17 m/s home-audio line. The same driver needs about 77.6 cm², a 9.94 cm round port, to sit on that line. Car builds often live with 25 to 30 m/s. A larger area is quieter and the port gets longer.
What if the port is too long to fit?
Keep about one port diameter of open space beyond the inner end. If the tube plus that clearance is longer than the box, a straight port will choke. Bend it with an elbow, fold a slot along a wall, use more ports of smaller area, or accept a smaller area and a higher air speed. Leave a little extra on a flared port and trim it to the measured tuning.
Do multiple ports change the length?
Yes. The tuning uses the total area, and every port is cut to the same length. Two 7.5 cm ports in 80 litres at 32 Hz, one flange and one free end, are 26.7 cm each. Splitting the area across more tubes shortens each one. It also raises the air speed if you split a port that was already small.
What is a Helmholtz resonator?
It is a cavity of air sprung against the mass of air in a neck. A ported box is that resonator. So is blowing across a bottle. A 750 mL cavity with a 2 cm neck, 7.5 cm long and both ends free, resonates at 119.6 Hz. This page stays with the acoustic formula. It is not an exhaust or an engine calculation.
Sources
- Lawrence E. Kinsler, Austin R. Frey, Alan B. Coppens, and James V. Sanders, Fundamentals of Acoustics. The Helmholtz resonator and the flanged and unflanged end corrections used here.
- Richard H. Small, “Vented-Box Loudspeaker Systems,” Parts I–IV, Journal of the Audio Engineering Society, 1973. The ported box as a Helmholtz resonator.
- Vance Dickason, Loudspeaker Design Cookbook. Port area, port velocity, and the practical warning around 17 m/s for a home subwoofer. A measurement replaces the estimate.