Ported box calculator

A ported box is two numbers instead of one — the volume and the tuning — and a vent that has to be big enough not to whistle and short enough to fit. Here is how all three are decided.

What the vent does

The air in the vent is a mass; the air in the box is a spring. Together they are a Helmholtz resonator, and at its resonance — the tuning frequency Fb — the vent radiates strongly while the cone barely moves. That is the trade in one sentence: near tuning you get several dB of extra output for free, and below tuning the vent stops loading the cone entirely and the whole thing falls apart at 24 dB per octave.

The alignment

The standard empirical vented alignment gives a good starting box and tuning straight from the driver:

Vb = 20 · Vas · Qts³·³ Fb = Fs · (Vas / Vb)⁰·³¹ F3 = Fs · (Vas / Vb)⁰·⁴⁴Vas and Vb in the same units; Fs and Fb in hertz. This is a starting point — the solver is the authority on what the box actually does.

Then the vent geometry comes from the Helmholtz relation, rearranged for duct length:

Fb = (c / 2π) · √( Sv / (Vb · Leff) ) For a round vent, diameter d cm, box Vb litres: L = ( 2.356 × 10⁷ · d² ) / ( Fb² · Vb ) − k · dk is the end correction — about 0.85 for one flanged end, 0.732 for two free ends.

Where to tune

The alignment above is a suggestion, not an instruction. Tuning is the knob you actually turn:

• Tune low (below Fs) — flatter, more extended, better transient behaviour, lower peak output. Closer to how a sealed box behaves, with more depth.
• Tune at the alignment — the flattest response the driver and box will give.
• Tune high (at or above Fs) — a peak at tuning, loud over a narrow band, and a steep cliff underneath. This is what SPL-competition boxes do, and it is not what you want for music.

Sizing the vent

A vent that is too small chuffs — you hear the air rather than the music — and it also compresses output, because a turbulent vent is a lossy one. The working rule is vent area of roughly a tenth of cone area:

Sv ≈ 0.1 · Sd (per driver; split across the vents you fit)

Then check air speed. The solver reports it directly; the number to beat is about 17 m/s for a vent you will never hear, and 25–30 m/s as the point past which a well-flared vent is still audible. Straight-cut tubes are worse than that and should be kept lower.

The catch: effective length grows with vent area, so a bigger vent needs a longer duct at the same tuning. Double the area and you roughly double the length. This is how ported builds run out of room, and it is why slot vents — which use the cabinet walls as three sides of the duct and can be folded along a wall — usually win in a car. The port length calculator works this out for round, slot, wall-slot and aero vents.

Worked example

Fs = 28 Hz, Vas = 60 L, Qts = 0.42, Sd = 490 cm².

Vb = 20 · 60 · 0.42³·³ = 20 · 60 · 0.0526 = 63.1 L Fb = 28 · (60 / 63.1)⁰·³¹ = 28 · 0.9845 = 27.6 Hz F3 = 28 · (60 / 63.1)⁰·⁴⁴ = 28 · 0.9781 = 27.4 Hz Vent area: 0.1 · 490 = 49 cm² → a single 79 mm (3″) round vent is 49 cm² Length: L = (2.356×10⁷ · 7.9²) / (27.6² · 63.1) − 0.85 · 7.9 = 1.470×10⁹ / 48,060 − 6.7 = 30.6 − 6.7 = 23.9 cm

So: 63 litres net, tuned to 27.6 Hz, with one 79 mm vent 24 cm long — and F3 at 27 Hz against the sealed box's 47 Hz from the same driver. That is the ported trade in numbers: twice the box, an octave lower, and a 24-centimetre tube to find room for.

Ported box checklist

1. Net volume, with the driver, vent and bracing displacement added back on.
2. Vent clearance — at least one vent diameter between the inner end and the opposite wall, or the duct is effectively longer than you calculated and it tunes lower.
3. Air speed checked at the power you will actually use, not at one watt.
4. Excursion below tuning checked against Xmax.
5. Subsonic filter set 3–5 Hz below Fb.
6. Sealed everywhere — a leak is a second, badly tuned vent.
7. No stuffing in the vent path. Light lining on the walls is fine; blocking airflow to the vent detunes the box.

Frequently asked questions

What should I tune my ported box to?

For music, tune at or slightly below the driver's free-air resonance Fs — flattest response, and excursion stays under control. A home sub is typically 20–28 Hz; a car sub 30–35 Hz, because cabin gain supplies the rest.

Tuning above Fs gives a peak and a cliff beneath it: loud over a narrow band, hard on the driver, poor for music.

How big should the port be?

Aim for vent area around a tenth of cone area (Sd), then check the air speed. Below about 17 m/s it is inaudible; 25–30 m/s is the practical limit for a well-flared vent, and straight-cut tubes should stay lower.

Bigger vents need longer ducts at the same tuning, so past a point the answer is a slot vent or a bigger box rather than a bigger tube.

Why does my port need to be so long?

Because effective length scales with vent area. Doubling the area roughly doubles the duct needed for the same tuning, so a low tuning in a small box with a generous vent is where ducts stop fitting.

The fixes, in order of preference: fold a slot vent along a cabinet wall, enlarge the box slightly, or accept a higher tuning.

Can I use a square port instead of a round one?

Yes. Acoustically what matters is cross-sectional area and effective length, not shape — as long as the duct is not so thin that friction dominates. Keep any slot at least about 15 mm across.

Slot vents are often better in practice: the cabinet walls form three sides of the duct, so they are stiffer, easier to build, and easy to fold along a wall where a round tube would not fit.

What happens below the tuning frequency?

The vent stops loading the cone and reverses phase, so it works against the driver rather than with it. Output falls at 24 dB per octave and excursion climbs steeply, because the restraint has effectively disappeared.

This is why a ported box needs a subsonic filter a few hertz below tuning — and why a ported driver can be destroyed by content you cannot hear, where a sealed box would have survived.

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