What sets port length
A ported (bass reflex) box works as a Helmholtz resonator. Rod Elliott (ESP) describes it as the box volume plus the vent’s length and diameter forming the resonator. Bohdan Raczynski (audioXpress) puts it in physical terms: the springiness (compliance) of the air in the box works against the mass of the air in the port. Done right, it reinforces the bass without excessive boom or poor transient response. If you’re still deciding whether to port at all, start with sealed vs ported. Three inputs set the length:
- Vb, the net box volume: the air the driver actually sees, after you subtract the driver, bracing and the port itself (how to calculate net box volume). ESP notes that an internal port’s volume has to be included in your volume sums.
- Fb, the tuning frequency: the frequency where the box and port resonate. Your box model or the driver’s recommended alignment gives you a target (how to read a driver datasheet).
- Port size. For a round tube, that’s its inside diameter. A wider port has to be longer to hit the same tuning.
Most box programs output both volume and port size. ESP warns that they usually can’t give you a complete design, and that further tweaking is nearly always needed.
The formula and its units
Troels Gravesen tested a port-length formula from diysubwoofers.org on his vent-tuning page. He prints it as: Lv = (23562.5*Dv^2*Np/(Fb^2*Vb))-(k*Dv) where, as he lists them:
- Lv = length of each port (cm)
- Dv = port diameter (cm)
- Np = number of ports
- Fb = tuning frequency (Hz)
- Vb = net volume (liters)
- k = end correction (normally 0.732)
Work in centimeters and liters as printed. Convert from inches or cubic feet first, or the answer will be wrong. Worked example (illustrative, Gravesen’s own numbers). He used a 29.5-liter box, a 7.2 cm (inside diameter) tube, one port, Fb = 28.7 Hz and k = 0.732. The formula gives 45.00 cm, and JBL’s box software gave 46.79 cm with no damping. So the formula and the software roughly agree on where to start.
End correction
A port behaves as if it were a little longer than the tube you cut. The end correction (k in the formula) accounts for that: the formula subtracts k × Dv so the tube you cut comes out shorter than the acoustic length. Gravesen quotes a note from Bjorn Johannesen: the acoustic impedance at the opening makes the line act slightly longer than its physical length at low frequencies. The source formula sets k per end, then adds the two ends together:
| Port ends | k |
|---|---|
| Both ends flanged | 0.425 + 0.425 = 0.850 |
| One end flanged, one end free | 0.425 + 0.307 = 0.732 |
| Both ends free | 0.307 + 0.307 = 0.614 |
Roughly, a flanged end finishes flush with a panel, like a port mouth set into the baffle. A free end is a bare tube end standing in open air. Gravesen points out that the source doesn’t say how big a flange has to be to count, so for his tests he made one from a 25 × 25 cm panel. In his tests, flanging mattered less than the table suggests. His measured tuning was 34.6 Hz with no flange, 33.9 Hz with one end flanged and 33.7 Hz with both, a 0.9 Hz spread. Flaring (rounding) the outer end raised Fb by about 1 to 1.5 Hz. He still recommends rounding the edges because it significantly reduces vent noise when the speaker plays a lot of bass. The formula uses a diameter, so it’s for round tubes. None of the sources here give a slot-port version, so model a slot in your box software and then measure it.
Why the formula and the measurement disagree
This is the part spreadsheets leave out. In Gravesen’s damped box, the 28.7 Hz tuning that the formula put at 45 cm actually took a 30 cm port. Even JBL’s software, set to heavy damping, predicted 37.79 cm. His rule from experience is to multiply the calculated length by 0.6 to 0.7 to hit the target Fb. He calls it “quite some deviation from all the nice math” and suggests getting help from someone with measuring equipment if you want it right. The biggest factor in his tests was damping material. Stuffing makes the box act larger, which lowers Fb. In one test it dropped tuning from 37 Hz with no damping to 33 Hz with heavy damping, using the same 72 × 200 mm vent. In the same box with no damping, the gap between calculated and measured length shrank. So tune with the final stuffing already in the box (enclosure mistakes, Mistake 5). The upshot: treat the calculated length as a starting point. Cut the port a little long, measure, and trim. A longer tube lowers Fb, and a shorter one raises it.
Port area and chuffing
A port that’s too small for the air it has to move makes noise. ESP calls it “chuffing” and says it happens when the air velocity is too high. Bohdan Raczynski (audioXpress) explains why size matters so much: air speed in the port depends on the inverse square of its radius, so he says to keep the radius as large as possible. The catch is length. His example is a 15 cm (6″) port tuned to 25 Hz in a 120-liter box, which needs a tube nearly 60 cm long. Raczynski also cites Vance Dickason’s minimums: 15 cm (6″) ports for 15″ woofers and 10 cm (4″) ports for 12″ woofers. Gravesen saw early signs of this in a measurement too. As drive voltage rose, the impedance peaks got lower, which he says may mean even his 72 mm vent was too small for high levels. See enclosure mistakes that kill DIY speakers, Mistake 3, for the build-side rules. ESP adds two placement cautions. A rear-facing port is a poor choice for a speaker that sits against a wall, and a port right next to the tweeter isn’t sensible. He also says not to use fiberglass in a vented box, because glass fibers can be blown out of the port.
Check the tuning by measuring
You don’t need a microphone to find Fb. An impedance sweep shows it. A ported box has two low-frequency peaks (speaker impedance curves, explained). Claudio Negro’s measurement guide says the minimum of the dip between them is the box’s tuning frequency, and that reading the point where the impedance phase crosses zero between the peaks is more precise. Raczynski’s modeled low-loss box shows the same thing, with the dip sitting exactly on Fb. Room EQ Wizard (REW) can make this measurement with a sense resistor and both sound card inputs. Its help page recommends sweeps of 10 seconds or longer, and says loudspeaker impedance is typically best measured at about 100 to 200 mV at the terminals. If you’ve measured your driver’s Thiele-Small parameters, it’s the same rig (measure Thiele-Small parameters; REW basics). Negro also describes a cross-check credited to J. E. Benson. Seal the port, measure the closed-box resonance Fc, then compute Fb = (Fl² + Fh² − Fc²)^½, where Fl and Fh are the two peak frequencies from the ported measurement.
Checklist
Building a radiator instead of a vent? See passive radiator vs port.